Abstract

Density dependence occurs when the population growth rate, or constituent gain rates (e.g. birth and immigration) or loss
rates (death and emigration), vary causally with population size or density (N). When these parameters do not vary with N, they are density‐independent. Direct density dependence, where the population growth rate or gain rates vary as a negative
function of N, or the loss rates vary as a positive function of N, is necessary but not always sufficient for population regulation. The opposite patterns, inverse density dependence or the
Allee effect, may push endangered populations towards extinction. Direct density dependence is caused by competition, and
at times, predation. It is detected observationally by analysis of abundance time‐series; however, experimental field manipulations
provide the most rigorous analytical methods for both detecting and understanding underlying mechanisms. Future directions
include expanded and more detailed mechanistic field data integrated with more sophisticated population models.

Key concepts:

Direct density dependence occurs when the population growth rate varies as a causative inverse function of population size
or density.

Inverse density dependence – the Allee effect – may occur in a small population, driving it extinct.

Direct density dependence is necessary but not always sufficient for a population to be regulated and may occur simultaneously
with density independence.

The ecological mechanisms of density dependence are competition, and in some circumstances, predation (including parasitism
and disease).

Density dependence is most commonly tested by examining the relationship between the population growth rate (or individual
demographic rates) and population density, either observationally or experimentally.

Understanding density dependence and regulation within the context of a metapopulation – a population of local populations
linked by occasional dispersal – faces major empirical challenges.

Recommended future research on density dependence includes detailed, mechanistic field observations and experiments, as well
as modelling of complex dynamics in complex systems, such as metapopulations.

Possible effects of population density on per capita demographic rates. Panels A and B illustrate density‐dependent (DD), density‐independent (DI) and inversely density‐dependent (IDD) gain rates (e.g. population or individual growth, fecundity, birth or immigration) and loss rates (e.g. death or emigration),
respectively. Panel C illustrates both density‐dependent (dd) and density‐independent (di) components of a density‐dependent loss rate. The dd component is estimated by the slope of the curve, whereas the di component is estimated by the y‐intercept.

Figure 2.

Density dependence does not necessarily result in population regulation. Curves a and b both illustrate direct density dependence, because the instantaneous population growth rate (r) decreases with population density (N). However, only the population represented by curve a is regulated, because growth is positive at low densities and negative at high densities (i.e. the density‐dependent curve
crosses the dashed zero‐growth line). Despite density‐dependent growth of population b, this population never exhibits a positive growth rate and will eventually go extinct.

Figure 3.

An example of observational data from a population that is regulated by density dependence. Panel A illustrates variation
in abundance (Nt) through time (t). Note that the observed values of abundance tend to exhibit bounded fluctuations about a long‐term average. Panel B examines
the relationship between density and an estimate of the instantaneous population growth rate during the subsequent time interval,
which yields a decreasing pattern, indicating direct density dependence.

Figure 4.

Examples of experimental designs that help to identify factors causing and/or modifying density dependence of a demographic
loss rate. Manipulations of population density (N) are crossed with manipulations of putative causal agents (e.g. the presence or absence of predators: P+ or P−) or modifying
factors (e.g. addition or removal of some resource: R+ or R−). Panel A indicates that density dependence only occurs in the
presence of predators or when resources are in short supply. If only predator presence was the manipulated variable, then
this pattern would indicate predation as the proximate mechanism of density dependence. If only the resource was manipulated,
then this pattern would indicate that low resource availability causes density dependence via competition. In panel B, the
presence of predators or removal of the resource has no effect on density dependence, though these manipulations impose a
density‐independent increase in the loss rate. If only predator presence was the manipulated variable, then this pattern would
indicate that predation was not the source of density dependence. