text:
\section{Introduction}
\label{Sec:Intro}

In the standard paradigm of hierarchical structure formation, galaxies reside
inside dark matter halos.  The formation and evolution of these halos is
dominated by gravity and can be well predicted using high-resolution numerical
simulations and in some cases analytic models.  The formation of the galaxies
and their relation to the dark matter halos is more complex and depends on
the detailed physical processes leading to the varied observed galaxy
properties.

It has been well established that the
local halo environment of galaxies plays a fundamental role in shaping
their properties. In particular, local effects are thought to be
responsible for the transformation of blue, late-type and star-forming
galaxies into red, early-type and passive galaxies (see, e.g.,
\citealt{oemler74,dressler80,lewis02,balogh04b,baldry04,blanton09}),
even though there is no consensus on the relative importance of the
specific processes that play a role. Different mechanisms such as mergers
and interactions, ram-pressure stripping of cold gas,
starvation or strangulation and harassment all lead to changes in galaxies
morphologies within the host halo environment. It is not clear, however,
to what extent are galaxy properties affected by their overall ``global''
environment on scales larger than the individual halos. While there is
evidence that global environments affect galaxy populations ---
for example, red galaxies frequent high-density environments while blue
galaxies are prevalent in low-density regions (e.g.,
\citealt{hogg03,blanton05,blanton06,blanton09}) --- it is debatable whether
the large-scale environment has an actual impact on the physical processes
involved in galaxy formation and evolution.

A useful approach for studying the predictions of galaxy formation processes
is with semi-analytic modeling (SAM) of galaxy formation, in which halos
identified in large N-body simulations are populated with galaxies and evolved
according to specified prescriptions for gas cooling, gas formation, feedback
effects and merging (e.g., \citealt{Cole00,Baugh06,Croton06}).
These models have been successful in reproducing several measured properties
such as the galaxy luminosity and stellar mass functions  (see e.g.,
\citealt{Bower06,Guo11,Guo13Sams,Lacey16}).
An alternative way of studying galaxy formation is using hydrodynamic
simulations which follow the physical baryonic processes by a combination
of solving the fluid equations and sub-grid prescriptions (see, e.g.,
\citealt{somerville15,Guo16}). Cosmological hydrodynamical simulations are
starting to play a major role in the study of galaxy formation and evolution.
Comparisons of such simulations with observations show broad agreement
(e.g., \citealt{Vogelsberger14,Schaye15,Artale16}).

A popular approach to empirically interpret observed galaxy clustering
measurements as well as to characterize the predictions of galaxy formation
theories is the Halo Occupation Distribution (HOD) framework (e.g.,
\citealt{peacock00,seljak00,scoccimarro01,berlind02,cooray02,zheng05}). The HOD
formalism characterizes the relationship between galaxies and dark matter halos
in terms of the probability distribution, $P(N|M_{\rm h})$, that a halo of
virial mass $M_{\rm h}$ contains $N$ galaxies of a given type, together with
the spatial and velocity distribution of galaxies inside halos. The
fundamental ingredient of the modeling is the halo occupation function,
$\langle N(M_{\rm h}) \rangle$, which represents the average number of galaxies
as a function of halo mass. The typically assumed shape for the halo occupation
function is motivated by predictions of hydrodynamic simulations and
semi-analytic models (e.g, \citealt{zheng05}).
It is often useful to consider separately the contributions from the
central galaxies, namely the main galaxy at the center of the halo,
and that of the additional satellite galaxies that populate the halo
\citep{kravtsov04,zheng05}.
The HOD approach has been demonstrated to be a powerful theoretical tool to
study the galaxy-halo connection, effectively transforming measurements
of galaxy clustering into a physical relation between galaxies and dark matter
halos. This approach has been very successful in explaining
the shape of the galaxy correlation function, its environment dependence
and overall dependence on galaxy properties (e.g.,
\citealt{zehavi04,zehavi05b,zehavi11,berlind05,abbas06,skibba06,tinker08,coupon12}).

A central assumption in the conventional applications of this framework is that
the galaxy content in halos only depends on halo mass and is statistically
independent of the halo's larger scale environment. This assumption has its
origins in the uncorrelated nature of random walks describing halo assembly in
the standard implementations of the excursion set formalism which results
in the halo environment being correlated with halo mass, but uncorrelated
with formation history at fixed mass \citep{bond91,white99,lemson99}.
In this picture, the change in the fraction of blue and red galaxies in
different large-scale environments, for example, is fully derived from the
change in the halo mass function in these environments \citep{mo96,lemson99}.
Consequently, it is not evident that global environments play a major role
in directly shaping galaxy properties and in particular the HOD.

This ansatz has been challenged in the last
decade by the demonstration in simulations that the clustering of halos of
fixed mass varies with halo formation time, concentration and substructure
occupation
\citep{sheth04,gao05,gao07,Jing06,Harker06,Wechsler06,Wetzel06,Angulo08,Pujol14,Lazeyras17}. The dependence of halo clustering on properties other
than the halo mass has broadly been referred to as {\it halo assembly bias}.
The dependences on the various halo properties manifest themselves in
different ways and are not trivially derived from the correlation between
these properties (see, e.g., \citealt{mao17}).  While a prediction of
$\Lambda$CDM, the exact physical origin of assembly bias remains unclear,
but different explanations have been put forth, such as
correlated modes which break down the random walk assumption, statistics of
peaks and truncation of low-mass halo growth in dense environments
\citep{keselman07,sandvik07,zentner07,dalal08,desjacques08,hahn09,ludlow11,lacerna11,zhang14,borz16}.

A current topic of active debate is to what extent are galaxies affected
by the assembly history of their host halos. The stochasticity in the
complex baryonic physics may act to erase the record of halo assembly history.
If, however, the galaxy properties closely
correlate with the halo formation history, this would lead to a dependence
of the galaxy content on large-scale environment and a corresponding clustering
signature. This effect has commonly been referred to as {\it galaxy assembly
bias} both colloquially and in the literature, and we adopt this distinction
here. We stress, however, that what is referred to here is the
manifestation of halo assembly bias in the galaxy distribution.
The predictions for galaxy assembly bias have been explored with simulated
galaxies \citep{croton07,reed07,Zhu06,Zu08,zentner14,angulo16,bray16}.
Detecting (galaxy) assembly bias is much more challenging since halo
properties are not directly observed.
Observational studies of assembly bias have generally produced mixed results.
There have been several suggestive detections in observations \citep{yang06,berlind06,wang08,cooper10,tinker12,wang13b,lacerna14b,watson15,Hearin15,miyatake16,saito16,zentner16,montero17,tinker17b}  while numerous other studies indicate the impact of assembly bias to be small \citep{abbas06,blanton07,croton08,tinker08,tinker11,deason13,lacerna14a,lin16,ZuMan16,vakili16,dvornik17}.
The situation is further complicated as various systematic effects can mimic
the effects of assembly bias
(e.g., \citealt{campbell15,Zu16,Zu17,Busch17,Sin17,tinker17a,lacerna17}) and
the evidence for assembly bias to date remains inconclusive and controversial.

Such galaxy assembly bias, if significant, would have direct implications
for interpreting galaxy clustering using the HOD framework (e.g.,
\citealt{Pujol14,zentner14}), as secondary halo parameters in addition to
the mass or, more generally, the large-scale environment in which the halo
formed,  would also impact the halo occupation function.  For clarity, we
term these variations of the halo occupation functions as {\it occupancy
variation}.  These effects are all directly related of course, as it is
exactly this occupancy variation coupled with halo assembly bias that gives
rise to galaxy assembly bias.

In this paper, we aim to gain further insight and clarify this important
topic by exploring explicitly the dependence of the halo occupation functions
on the large-scale environment and formation redshift in semi-analytic models.
Limited work has been carried out in directly studying the environmental
dependencies of the HOD of galaxies, with varied results.
Different works examined the dependence of the subhalo occupation on
age (e.g., \citealt{jiang16}) and environment \citep{Croft12}, that can
be regarded as a proxy of the satellite occupation, if neglecting the
effects of baryons.
\citet{Zhu06} explore the age dependence of the conditional luminosity
function in a semi-analytic model and a hydrodynamical simulation.
\citet{berlind03} and \citet{mehta14} explore the variations of the HOD in
cosmological hydrodynamical simulations finding no detected dependence on
environment. \citet{mcewen16} have recently investigated this using
the age-matching mock catalogs of \citet{Hearin13} (which by design
exhibit significant assembly bias) detecting a dependence of the HOD on
environment, mostly for the central galaxy occupation function.
While the impact of assembly bias on galaxy clustering has already been
demonstrated using a SAM applied to the Millennium simulation
\citep{croton07,Zu08}, the variation of the HOD itself with large-scale
environment or other halo properties has not been explored for it.

Here, we use the HOD formalism to directly study the impact of galaxy
assembly bias as predicted by SAMs. We use the output of two independently
developed SAMs, from the Munich and Durham groups, at different number
densities. We measure the halo occupation functions for different large-scale
environment regimes as well as for different ranges of halo formation redshift.
This allows us to assess which features of the HODs vary with environment
and halo age, and we present the corresponding changes in the HOD parameters.
Additionally, we investigate the galaxy cross-correlation functions for these
different regimes, which highlights the impact of assembly bias on
clustering. Such studies will inform theoretical models incorporating assembly
bias into halo models as well as attempts to determine it in observational
data. Additionally, it can facilitate the creation of mock catalogs
incorporating this effect.

The outline of the paper is as follows.  In Section~\ref{Sec:GFM} we describe
the galaxy formation models used.  In Section~\ref{Sec:HOD} we explore the
dependence of the HOD on large-scale environment and halo age. We discuss
the origin of the trends and the connection to the stellar mass -- halo mass
relation in Section~\ref{Sec:SMHM}. In
Section~\ref{Sec:clustering} we investigate the clustering dependence on these
properties and we conclude in Section~\ref{Sec:summary}.
Appendix~\ref{Sec:Cuts} shows our halo-mass dependent sample cuts, while
Appendix~\ref{Sec:AutoCorr} presents further measurements of the
auto-correlation functions.

\vspace{0.2cm}
\section{The galaxy formation models}
\label{Sec:GFM}

\vspace{0.1cm}
\subsection{Semi-analytic models}
\label{SubSec:SAM}

The SAMs used in our work are those of \citet{Guo11} (hereafter G11) and
\cite{Lagos12} (hereafter L12) \footnote{The G11 and L12 outputs are publicly
available from the Millennium Archive in Garching
\url{http://gavo.mpa-garching.mpg.de/Millennium/} and Durham
\url{http://virgodb.dur.ac.uk/}}.
The objective of SAMs is to model the main physical processes
involved in galaxy formation and evolution in a cosmological context:
(i) the collapse and merging of dark matter halos;
(ii) the shock heating and radiative cooling of gas inside dark matter
halos, leading to the formation of galaxy discs; (iii) quiescent star
formation in galaxy discs; (iv) feedback from supernovae (SNe), from accretion
of mass onto supermassive black holes and from photoionization heating of
the intergalactic medium (IGM); (v) chemical enrichment of the stars and gas;
(vi) dynamically unstable discs; (vii) galaxy mergers driven by dynamical
friction within dark matter halos, leading to the formation of stellar
spheroids, which may also trigger bursts of star formation.
The two models have different implementations of each of these processes.
By comparing models from different groups we can get a sense for
which predictions are robust and which depend on the particular
implementation of the galaxy formation physics (e.g., \citealt{Contreras13}).

The G11 model is a version of {\tt L-GALAXIES}, the SAM code of the Munich
group and is an updated version of earlier implementations
\citep{Delucia04,Croton06,Delucia07}. The L12 model is a development of the
{\tt GALFORM} Durham model \citep{Bower06,Font08}, which includes an improved
treatment of star formation, separating the interstellar
medium into molecular and atomic hydrogen components \citep{Lagos11}.
An important difference between G11 and L12 is the treatment of
satellite galaxies. In L12, a galaxy is assumed to be stripped of
its hot gas halo completely once it becomes a satellite and start
decaying onto the central galaxy. In G11, these processes are more
gradual and depend on the destruction of the subhalo and the orbit of
the satellite.

\vspace{0.1cm}
\subsection{N-Body simulation and halo merger trees}
\label{SubSec:NBody}

The SAMs used here are both implemented in the Millennium simulation
\citep{Springel05}. This simulation has a periodic volume of $(500 \,h^{-1}\,{\rm Mpc})^3$ and
contains $2160^3$ particle with a mass of $8.61 \times 10^8 M_{\odot}/h$ each.
The simulation has 63 snapshots between $z=127$ and $z=0$ and was run with a
$\rm \Lambda CDM$ cosmology\footnote{The values of the
cosmological parameters used in the Millennium simulation are:
$\Omega_{\rm b}$ =0.045, $\Omega_{\rm M}$ = 0.25, $\Omega_{\Lambda}$ = 0.75,
h = $H_0/100$ = 0.73, $n_{\rm s}$ = 1, $\sigma_8$ = 0.9.}.
The G11 and L12 models both use a friends-of-friends
({\tt FoF}) group finding algorithm \citep{Davis85} to identify halos in each
snapshot of the simulation, retaining those with at least 20 particles.
{\tt SUBFIND} is then run on these groups to identify subhalos
\citep{Springel01}. The merger trees differ from this point on.
G11 construct dark matter halo merger trees by linking a subhalo
in one output to a single descendant subhalo in the subsequent snapshot.
The halo merger tree used in {\tt L-GALAXIES} is therefore a subhalo merger
tree. L12 employ the {\tt Dhalo} merger tree construction
(\citealt{Jiang14}; see also \citealt{Merson13}) that also uses
the outputs of the {\tt FoF} and {\tt SUBFIND} algorithms.
The {\tt Dhalo} algorithm applies conditions on the amount of mass
stripped from a subhalo and its distance from the center of the
main halo before it is considered to be merged with the main subhalo.
Subsequent output times are examined to see if the subhalo moves
away from the main subhalo, to avoid merging subhalos which have merely
experienced a close encounter before moving apart. {\tt GALFORM}
post-processes the {\tt Dhalo} trees to ensure that the halo mass increases
monotonically with time.

Consequently, the definition of halo mass used in the two models is not
the same. The {\tt Dhalo} mass used in {\tt GALFORM} corresponds to an integer
number of particle masses whereas a virial mass is calculated in
{\tt L-GALAXIES}. This leads to slight differences in the halo mass function
between the models. In previous works that focused on comparing the HODs of
the different models (e.g., \citealt{Contreras17}), we had matched the halo
mass definitions.  Here, since it is not our aim to compare the HODs themselves
in detail, but rather examine the environmental effects on each,
we prefer to leave the halo mass definitions as is, but we point out that
some differences between the models are due to this. A comparison of
{\tt Dhalo} masses and other halo definitions is presented in \citet{Jiang14}.

\vspace{0.2cm}
\section{The HOD dependence on environment and halo age}
\label{Sec:HOD}
A fundamental assumption of the HOD approach is that the galaxy content in
halos depends only on the mass of the host halo. Any dependence of the HOD on
secondary parameters, like halo age or large-scale environment, is a direct
reflection of galaxy assembly bias (as discussed in \S~\ref{Sec:Intro}).
In this section we examine the impact of halo age and environment on the HOD,
as predicted in the SAMs. In \S~\ref{SubSec:samples} we provide details on
how the halo age and large-scale environment are defined and their relation to
one another.
Our main results regarding how the halo occupation functions vary with
environment and halo age are presented in \S~\ref{SubSec:HOD}, additional
cases are studied in \S~\ref{SubSec:otherHODs}, and the impact
on HOD parameters is shown in \S~\ref{SubSec:param}.

\vspace{0.1cm}
\subsection{Halo formation time and environment}
\label{SubSec:samples}
We define the formation redshift of a halo, as is commonly done, as the
redshift when the main progenitor reached (for the first time) half of its
present-day mass.  We obtain this by following the halo merger trees of the
different models
and linearly interpolating between the time snapshots available.
For defining the large-scale environment of the halos we use the density
field obtained directly from the dark-matter particle distribution with a
$5 \,h^{-1}\,{\rm Mpc}$ Gaussian smoothing (which we denote as $\delta_5$).
This was calculated in cells of $\sim 2 \,h^{-1}\,{\rm Mpc}$ and is provided in the
database. The $5 \,h^{-1}\,{\rm Mpc}$ smoothing scale is chosen as it is
significantly larger than the size of the largest halos, so as to reflect
the large-scale environment,  and yet have enough different environments
sampled. We test also the other smoothing radii provided in the database,
$1.25$, $2.5$ and
$10 \,h^{-1}\,{\rm Mpc}$, finding the same qualitative trends we find with $5 \,h^{-1}\,{\rm Mpc}$ for all
the results shown in this paper.  Alternative density and environment
definitions are explored in the literature (e.g., \citealt{muldrew11}).
Observationally, one naturally
must resort to using the galaxy distribution to define the environment. Here,
as it is available,  we prefer to directly use the underlying dark matter
density field, though in practice we expect
our results to be insensitive to the details of the definitions.

\begin{figure}

\vspace{-0.4cm}
\hspace{-0.6cm}
\includegraphics[width=0.53\textwidth]{Fig01a.ps}

\hspace{-0.6cm}
\includegraphics[width=0.53\textwidth]{Fig01b.ps}
\caption[]{\label{Fig:CW}
(Top panels) A $120 \,h^{-1}\,{\rm Mpc}$ x $120 \,h^{-1}\,{\rm Mpc}$ x $20 \,h^{-1}\,{\rm Mpc}$ slice of the
Millennium simulation showing the distribution of the halos in it.
Red (blue) dots represent the 20\% of halos that live in the densest
(least dense) environments, and the remainder are represented as black dots.
The density selection is made in 0.2 dex bins of fixed halo mass (see text).
The bigger plot on the left includes all halos, while the smaller ones on the
right hand side show separately only the 20\% of halos that live in the
densest and least dense environments.
(Bottom panels) Same as in the top panels, for the identical slice from the
Millennium simulation, but now color-coding halos by formation time instead
of environment. Red (blue) dots represent the 20\% most early (late) formed
halos.
}
\end{figure}

To classify the halos by environment, we rank the halos by density in narrow
(0.2 dex) bins of halo mass and select in each bin the 20\% of halos that
are in the densest environment and the 20\% of halos in the least dense
environment. This factors out the dependence of the
halo mass function on environment and allows us to compare the HODs in the
different environments for halos of nearly equal mass. We follow a similar
procedure to select the 20\% of halos with the highest and lowest
formation redshifts. We illustrate how our environment and halo age cuts
vary with halo mass in Appendix~\ref{Sec:Cuts}.
We have verified that our mass bins are sufficiently small by using also
0.1 dex bins and confirming that our results do not change.
We also test splitting the sample into the 10\% and the 50\% extremes of the
population, and find similar trends as found for the 20\% subsamples.

The distribution of halos classified as residing in the 20\% most
and least dense environments is shown using
red and blue dots, respectively, in the top panels of Fig.~\ref{Fig:CW},
for a slice from the Millennium simulation. The remainder of the halos are
shown as black dots.
The dense and under dense regions appear to ``carve out'' disjoint regions in
the cosmic web of structure, with the densest ones being more compact than the
underdense regions, as can be expected. The corresponding classification for
the early- and late-forming halos, for the same slice, is shown in the
bottom panels of Fig.~\ref{Fig:CW}.
It is apparent that the distribution of early- and late-forming halos is
distinctly different than that of halos in dense and underdense environments.
There is perhaps a tendency for the early-forming halos to preferentially
occupy the dense environments, and a slight trend for late-forming halos to
populate also the underdense regions. However, the general distribution is very
different with both early- and late-forming  halos tracing well the cosmic
web, in contrast to the strong environment patchy pattern. It is also
clear, even by visual inspection, that the early-forming halos are more
clustered than the late-forming ones.   We examine the clustering of the
galaxies in these halos later on in \S~\ref{Sec:clustering}.

To further examine the correlation between formation redshift and large-scale
environment, we plot in Fig.~\ref{Fig:Cont} the joint distribution of the two
properties. We do this separately for three narrow ranges of halo mass, as
labelled, since the two properties by themselves also correlate with halo
mass, which is apparent from the individually marginalized distributions also
shown. These demonstrate the known trends that more massive halos reside in
denser environments and are formed later than less massive halos.
The 2D distribution appears very broad with no obvious strong trend. To
quantify that we also plot the medians of one property as a function of the
other: the solid lines are the median of formation redshift for fixed
density and the dashed lines the median of environment for a given
formation redshift. The fact that the solid lines are roughly horizontal
and the dashed lines nearly perpendicular (or that the two sets of medians
are almost perpendicular to each other) over most of the range reflects
their lack of correlation on one another.  This is perhaps somewhat surprising
given the measurements of assembly bias (e.g., \citealt{gao05,gao07}) showing
that early-formed halos are more clustered than late-forming ones, and as
such expected to reside in dense environments. Only such a weak dependence
is apparent, at the high density and high formation redshift end, where the two
sets of lines slightly curve toward each other.

\begin{figure}
\includegraphics[width=0.48\textwidth]{Fig02.ps}
\caption[]{\label{Fig:Cont}
Joint distribution of large-scale environment ($\rm \delta_5$) and
formation redshift ($\rm z_{\rm form}$) for present-day halos in the
Millennium simulation, for three narrow ranges of halo mass. The
red, blue and green contours represent halos with low, intermediate and high
masses, respectively, as labelled in the top part of the figure. The
different contour levels correspond to 1, 2 and 3 $\sigma$ of the distribution.
The marginalized distributions of each property separately are shown as well,
for each halo mass bin.
The (roughly horizontal) solid lines represent the median values of the
formation redshift as a function of environment. The (roughly perpendicular)
dashed lines are the median values of environment at each formation redshift.
}
\end{figure}

\vspace{0.1cm}
\subsection{The HOD as a function of halo age and environment}
\label{SubSec:HOD}

It is of fundamental importance and interest to investigate how the halo
occupation functions themselves vary as a function of each of these
properties. For the galaxy sets we use fixed number-density samples drawn
from the SAM catalogs when ranked by stellar mass.
We have examined a range of different number density samples and present
the results for three representative cases with number densities of
$3.16 \times 10^{-2} \,h^{3}\,{\rm Mpc}^{-3}$, $ 10^{-2} \,h^{3}\,{\rm Mpc}^{-3}$ and
$3.16 \times 10^{-3} \,h^{3}\,{\rm Mpc}^{-3}$.
The corresponding minimum stellar mass thresholds for each of these are
provided in Table~\ref{table}.  Naturally, the stellar masses increase with
decreasing number density.  Differences between the stellar mass values
of G11 and L12 are expected, given the differences in galaxy formation
prescriptions and corresponding stellar mass functions.

\begin{table}
\centering
\caption{\label{table}
Stellar mass thresholds (in units of $h^{-1}M_{\odot}$)
for the three main number-density samples (in units of $\,h^{3}\,{\rm Mpc}^{-3}$)
presented in this work, for the G11 and L12 models.}
\hspace{-0.2cm}
\begin{tabular}{c c c c}
\hline
\hline
  & $3.16 \times 10^{-3}$ & $1 \times 10^{-2} $ & $3.16 \times 10^{-2} $ \\
\hline
G11    & $3.88 \times 10^{10}$ & $1.42  \times 10^{10}$ & $1.85 \times 10^{9}$\\
L12    & $2.92 \times 10^{10}$ &$6.50 \times 10^{9}$ & $9.39 \times 10^{8}$\\
\hline
\end{tabular}
\end{table}

Fig.~\ref{Fig:HOD_Err} shows how the halo occupation functions vary with
environment and halo age for a galaxy sample from the G11 SAM model
with a number density of $10^{-2} \,h^{3}\,{\rm Mpc}^{-3}$. The top panel shows the HODs
for the full galaxy sample (black) as well as for the subsets of galaxies
that reside in the 20\% of halos in the densest environments (red) and
20\% of halos in the least dense environments (blue). We remind the
reader that the division to 20\% most/least dense regions is done for each
bin of halo mass, so that the different samples equally probe the full
halo mass range. Also, we note that, by construction, these samples have
equal numbers of halos but not equal number of galaxies.

\begin{figure}
\includegraphics[width=0.48\textwidth]{Fig03a.ps}
\includegraphics[width=0.48\textwidth]{Fig03b.ps}
\caption{\label{Fig:HOD_Err}
(Top panel) The halo occupation functions for a galaxy sample with number
density $ 10^{-2} \,h^{3}\,{\rm Mpc}^{-3}$, for the G11 model. The solid black line shows the
HOD of all galaxies in the sample. The solid red line shows the HOD for the
galaxies in the 20\% of halos in the densest environments, while the solid
blue line presents the HOD for the galaxies in the 20\% of halos in the least
dense environments. The red and blue shaded regions (apparent only at the
high-mass end) represent jackknife errors calculated using 10 subsamples. In
all cases, dotted lines show separately the central galaxy occupation
contribution and  dashed lines represent the satellite galaxies occupation.
(Bottom panel) Same as in the top panel, but here for halo samples selected
by their formation time instead of their environment. The occupation for
galaxies in the 20\% earliest-formed halos is shown in red, and for the
20\% latest-formed halos is shown in blue.}
\end{figure}

We find distinct differences in the HODs for both the central and satellite
occupation functions. For the central occupation, the differences are
noticeable at the ``knee'' of the occupation function and below. We find that
in the densest environments, central galaxies are more likely to reside also
in lower-mass halos, and the trend reverses in underdense regions. Stated in
a slightly different way, in the regime where the halo occupation rises from
0 to 1, halos are more likely to host central galaxies if they reside in
dense environments. This may be related to preferential early formation
of halos in dense regions, though as we saw above the correlation is rather
loose. We discuss below further insight into  the resulting trends for
central galaxies (see \S~\ref{Sec:SMHM}).

The satellite occupation function in the G11 model also exhibits
a dependence on large-scale environment. The satellite occupation function
in dense environments exhibits a slight shift toward larger numbers, so
that halos in dense environments are more likely to have more satellites
on average.  This behavior is perhaps naturally expected, due to the
increased interactions and halo mergers in dense environments.

The bottom panel of Fig.~\ref{Fig:HOD_Err} shows how the occupation function
varies with halo age for the same G11 galaxy sample with number density
$10^{-2} \,h^{3}\,{\rm Mpc}^{-3}$. In the case of halo age, there are much larger effects on
the occupation functions than we saw with environment. For the central
occupation, we find a clear trend of early forming (old) halos being more
likely to host galaxies also at lower masses than late
forming (young) halos.  This likely arises from the fact that the early formed
halos have more time for stars to assemble and for the galaxy to form. The
sense of the trend is the same as that for the environmental dependence but is
a much more stronger one, with the ``shoulder'' of the occupation function
extending significantly toward lower masses with larger age.

We find a strong reverse effect for the satellites occupation at the
low mass end:  early-forming halos have significantly fewer satellites than
late-forming halos.  This trend is pronounced at low occupation numbers of
$\langle N(M_{\rm h})\rangle<10$ and becomes negligible at higher occupation
numbers.  This is probably due to the fact that in the early-forming halos
there is simply more time for the satellites to merge with the central galaxy,
which will be a more dominant process at the low halo mass / low occupation
regime.   This trend is similar to the predicted dependence of subhalo
occupation on halo formation time \citep{bosch05,zentner05,giocoli10,jiang16},
indicating that baryonic physics does not play an important role in the
variation of the satellites occupancy.

These differences in the halo occupation functions, for both age and
environment, are significant. We
estimate the uncertainties on the HOD calculations using jackknife
resampling, dividing the full simulation volume into 10 slices. Incidentally,
when separating the different subregions, if the center of a given halo is
in a certain subvolume we include with it all galaxies in that halo,
regardless of where the physical boundary between the subvolumes lie.  The
resulting errors are shown as shaded regions in the figure, and are in fact
negligible over most of the range and only become significant at the
high-mass range where the number of halos is small.

The HOD dependences on age and environment are different in magnitude
(for centrals) and sense (for satellites). The strength of the trends with
age versus environment perhaps indicates that formation time is the
more fundamental property related to assembly bias. Varying the Gaussian
smoothing length used to define the environment impacts slightly
the size of the deviations, with the differences becoming a bit more
pronounced for small smoothing lengths, as expected. However, we choose
to stick with our $5 \,h^{-1}\,{\rm Mpc}$ Gaussian smoothing so as to robustly infer
the large-scale environment.

We describe and model these differences in terms of the HOD parameters in
\S~\ref{SubSec:param}.   The dependence on environment we find for the
central occupation is very similar to that measured by \citet{mcewen16}.
However, they do not find any noticeable difference for the satellite
occupation. Our results differ from those of \citet{mehta14} who find no
significant dependence of the HOD on environment. The level of occupancy
variation that is present appears to depend on the specifics of the galaxy
formation model utilized.

\begin{figure}
\includegraphics[width=0.48\textwidth]{Fig04a.ps}
\includegraphics[width=0.48\textwidth]{Fig04b.ps}
\caption{\label{Fig:HOD_L12}
The same as Fig.~\ref{Fig:HOD_Err} but for the L12 model.}
\end{figure}

\begin{figure*}
\includegraphics[width=0.48\textwidth]{Fig05a.ps}
\includegraphics[width=0.48\textwidth]{Fig05b.ps}
\includegraphics[width=0.48\textwidth]{Fig05c.ps}
\hspace{0.6cm}
\includegraphics[width=0.48\textwidth]{Fig05d.ps}
\caption{\label{Fig:HOD_envir}
The dependence of the halo occupation functions on large-scale environment for
different number densities than that shown in Fig.~\ref{Fig:HOD_Err} and
Fig.~\ref{Fig:HOD_L12}, $3.16 \times 10^{-3} \,h^{3}\,{\rm Mpc}^{-3}$ on the left-hand
side  and $3.16 \times 10^{-2} \,h^{3}\,{\rm Mpc}^{-3}$ on the right. The top panels
are for the G11 model and the bottom ones are for L12.}
\end{figure*}

\vspace{0.1cm}
\subsection{The HOD for different models and samples}
\label{SubSec:otherHODs}

\begin{figure*}
\includegraphics[width=0.48\textwidth]{Fig06a.ps}
\includegraphics[width=0.48\textwidth]{Fig06b.ps}
\includegraphics[width=0.48\textwidth]{Fig06c.ps}
\hspace{0.6cm}
\includegraphics[width=0.48\textwidth]{Fig06d.ps}
\caption{\label{Fig:HOD_age}
The same as Fig.~\ref{Fig:HOD_envir}, but for galaxy samples selected using
halo formation time, instead of environment.}
\end{figure*}

To further investigate the dependence on the galaxy formation model we repeat
the analysis in \S~\ref{SubSec:HOD} using the independently derived L12 Durham
model. Figure~\ref{Fig:HOD_L12} shows the HOD dependence on environment and
halo age for a galaxy sample with number density of  $10^{-2} \,h^{3}\,{\rm Mpc}^{-3}$ from the
L12 SAM.  The environmental dependence for L12 shows a similar, but more
subtle, trend for the central occupation, while the trend for the satellite
occupation disappears.
The difference in the satellite occupations between L12 and G12 could arise
due to the different treatment of satellites in the two models
(\S~\ref{SubSec:SAM}). As the satellite destruction processes are more
immediate in L12, perhaps there is less time for the environmental effects
to impact the occupation in that case.

The HOD dependence on halo formation time for L12 and G11 is very similar,
with L12 as well showing the strong trends for both the central and satellite
occupation.  The tendency of centrals to shift toward occupying lower
mass halos is slightly stronger for L12. We note the distinct change
of shape of the central occupation, giving rise to a non-monotonic occupation
for the galaxies in early-forming halos. This is likely to be related to the
form of AGN feedback in the Durham models, as discussed in \citet{nuala17}.

We also examine the dependence of the different trends with stellar mass
of the galaxies, by varying the number density of the samples. As the samples
are ranked by stellar mass, larger number densities include smaller stellar
masses, while small number densities are limited to more massive galaxies.
We present our results for two additional number densities than the one
previously used (one smaller and one larger) in Figures~\ref{Fig:HOD_envir}
and \ref{Fig:HOD_age}, for environment and age, respectively. In both
cases, the HODs change globally as expected, shifting overall towards lower
halo masses with increasing number density (decreasing stellar mass).

The specific signatures of the environmental dependence of the HOD change as
well with number density. For G11 (top panels of Fig.~\ref{Fig:HOD_envir}),
the differences in the central occupations
increase with number density. This is in accordance with the findings
of \citet{croton07} that galaxy assembly bias is stronger for fainter (less
massive) galaxies.  For the lowest number density shown, corresponding to
galaxies with stellar masses larger than $3.88 \times 10^{10} h^{-1}M_{\odot}$
(Table~\ref{table}), the differences between the central occupations are
barely noticeable. In contrast, the G11 satellite occupation differences
decrease slightly with number density.  These opposing changes with
number density suggest that the environment dependence of the central and
satellite occupations  have different origins.
We find a similar change with number density of the central occupation
environment dependence for L12 (bottom panels of Fig.~\ref{Fig:HOD_envir}),
while the satellite occupancy variation remains effectively undetected.

The halo age signatures for the different number densities
(Figs.~\ref{Fig:HOD_Err}, \ref{Fig:HOD_L12} and \ref{Fig:HOD_age}) are quite
robust and do not exhibit any clear dependence on the number density for
either model, again indicating that these may be of different physical nature.
The non-monotonic occupation behavior for the early-forming halos
\citep{nuala17} is also apparent in the smallest number density case for the
G11 model.

\vspace{0.1cm}
\subsection{Extending the HOD parametrization}
\label{SubSec:param}

\begin{figure*}[bt]
\includegraphics[width=1\textwidth]{Fig07.ps}
\caption{\label{Fig:HODfit_Env}
(Left) The HOD of the G11 SAM for a number density of $3.16 \times 10^{-2}
\,h^{3}\,{\rm Mpc}^{-3}$. Dots represent the HOD calculated in the simulation: the black ones
show the HOD for all galaxies; the red ones the HOD for the $10\%$ of
halos in the densest environments; and the blue ones show the HOD for the
$10\%$ of halos in the least dense environments. The solid lines, in
corresponding colors, show the 5-parameter best-fit models for these.
(Right) The values of the best-fitting parameters of the HODs as a function
of the environment percentile for $M_{\rm min}$ (top left),
$\sigma_{\rm logM}$ (bottom left), $M_{\rm cut}$ (top middle), $M_{\rm 1}$ (bottom
middle), $\alpha$ (top right) and $M_{\rm 1}/M_{\rm min}$ (bottom right).  Each
dot in these plots represents a
different subsample selected by its large-scale environment, each with
$10\%$ of the full halo population, with the environment density increasing
from left to right. The left-most dots and right-most dots in these panels
represent the parameter values of the models plotted in blue and red,
respectively, in the left-hand side HOD panel.  The errorbars reflect the
$1\sigma$ uncertainty on the parameters.
The green horizontal lines with shaded regions in the parameters panels are
the values fitted for the full sample and their uncertainty.
}
\end{figure*}

\begin{figure*}
\includegraphics[width=1\textwidth]{Fig08.ps}
\caption{\label{Fig:HODfit_Age}
Same as Fig.~\ref{Fig:HODfit_Env}, but for subsamples selected by
halo formation time instead of large-scale environment. In the panels for
the individual parameters, the halo formation redshift (age) increases
going from left to right. Please note that for the parameter values on
the right, the y-axis ranges are different than those of
Fig.~\ref{Fig:HODfit_Env}.}
\end{figure*}

It is customary to parametrize the shape of the HOD using a 5-parameter model
which captures the main features of the halo occupation function, as predicted
by SAMs and hydrodynamic simulations \citep{zheng05}. This model is commonly
used when interpreting galaxy clustering measurements to infer the galaxy--halo
connection (e.g., \citealt{zheng07,zehavi11}).  Here, we characterize the
HOD dependences on age and environment in terms of the 5 parameters, as a
first step toward incorporating these variations into the HOD model.

The halo occupation function is usually modeled separately for
central galaxies and satellites. The occupation function for
centrals is a softened step-like function with the following form:
\begin{equation}
 \langle N_{\rm cen}(M_{\rm h})\rangle = \frac{1}{2}\left[ 1 + {\rm erf} \left( \frac{\log M_{\rm h} - \log M_{\rm min}}{\sigma_{\log M}}  \right) \right],
\label{Eq:Cen_HOD}
\end{equation}
where $ {\rm erf}(x)$ is the error function,
$ {\rm erf}(x) = \frac{2}{\sqrt{\pi}} \int_{0}^{x} e^{-t^2} {\rm d}t. $
$M_{\rm min}$ characterizes the minimum halo mass for hosting a central galaxy
above the specified threshold.
In the form adopted here, it is the halo mass for which half of the halos
are occupied.  $\sigma_{\log M}$ indicates the width of the transition from
zero to one galaxy per halo and reflects the scatter between stellar mass
and halo mass.

For satellite galaxies, the occupation function is modeled as:
\begin{equation}
 \langle N_{\rm sat}(M_{\rm h})\rangle = \left( \frac{M_{\rm h}-M_{\rm cut}}{M^*_1}\right)^\alpha,
\label{Eq:Sat_HOD}
\end{equation}
for $M_{\rm h}>M_{\rm cut}$,
representing a power-law occupation function with a smooth cutoff at the
low-mass end. Here $\alpha$ is the slope of the power-law, with typical
values close to one,
$M_{\rm cut}$ is the satellite cutoff mass scale (i.e., the minimum mass
of halos hosting satellites), and $M^*_1$ is the normalization.
Often, instead of the latter, a related parameter is used, $M_{1}$, which
is the mass of halos that host one satellite galaxy on average
($M_{1} = M^*_1 + M_{\rm cut}$).
The total occupation function is then specified by these 5 parameters and
given by the sum of the two terms:
\begin{equation}
 \langle N_{\rm gal}(M_{\rm h})\rangle =  \langle N_{\rm cen}(M_{\rm h})\rangle +  \langle N_{\rm sat}(M_{\rm h})\rangle.
\end{equation}

Figure~\ref{Fig:HODfit_Env} shows how these 5 parameters vary with environment.
The left-hand side presents the HOD of the G11 SAM for
$n=3.16 \times 10^{-2} h^{3} Mpc^{-3}$ for the full sample, and the $10\%$ of
halos in the most dense regions and the $10\%$ of halos in the least dense
regions. The dots represent the directly-measured HODs and the lines are
the best-fit 5-parameter models to them. The right-hand side examines how
each of the parameters varies with environment in $10\%$ bins of halo
environment.  The fits are done assuming equal weight to all measurements and
using only those with  $\langle N(M_{\rm h})\rangle > 0.1$.  The errorbars on
the parameters are obtained by requiring $\chi^2/{\rm dof}=1$, as in
\citet{Contreras17}.

For this G11 sample, we see that the changes to the parameters when varying
the environment are subtle, but all are affected.
The changes in the central occupation with density
are in fact quite small, with $M_{\rm min}$ decreasing and $\sigma_{\rm logM}$
increasing slightly with density.  The variations in best-fitting
parameters are influenced by the limited flexibility in the assumed shape of
the HOD.
The changes in the satellite occupation with increasing density act to
gradually decrease $M_{\rm cut}$ and $M_{\rm 1}$ and increase the slope
$\alpha$, over at least part of the density range.
We note that we find more intricate changes to the HOD parameters than those
modeled in \citet{mcewen16}, since that work saw differences only in the
centrals occupation function and not the satellites one. The resulting
variation in the $M_{\rm 1}/M_{\rm min}$ ratio (bottom-right panel) is a
noticeable decrease with increasing density over most of the range, but
then a turnover and a slight increase for halos in the densest regions.

Fig~\ref{Fig:HODfit_Age} examines the change in the parameters, but now
with halo formation time. The change in parameters in this case is more
distinct and significant, since the dependence of the HOD on halo age is
stronger than on environment. $M_{\rm min}$ monotonically decreases with
increasing formation redshift (earlier formation). $\sigma_{\rm logM}$ varies
with halo age but does not show a clear trend.
The satellite occupation changes in the
opposite sense, with all three parameters $M_{\rm cut}$, $M_{\rm 1}$ and
$\alpha$ increasing significantly with larger formation redshift.
(The change in the slope $\alpha$ again may be somewhat
affected by the limitations of the assumed HOD shape.)

The combined effect on the $M_{\rm 1}/M_{\rm min}$ ratio is a dramatic
increase with formation redshift, of about a factor six over the full range!
This change is much stronger than the variation of this ratio
with either number density or redshift, as explored by \citet{Contreras17},
about twice as large as the variation with number density and close to four
times larger than the evolution in the ratio from redshift 3 to 0.
This significant change, however, is easily understood from the predicted
occupancy variation (e.g., bottom part of Fig.~\ref{Fig:HOD_Err}).
For earlier-forming halos, $M_{\rm 1}$ shifts toward larger halo masses
while $M_{\rm min}$ shifts toward smaller halo masses, resulting in a
substantial increase in their ratio. Still, it is noteworthy that the
$M_{\rm 1}/M_{\rm min}$ ratio is such a sensitive indicator of halo age.

These results can inform theoretical modeling efforts extending the standard
HOD framework. We can envision modeling each of the parameters change with
halo age as a power-law function with an additional assembly bias parameter
(similar to our modeling of the evolution of the HOD in
\citealt{Contreras17}).  Such a model may aid in obtaining constraints on
assembly bias from observational data, as well as providing a straight-forward
method of incorporating the age-dependence of the HOD into galaxy mock
catalogs.

\vspace{0.2cm}
\section{The stellar mass -- halo mass relation}
\label{Sec:SMHM}

To gain a better understanding of the origin of the trends seen in the
central galaxy occupation function with age and environment, we examine
the stellar mass -- halo mass (SMHM) relation. As we
show, it is the dependence of the scatter in this relation on the secondary
parameters that gives rise to the occupancy variation and to galaxy assembly
bias.

Figure~\ref{Fig:SMHM} shows the stellar mass of central galaxies as
a function of halo mass for galaxies in the G11 SAM. We plot $1\%$ of
all central galaxies, for clarity. The stellar mass
increases with halo mass, with the median of the relation (black line)
exhibiting a relatively steep slope up to $M_{\rm h} \sim 10^{12} h^{-1}M_{\odot}$
and a shallower increase for more massive halos, when the AGN feedback
becomes important. This was studied in detail in \citet{Mitchell16} for
{\tt GALFORM} (see also \citealt{Contreras15}).  There is significant
scatter in the relation which decreases at the high-mass end. This scatter
is expected to be due to stochasticity in both galaxy and halo
assembly histories and the various physical processes. Thus we may expect
the scatter to relate to the properties of the host halos. We examine this
visually by color-coding each galaxy by its large-scale environment (top
panel) and by the formation redshift of its host halo (bottom panel).

\begin{figure}
\hspace{-0.2cm}
\includegraphics[width=0.5\textwidth]{Fig09.ps}
\caption{\label{Fig:SMHM}
(Top) The stellar mass of central galaxies as a function of host
halo mass for the G11 SAM and its dependence on environment.
Each dot represents a central galaxy, plotted for a representative
(randomly chosen) $1\%$ of the galaxies.
Galaxies are color-coded by their $5 \,h^{-1}\,{\rm Mpc}$ Gaussian smoothed
density, $\delta_5$, according to the color scale shown on the right.
The plotting order is also chosen randomly, so as to avoid any overplotting
issue. The black solid line represents the median of the distribution with the
errorbars designating the $20\%$--$80\%$ range of the distribution.
(Bottom) Same as for the top panel, but now color-coded by the formation
redshift, calculated as the time when the halo reaches half of its final mass.
For fixed halo mass, more massive central galaxies tend to live in halos that
formed early or reside in denser environments (with the latter being a weaker
trend than the former).
}
\end{figure}

As is apparent from Fig.~\ref{Fig:SMHM} the spread around the median SMHM
relation is not random, but depends on the secondary property. For halos less
massive than about $10^{12} h^{-1} M_{\odot}$, there is an apparent dependence
on the large-scale environment (top panel), where for fixed halo mass, more
massive central galaxies tend to reside in denser environments. This trend
appears to have a fairly sharp transition between relatively low and high
densities, even though there is a large scatter of different environments
at each location on the SMHM relation (as is evident by the mix of colors).
The trend does not persist toward larger masses, where there is no variation of
environment for fixed halo mass (or else it is impossible to see one due to
the large scatter of different densities).
We find that the central galaxies in the densest environments (in
absolute terms, not per halo mass bin, i.e., the red/maroon colored ones
in the top panel) populate two distinct regions in this diagram: they
predominantly populate the most massive halos, albeit at smaller numbers
according to the halo mass function, and they also comprise the most massive
centrals in low-mass halos. The former simply stems from the fact that the
most massive halos tend to reside in dense environments, while the latter
is related to the occupancy variation we discuss here.

The bottom panel of Fig.~\ref{Fig:SMHM} shows the same SMHM relation,
but now color-coded by the formation redshift (age) of the halos. The trend
with halo age for fixed halo mass is particularly striking, with
more massive central galaxies generally residing in halos that formed early.
This dependence on halo age is gradual but very distinct, due to the small
scatter of halo ages at each location in the stellar mass -- halo mass
diagram for halos below
$\sim 10^{12} h^{-1} M_{\odot}$. The trend persists for all halo masses,
but with a significantly larger scatter of halo ages at the high-mass end,
as the formation redshifts also progressively become more recent, as expected.
A similar trend with halo formation
time has been measured in  SAMs by \citet{wang13a} and more recently
also for galaxies in the EAGLE hydrodynamical simulation \citep{matthee17}.
It likely arises because central galaxies in early-formed halos have more
time for accretion and star formation and thus end up being more massive.
Once again it appears that halo age is the more fundamental characteristic
here that affects galaxy properties.

The dependence on environment is more complex and harder to interpret.
\citet{jung14} investigate the stellar mass dependence on environment for
fixed halo mass using a different SAM. They find only small differences
between halos in the densest and least dense environments for low
halo masses, and these differences diminish with increasing halo mass
(cf. \citealt{tonnesen15}). This suggests that the level of secondary
correlations present (and by association, galaxy assembly bias) depends
on the details of the galaxy formation model adopted.
We note also the counter-intuitive fact that, at least according to the study
of \citet{matthee17},  while some fraction of the scatter in the SMHM
relation is accounted for by formation time, the large-scale environment
seems to make a negligible contribution.

The fundamental importance of these dependences of stellar mass on secondary
properties at fixed halo mass is that they provide a direct explanation
for the central galaxy occupancy variation with environment and halo age
(as shown in, e.g., Fig.~\ref{Fig:HOD_Err}). For fixed halo mass, early-formed
halos or halos in denser environments host more massive galaxies. Consequently,
any fixed stellar-mass cut (e.g., the $1.42 \times 10^{10} h^{-1}M_{\odot}$
threshold used to define the sample analyzed in Fig.~\ref{Fig:HOD_Err})
would include these first.  Thus the central galaxies in early-forming halos
or dense environments populate relatively lower-mass halos, extending the
central occupation function in that direction.
And, conversely, late-forming halos or halos in underdense
environments generally host lower-mass galaxies. Therefore, only centrals
hosted by more massive halos will make it into the sample and the central
occupation function in that case will be shifted toward more massive halos.

The level of scatter in halo age or environment at each location directly
determines the strength of the occupancy variation. The tight correlation
between stellar mass and halo age (for fixed halo mass) results in a large
variation of the HOD,  while the large scatter involved with environment
results in only a moderate change of the HOD in that case.
Furthermore, as noted already, the SMHM trend with environment holds only
at the low-mass end, while the general trend with halo age persists for all
halo masses. This explains the change in occupancy variation with number
density, demonstrated in Fig.~\ref{Fig:HOD_envir} and \ref{Fig:HOD_age}.
For age, the occupancy variation remains at comparable levels for all
number densities, similar to the trend in the SMHM relation.
For environment, the level of occupation variation decreases for smaller
number densities (larger stellar mass thresholds), as these correspond to
larger halo masses where the trend with environment diminishes.

In any case, we are seeing that the correlated nature of the scatter in
the SMHM relation is intimately related to the trends
in the occupation functions.  It is exactly this coupling between halo
properties (such as large-scale environment and formation time) and galaxy
properties (such as stellar mass or luminosity) that causes the dependence
of the HOD on halo assembly.
A more extensive study of the connection between the SMHM relation and the
occupancy variation and galaxy assembly bias will be presented elsewhere
(Zehavi et al., in preparation).

\vspace{0.2cm}
\section{The impact on galaxy clustering}
\label{Sec:clustering}
To see the impact of the occupancy variation with halo age and environment
(\S~\ref{Sec:HOD}) on galaxy clustering, we measure and examine the
correlation functions of galaxies in these samples. The variations in the
HODs couple with the different clustering properties of the halos to produce
a signature of assembly bias in the galaxy distribution.

\vspace{0.1cm}
\subsection{The shuffling mechanism}
\label{SubSec:Shuffle}

To measure the effects of assembly bias on the galaxy correlation function,
we need to create a control sample of galaxies where we explicitly remove
the galaxy assembly bias, and then compare to the clustering of the
original sample. In order to do that we shuffle the full galaxy population
among halos of similar masses, following the  procedure of \citet{croton07}.
Specifically, we select halos in 0.2 dex bins of halo mass and randomly
reassign the central galaxies hosted by these halos among all halos in that
mass bin, placing them at the same location as the original central galaxy
in the halo. The satellite galaxies are moved together with their original
central galaxy, preserving their distribution around it.
The shuffling eliminates a dependence of the galaxy population on any
inherent properties of their host halos other than mass (since these are
now randomly assigned).
Practically, what the shuffling does is remove the occupancy variation,
namely the dependence of the HOD on halo properties other than mass.
For these shuffled samples,  the HOD of the full galaxy sample remains
the same, but the differences between the HODs of different halo populations,
e.g., split by age or environment, are now eliminated and all share the
same HOD as that of the full sample.

We have verified that the results we present below are insensitive to our
specific choice of the bin size in halo mass. We also note that alternative
shuffling
algorithms have been proposed in the literature, where the satellites are
also shuffled among different halos of the same mass independent of the
central galaxies (e.g., \citealt{Zu08,zentner14}). This additional satellite
shuffling is important only when one is specifically concerned with features
that correlate the properties
of centrals and satellites or the satellites with themselves, such as
galactic conformity or satellite alignment.  For our purposes, the
combined central+satellite galaxies shuffling completely suffices to erase the
signature of the occupancy variation.  We clarify that our shuffling does
impact the small scales (1-halo term) of the correlation function of our
subsamples, as we show below (in contrast to the statement made in some works
that this shuffling preserves the 1-halo term, which only holds when
considering the {\it full} galaxy sample).

\vspace{0.1cm}
\subsection{The correlation functions}
\label{SubSec:clustering}

Figure~\ref{Fig:CF_Err} show the correlation functions measured for the
galaxy subsamples analyzed in Fig.~\ref{Fig:HOD_Err}, for the
$n=10^{-2} \,h^{3}\,{\rm Mpc}^{-3}$ sample from the G11 SAM.  We calculate the
auto-correlation function of the full galaxy sample (solid black lines) and
the cross-correlation function between the full sample and the galaxies
in the different subsets of 20\% of the halos (red and blue solid lines, as
labelled), showing the environmental dependence on the top and formation time
on the bottom.  The dashed lines in all cases show the results when
shuffling the galaxy samples, effectively removing the occupancy variation,
as described in \S~\ref{SubSec:Shuffle}. The top subpanels are the correlation
functions themselves, and the middle and bottom subpanels show ratios
derived from these correlation functions, to highlight different features
as described in the figure caption and discussed below.

\begin{figure}
\includegraphics[width=0.48\textwidth]{Fig10a.ps}
\includegraphics[width=0.48\textwidth]{Fig10b.ps}
\caption{\label{Fig:CF_Err}
Correlation functions for the G11 $n=10^{-2} \,h^{3}\,{\rm Mpc}^{-3}$ sample.
(Top panel)
The top subpanel shows the auto-correlation function of the full galaxy
sample (black solid line) and the cross-correlation functions of the
full sample and galaxies in the 20\% of halos in the most and least dense
regions (solid red and blue lines, respectively).
Dashed lines are the corresponding correlation functions
of the shuffled galaxies (see text).  The middle subpanel displays these
now divided by the full sample auto-correlation function, highlighting
the different clustering properties in different environments.  This is
shown for both original and shuffled galaxy samples, e.g.,
the dashed red line is the ratio of the cross-correlation of the shuffled
galaxies in the dense regions and the auto-correlation of the full shuffled
sample.  The bottom subpanel shows, for the three
cases, the ratio between the correlation functions of the original and
shuffled galaxy samples.   In all subpanels, the shaded regions represent
the errorbars estimated from 10 jackknife realizations.
(Bottom panel) Same as in the top panel, but now for galaxies residing in
halo samples chosen by their formation redshift instead of environment.
Red (blue) lines correspond to the cross-correlation function
of the full galaxy sample with the subset of galaxies residing in the 20\%
earliest- (latest-)formed halos.
}
\end{figure}

The shaded regions represent the uncertainties on these measurements
estimated from jackknife resampling, when dividing the full simulation volume
into 10 slices along one axis (identical subvolumes to those used to estimate
the errors in Fig.~\ref{Fig:HOD_Err}).
The uncertainties on the ratios in the middle and bottom subpanels are the
jackknife errors on the ratios themselves, which are significantly smaller
than propagating the individual measurement errors, as can be seen by
comparing the red and blue shaded regions in the middle subpanels with the
grey shaded regions in the middle subpanels (the jackknife measurement errors
for the full sample). This is expected as the variations of the different
auto-correlation and cross-correlation functions among the different
jackknife samples are naturally correlated.
(Note that the y-axis range in the two subpanels is different and the grey
uncertainty regions plotted in the top and bottom parts of the figure are
identical.)

We start by examining the top part and top subpanel of Figure~\ref{Fig:CF_Err}
which illustrates the dependence of clustering on environment.  We find
distinct differences on large scales between the clustering of the galaxies
in the most dense environments versus the least dense regions. The galaxies
in dense environments are significantly more clustered than the full sample,
while the galaxies in the underdense regions are much less clustered, as
expected. The cross-correlation functions do not have the same shape on large
scales as the full auto-correlation function, due to the way these samples
were defined using the $5 \,h^{-1}\,{\rm Mpc}$ Gaussian smoothed density fields,
which effectively carves out different regions of dense and underdense
environments as is seen in Fig.~\ref{Fig:CW}.  In particular, the
cross-correlation function for the underdense regions exhibits a fairly sharp
dropoff above $\sim 1 \,h^{-1}\,{\rm Mpc}$ and goes below 0 at $\gtrsim 3 \,h^{-1}\,{\rm Mpc}$ (which is
where we stop plotting $\log \xi$).

The middle subpanel shows the ratios of the cross-correlations of the
subsamples to the full sample auto-correlation and highlights the dependence on
environment.  These differences arise due to the dependence of clustering on
large-scale environment, the fact that halos in dense environments are more
clustered than halos of the same mass in underdense environments.
We stress that this
dependence by itself is {\it not} what is commonly referred to as galaxy
assembly bias. To illustrate this we also plot the correlation functions
of the shuffled galaxies, where galaxies are randomly assigned
to halos of the same mass, which eliminates any connection to the assembly
history of the halos.  These correlation functions (the dashed lines) show
essentially the same trends with environment. This is in agreement with
the conclusions of \citet{abbas05,abbas06} who demonstrate that for the
most part the clustering dependence on large-scale environment can be
explained without resorting to occupancy variation.

The differences between the solid and dashed lines (in the top and middle
subpanels of Fig.~\ref{Fig:CF_Err}) are the ones reflecting galaxy
assembly bias. Namely, the occupancy variation we quantified in the HOD
coupled with halo assembly bias give rise to these systematic differences
in the clustering.  We illustrate these in detail in the bottom
subpanel which plots the ratio of original to shuffled correlation functions.
We find that the HOD differences with environment do induce significant
differences in the large-scale clustering, where for the full sample the
clustering of galaxies is stronger by about $15\%$ than the clustering of
the shuffled galaxies (with no occupancy variation and thus no galaxy
assembly bias). This translates to a $\sim 7\%$ change in the galaxy bias,
in good agreement with the predictions of \citet{croton07}.
The subsample of galaxies in the most dense environments
exhibits a similar trend, while the galaxies in the least dense regions
are significantly {\it less} clustered than their shuffled counterparts
over most of the range shown.  We discuss in \S~\ref{SubSec:origin} possible
reasons for this difference.

The bottom part of Fig.~\ref{Fig:CF_Err} investigates the dependence of
clustering on halo age. We see that galaxies in the earliest-formed halos
are more clustered on large scales than galaxies in the latest-forming halos.
The clustering differences in this case are much smaller than the differences
with large-scale environment and have similar shapes. This can be readily
seen in the top and middle subpanels, and we remind the reader that
the y-axis in the middle subpanel for halo age spans a much smaller range
than the corresponding one for environment.  Again, we note that while these
differences are directly due to age-dependent halo clustering,
namely reflecting halo assembly bias, these trends only marginally depend
on the occupancy variation with age, as seen by the relatively-small
differences on large scales between the solid and dashed lines in the middle
subpanel.

The small-scale clustering in this case shows bigger differences between
the solid and dashed lines (that are noticeable in all subpanels). This
arises mostly because of the large differences in the satellite
occupation functions, as seen in bottom panel of Fig.~\ref{Fig:HOD_Err}.
There are relatively more satellites in late-formed halos versus early-formed
halos, especially at the lower mass end of halos that host satellites,
likely simply due to having more time for the satellites to be destroyed
in the early forming halos. This leads to a reversal of the clustering
trend (most notable in the middle panel at $r \sim 1 \,h^{-1}\,{\rm Mpc}$) and a
stronger small-scale clustering for the galaxies in the most-recently forming
halos.  Interestingly, this is then a case where there is no halo assembly
bias but the galaxy clustering is still different due to occupancy variation
with halo age. This feature is evident only for the clustering as a function
of halo age and is negligible for the dependence on environment, since in
the latter case the differences between the satellite occupations are
minuscule (as we have seen in the top panel of of Fig.~\ref{Fig:HOD_Err}).

The bottom subpanel focuses on the galaxy clustering differences due to
the occupancy variations by showing the ratio of the correlation functions
of the original galaxy samples to the shuffled ones. On small scales, we
can see the strong signature of the satellite occupancy variation that we
had just discussed (differences between blue and red lines in the 1-halo
regime below $r \sim 1 \,h^{-1}\,{\rm Mpc}$).  The ratio for the full sample (black line)
on these scales remains unity, since the shuffling doesn't alter at all
the 1-halo contribution in that case. On larger scales, in the 2-halo regime,
we see that all three samples exhibit a similar galaxy assembly bias trend,
where the clustering of galaxies is stronger than that of the shuffled
galaxies.  We discuss this further below. Appendix~\ref{Sec:AutoCorr}
presents the auto-correlation functions for these subsets of galaxies
(instead of the cross correlation with the full sample).

\vspace{0.1cm}
\subsection{Origin of galaxy assembly bias trends}
\label{SubSec:origin}

We note an additional subtle feature in the middle subpanel of the bottom
part of Fig.~\ref{Fig:CF_Err}. As we explained above, the large-scale
clustering of galaxies as a function of halo age is dominated by the fact
that, at fixed mass, early-formed halos cluster more strongly than
late-forming halos (i.e., halo assembly bias). This is reflected by
the difference between the dashed red and blue lines.  When including
the occupancy variation (red and blue solid lines), we see that it acts
to slightly {\it decrease} the clustering differences between early- and
late-formed halos, for separations larger than $\sim 5 \,h^{-1}\,{\rm Mpc}$.

These small differences can be understood by examining the changes to the
HOD (as shown in the bottom panel of of Fig.~\ref{Fig:HOD_Err}). The
central galaxy occupation function for the late-forming halos is shifted
toward higher halo masses, which acts to slightly increase their clustering
(the blue solid line being above the blue dashed line in the middle subpanel
corresponding to formation time). Conversely, the central galaxy occupation
function for the early-formed halos is shifted toward lower halo masses,
resulting in a slightly reduced clustering (the red solid line lying slightly
below the red dashed line).
The interpretation gets a bit more complicated since an opposite trend is seen
for the satellites,  however, we have calculated the effective bias
corresponding to these varying HODs and confirmed that the net effect is
as described above.
We further corroborate this origin of the trend by examining the clustering
of the different samples when considering only the central galaxies while
excluding the satellites.

We now turn back to the galaxy assembly bias trends shown on the bottom
subpanels in Fig.~\ref{Fig:CF_Err}, for both halo age and environment,
where we plotted the clustering of the different samples compared to the
clustering of shuffled galaxies where the occupancy variation was erased.
When comparing the galaxy assembly trends for halo age and environment,
we find a similar effect for the galaxies in early-formed halos and for
the galaxies in dense environment (the red solid lines in the two bottom
subpanels).  The clustering difference is in the same sense for galaxies
in late-forming halos (blue solid line in the bottom subpanel of the bottom
part of the figure). However, for galaxies in dense environments, this
trend reverses, with a weaker clustering than that of the shuffled sample
(blue solid line in the bottom subpanel of the top part of the figure).
We attempt to obtain some insight here regarding the origin of these trends.

We first consider the trends with regard to halo age. In that case,
we see that regardless of sample used (full sample, early forming, or late
forming) the galaxy assembly bias trends go in the same direction, with the
clustering of galaxies stronger than that of the shuffled samples.   We can
understand why that is by examining the variations in the central galaxies
HOD in Fig.~\ref{Fig:HOD_Err} and the systematic dependence on halo age in the
central galaxies SMHM relation (Fig.~\ref{Fig:SMHM}).
For any halo mass, we see that central galaxies tend to occupy first
the earlier-formed halos.
Thus, it is always the case -- for any range of halo ages -- that the
relatively earlier-formed halos will be preferentially populated.
Coupling this with halo assembly bias, namely the stronger clustering
of early-formed halos (for fixed halo mass), results in these galaxies
being more clustered than one would expect otherwise.  Therefore, the
clustering of {\it any} such sample would always be stronger than the
clustering of the corresponding shuffled sample.

The variations in the magnitude of the effect can be explained by looking
at the role of the occupancy variation for the satellite galaxies.
For the galaxies in the $20\%$ earliest-formed halos (the blue solid line)
this effect is even more prominent in fact, since these halos also have
relatively more satellites (compared to the same halos in shuffled case), which
acts to increase the clustering further (via central-satellite galaxy pairs
that contribute as well to the large-scale clustering).  On the other hand,
the $20\%$ latest-forming halos have relatively less satellites (compared
to the same halos in the shuffled case or relative to the HOD for the full
sample), and this acts to decrease the clustering and slightly reduce the
amplitude of the effect.

For the large-scale environment, we similarly find preferential formation of
central galaxies in dense environments. This again implies that halos in
relatively denser environments tend to be more populated,  and as these
halos are more strongly clustered, the galaxies in such halos end up being
more clustered (compared to the shuffled galaxies).
However, the central galaxies occupancy variation is more nuanced
for environment than for halo age  and the satellites trend is different
for them, so the interpretation is more complex.  In particular, it is
non-trivial to explain the sense of the galaxy assembly bias for the
underdense regions, where the clustering is weaker than for the corresponding
shuffled sample. From its occupancy variation, it appears that there are
less satellites overall in that case (for all halo masses), which is possibly
the origin of the reduced clustering we measure.

To confirm this explanation we calculate the effective bias for the
different HOD variants, by integrating over the halo mass function
weighted by the different occupation function. For the HOD of the
underdense regions, we find a reduced effective bias compared to that
of the full (or shuffled) sample. When calculating this separately for
the centrals and satellites occupations,  we find that the centrals
term increases a little while the satellites term decreases, in agreement
with the overall effect, leading to the reduced clustering.

We have also examined the clustering results for the L12 model, for which
there is no change in the satellites occupation function with environment
(Fig.~\ref{Fig:HOD_L12}), to aid our understanding of the role the
satellites play here.
The magnitude of the galaxy assembly bias for the underdense regions in
that case is significantly smaller (but still in the same sense
as for G11).  For lower number density samples (corresponding to more
massive galaxies), we find that the galaxy assembly bias even switches sign,
i.e., the L12 cross-correlation function for the underdense regions is
more strongly clustered than the shuffled case (while the trend remains
unchanged for G11). This further indicates that the trend observed for G11
for the underdense regions is due to the satellite occupancy variation.

Finally, we also measured the clustering of the G11 subsamples, when
considering only central galaxies. We find similar galaxy assembly bias
trends for the full sample and the dense regions, and a much reduced effect
for the underdense regions. This again supports our understanding that the
satellites occupancy variation is the main cause of the unique galaxy
assembly bias we see for the underdense regions, while the central
occupancy variation is the dominant factor in all other cases.
This difference may also be related to the general shape of the
cross-correlation function for the underdense regions (induced by the
large smoothing window) and the relative bias factor becoming
negative on large scales (when the cross-correlation function goes
below zero).

\vspace{0.2cm}
\section{Summary and conclusion}
\label{Sec:summary}

We have utilized semi-analytic models applied to the Millennium simulation
to study the occupancy variation leading to galaxy assembly bias.
We studied in detail the explicit dependence of the halo occupation functions on
large-scale environment, defined as the $5 \,h^{-1}\,{\rm Mpc}$ Gaussian smoothed dark
matter density field, and on halo formation time, defined as the redshift
at which the halo gained (for the first time) half of its present-day mass.
While related, these two halo properties have only a very loose relation
between them, and probe a different distribution of halos.
We focus our analysis on the $20\%$ subsets of halos at the extremes of the
distributions of each property,  defined separately for each halo mass bin,
so as to eliminate the dependence of the halo mass function on these properties.
We then study the different occupation functions of the galaxies in these
halos and investigate the origin of the variations. We stress that in all
analyses done here the HODs are calculated directly from the SAM galaxy
catalogs, and not inferred from clustering measurements. Our key results are
shown in Figures~\ref{Fig:HOD_Err}, \ref{Fig:SMHM} and \ref{Fig:CF_Err}.

For the dependence on environment, we find small but distinct differences in
the HOD, especially at the ``knee'' of the central occupation function. The
central galaxies in dense environments start populating lower mass halos, and
conversely, central galaxies in underdense environments are more likely to
be hosted by more massive halos.  This trend is robust among the two SAMs
we studied. For one of the SAMs (G11), the satellite occupation function
shows similar trends as the centrals, while the other (L12) does not exhibit
variation for the satellites. We quantify the occupancy variations in terms
of the changes to the HOD parameters.

When studying the dependence on halo formation redshift (halo age), we
find similar but significantly stronger trends for the central occupation
functions. The satellite occupation function shows a reverse trend, where
the early-formed halos tend to have much fewer satellites than late-formed
halos. This likely arises from having more time for the satellites to merge
with the central galaxy in the older halos.  The relatively stronger trends
for halo age suggest that this is the more fundamental property (among the
two) giving rise to galaxy assembly bias.

We gain insight regarding the origin of the central galaxies occupancy
variation by examining the scatter in the stellar mass -- halo mass relation
for them and its correlation with halo age and environment.  We find that,
at fixed halo mass, central galaxies in early formed halos or dense
environments tend to be more massive. This directly leads to the occupancy
variation we observe, as for any stellar-mass limited sample, the more
massive central galaxies will be ``picked'' first in lower-mass halos.
The dependence on halo age is very distinct, while the dependence on environment
shows more scatter, giving rise to the stronger trends with halo age.
The trends with halo age can be easily explained as the galaxies in the
early-formed halos have more time to accrete and form more stars.
These correlations, and the resulting occupancy variation, thus depend on
the specific details of the galaxy formation model.  This direct link to
the correlated nature of the stellar mass -- halo mass relation also
has important implications for models which use subhalo abundance matching
to connect galaxies with their host halos.

We also examine the auto-correlation and cross-correlation functions of these
different samples and the impact of these occupancy variations, by comparing
to the clustering of shuffled galaxy samples where the occupancy variation has
been erased.
We demonstrate the stronger clustering signal of galaxies in the most
dense regions versus least dense regions, and similarly the strong clustering
of galaxies in early-formed versus late-formed halos.  We clarify that while
these clustering differences arise from the dependence of halo clustering
on halo age and environment, they are only marginally affected by the
occupancy variations (and are not, for the most part, what we refer to as
galaxy assembly bias).

For all samples defined by halo age, the clustering of galaxies is stronger
than that of the shuffled samples. Namely, we see that the occupation
variation coupled with halo assembly bias act to increase the
clustering of galaxies. This effect is explained and dominated by the
central galaxy occupancy variation. For any range of halo
ages, the earlier-formed halos are preferentially populated. Since these
halos are more strongly clustered, the net effect is a stronger clustering
of the galaxies.  The satellite occupancy variation further modulates
this effect, but is secondary here.
The same behavior is found for the full sample of galaxies and for galaxies
in dense environments. This again is due to the tendency to populate more
the halos in denser environments, which are in turn more strongly clustered.
The galaxies in the most underdense regions exhibit the opposite trend,
however, with weaker clustering than for the corresponding shuffled sample.
This trend is less intuitive, but is likely caused by the satellites
occupancy variation, as discussed.

Our approach here has already provided considerable insight with regard
to the nature and origin of this complex phenomena. A companion paper
(Contreras et al., in preparation) is studying the redshift dependence of
the occupancy variation and galaxy assembly bias in the SAMs, which provides
a comprehensive view of the evolution of the different trends.
We are also investigating the environment and age occupancy variation
in the EAGLE and Illustris cosmological hydrodynamical simulations
(Artale et al., in preparation).

Our study can inform theoretical models of assembly bias as well as
attempts to determine it in observational data. Additionally, it can
facilitate creating mock catalogs that incorporate this effect, to
can aid in preparation for future surveys and in evaluating the impact of
assembly bias on cosmological analyses.
It remains an open (and hotly-debated) question as to what is the level
of assembly bias in the real Universe. We are hopeful that this work can
set the stage to developing and applying a method that will conclusively
determine that.

\smallskip
\acknowledgments
This work was made possible by the efforts of Gerard Lemson and
colleagues at the German Astronomical Virtual Observatory in setting
up the Millennium Simulation database in Garching, and John
Helly and Lydia Heck in setting up the mirror at Durham. We thank Celeste
Artale, Shaun Cole, Ravi Sheth and Zheng Zheng for useful discussions.
IZ and SC acknowledge the hospitality of the ICC at Durham and the helpful
conversations with many of its members. IZ and NJS acknowledge support by
NSF grant AST-1612085. IZ was further supported by a CWRU Faculty Seed Grant.
PN \& IZ acknowledge support from the European Research Council, through the
ERC Starting Grant DEGAS-259586. We acknowledge support from the European
Commission's Framework Programme 7, through the Marie Curie International
Research Staff Exchange Scheme LACEGAL (PIRSES-GA-2010-269264) and from a
STFC/Newton Fund award (ST/M007995/1-DPI20140114). SC further acknowledges
support the from CONICYT Doctoral Fellowship Programme. NP is supported by
``Centro de Astronomıa y Tecnologıas Afines'' BASAL PFB-06 and by Fondecyt
Regular 1150300. CMB \& PN additionally acknowledge the support of the
Science and Technology Facilities Council (ST/L00075X/1). PN further
acknowledges the support of the Royal Society through the
award of a University Research Fellowship.
The calculations for this paper were performed on the ICC Cosmology
Machine, which is part of the DiRAC-2 Facility jointly funded
by STFC, the Large Facilities Capital Fund of BIS, and Durham
University and on the Geryon computer at the Center for
Astro-Engineering UC, part of the BASAL PFB-06, which received additional
funding from QUIMAL 130008 and Fondequip AIC-57 for upgrades.

redpajama_set_name: RedPajamaArXiv


The smart design of the EQ Roller 40L gives you an impressive amount of space in a convenient carry on size. A zippered exterior pocket makes for handy storage of keys and travel papers, the zippered interior pocket is great for separating out smaller items like socks and belts, and compression straps with quick release buckle in the main compartment keep items secure. The retractable handle, polyurethane wheels and built-in ID card window make travel a breeze, even through crowded airport terminals.


text:
Why lizards are so diverse around the Andes
By Damien Esquerré, biologist and wildlife photographer Instagram: @damienesquerre_photo
Damien Esquerre
Postdoctoral Fellow, Research School of Biology, The Australian National University
Earlier this year, myself and a team of coauthors published a paper describing the effects of the uplift of the Andes on the biodiversity of one of South America's most iconic vertebrate groups - Liolaemidae lizards. This paper presented some exciting research, but also felt quite personal, as it reflected my own origins as a scientist growing up in the shadow of the Andes. I grew up around the titanic chain of mountains called the Andes. It is hard to ignore their presence from most major cities in my homeland of Chile. When I started as an undergrad researcher obsessed with reptiles, I made it my mission to document the species found around Santiago, Chile's capital, so that I could write a field guide. Quickly I learned that many species are found in the mountains, sometimes in very remote and hard to get places. I noticed that widely distributed lowland species tended to be more localised and micro-endemic in the mountains. This pattern has a foundation in the theory of island biogeography because mountains influence organismal distributions in a similar way to islands.
Speciation, or the process of one species becoming more than one, is usually a result of isolation plus time. When volcanic islands like the Hawaiian or Galapagos archipelagos emerged from the ocean, they provided fragmented and isolated patches of habitat that were colonised by terrestrial animals. If populations of the same species ended up on separate islands by rare dispersal events (e.g. animals drifting on a log after a big storm), with time and lack of gene flow between the islands, the populations will start diverging until they become different species. Mountains act in the same way for species adapted to high altitudes or cold climates. If organisms do not survive in warmer lowlands, then they become isolated at mountain tops, and hence biologists call mountains "sky islands". So there was a logical explanation of why I would observe more species in the mountains than in the lowlands.
I also learned that lizards living on colder mountain tops tended to be live-bearers (viviparous) and lizards in warmer lowlands tended to be egg layers (oviparous). For ectotherm (or "cold blooded") animals that depend on the environment's heat to incubate their embryos, eggs will do fine when it's warm. But in the cool and snow-capped heights of the Andes, it is just not hot enough under rocks for eggs to incubate, therefore animals like reptiles need to bask in the sun for their embryos to develop.
Most of the lizards you can find in the southern Andes, from southern Peru to Tierra del Fuego in Chile and Argentina's tip at the "end of the world", belong to the family Liolaemidae. The overwhelming majority of diversity in this family belongs to the genus Liolaemus, one of the most diverse terrestrial vertebrate genera in the word, with over 250 known species. I say "known" because every year researchers, including myself, describe new species from isolated mountain peaks. Their biodiversity is clearly linked to the Andes, but for years I wanted to find out how, and determine if this is also linked to their varying reproductive modes (with comparable proportions of oviparous and viviparous species).
I decided to explore this question as part of my PhD thesis at the Australian National University, in collaboration with a team of fantastic and talented scientists: my supervisor Prof. Scott Keogh, a Chilean collaborator Prof. Fernando Torres-Perez, my lab mate Dr. Ian Brennan and a former lab mate and now post-doc Dr. Renee Catullo. We gathered an enormous dataset of geographic records, reproductive mode, maximum altitude, and built the largest phylogeny or tree-of-life to date for Liolaemidae. We found that the Andes had a bigger role in their history than I imagined.
First, we found that the time these lizards started to diversify, or multiply in number of species, matched the origin of the uplift of the Andes, around 20 million years ago. This is quite a young age for such a high mountain range and also for such a diverse group of animals. The Himalayas and the Alps are 50 and 30 million years old, respectively. We found that the rate species were generated was strongly correlated with the rate of mountain uplift, supporting the hypothesis that sky-islands promote species diversity. We also found evidence supporting the hypothesis that the family originated in Andean regions and that groups of Liolaemus species found in other regions of South America, such as the Atacama Desert and the lowlands of eastern South America, had an origin in the Andes. This suggests that the uplift of the Andes increased reptile diversity both locally and in surrounding ecosystems.
We also found, as we expected, that there is a strong correlation between living in cold climates such as mountain tops and being viviparous. What we did not expect is to find evidence suggesting Liolaemus lizards defy a well-known evolutionary constraint: Dollo's law. This "law" (there are very few things such as laws in biology, unlike physics or chemistry) states than once complex structures are lost, they are really hard to re-gain. Among the best-known examples are limbs, eyes, and of course, eggs. For example, eggs were lost early on in the evolution of mammals, only retained by platypuses and echidnas today, and never re-evolved. Squamate reptiles (lizards and snakes) are known to have lost egg-laying more than 100 times independently. However, going the other way, re-gaining the ability to lay eggs, has been documented in only two snake species (an Arabian peninsula sand boa, genus Eryx, and neotropical bush master vipers, genus Lachesis). More evidence from reproductive physiology is needed, but our analyses suggest several reversals to egg-laying amongst Liolaemus. Interestingly, these tend to match dispersals to warmer lowlands. It seems that this special ability of Liolaemusto switch between reproductive modes might be one of the key traits of this group to adapt to such a variety of environments and, in combination with the uplift of the Andes, become one of the dominant lizard faunas in southern South America.
Gao Jianguo over 1 year ago
It's an interesting story behind the paper, but it would be better to provide a link of the research article in this text.
Copy the URL
The lizard picture behind the title is beautiful, can you kindly share it with me? (CC-BY-NC), my email address: gaojianguo9999@163.com
Humboldt, the Panama Canal, and Barro Colorado Island
Christina Riehl
Humbled by Humboldt?
Nature Research
About the community, Humboldt Anniversary
Ruth Milne
A history of the Ecuadorian vicuña
Greetings from now to then
Indrė Žliobaitė

redpajama_set_name: RedPajamaCommonCrawl


text:
function isValidTriangle(x, y, z) {
  // Forgetting to parseInt() took me a good hour to figure out. Lesson learned!
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  y = parseInt(y)
  z = parseInt(z)
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}

function process(input) {
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}

module.exports = { isValidTriangle, process }

redpajama_set_name: RedPajamaGithub


Eliza and Her Monsters / Francesca Zappia.
Esperanza rising [sound recording] / Pam Muñoz Ryan.
by Ryan, Pam Muñoz | Alvarado, Trini.
Fresh ink / edited by Lamar Giles, cofounder of We Need Diverse Books.
by Reynolds, Jason. Eraser tattoo | Lo, Malinda. Meet cute | Gansworth, Eric L. Don't pass me by | Safi, Aminah Mae. Be cool for once | Myers, Walter Dean, 1937-2014. Tags | Farizan, Sara. Why I learned to cook | Older, Daniel José. Stranger at the Bochinche | Flake, Sharon. Boy's duty | De la Cruz, Melissa, 1971-. One voice | Yang, Gene Luen. Paladin/samurai | Bailar, Schuyler. Catch, pull, drive | Yoon, Nicola. Super human | Giles, L. R. (Lamar R.) [editor.].
Gem & Dixie / Sara Zarr.
George [sound recording] / Alex Gino.
by Gino, Alex | Clayton, Jamie.
History is all you left me / Adam Silvera.
by Silvera, Adam, 1990- [author.].
How to make a wish / Ashley Herring Blake.
by Blake, Ashley Herring [author.].
I am Alfonso Jones / written by Tony Medina ; illustrated by Stacey Robinson and John Jennings ; foreword by Bryan Stevenson.
by Medina, Tony [author.] | Robinson, Stacey, 1972- [illustrator.] | Jennings, John, 1970- [illustrator.] | Stevenson, Bryan [author of introduction.].
by Sánchez, Erika L [author.].
If I was your girl / Meredith Russo.
Inventing Victoria / Tonya Bolden.
It's kind of a funny story / Ned Vizzini.
La lógica inexplicable de mi vida / Benjamin Alire Sáenz ; traducción, Jeannine Emery.
by Sáenz, Benjamin Alire [author.] | Emery, Jeannine [translator.].
Labyrinth lost / Zoraida Cordova.
Long way down / Jason Reynolds.
Love, hate & other filters / Samira Ahmed.
Mirror in the sky / Aditi Khorana.
Ms. Marvel. No normal / writer, G. Willow Wilson ; artist, Adrian Alphona, color artist, Ian Herring ; letterer, VC's Joe Caramagna ; cover art, Sara Pichelli & Justin Ponsor (#1), Jamie McKelvie & Matthew Wilson (#2-3 & #5) and Jamie McKelvie (#4).
by Wilson, G. Willow, 1982- [author.] | Alphona, Adrian [illustrator.] | Herring, Ian (Illustrator) | Caramagna, Joe [letterer.] | Pichelli, Sara [cover illustrator.] | Ponsor, Justin [cover illustrator.] | Mckelvie, Jamie [cover illustrator.] | Wilson, Matthew, 1981- [cover illustrator.].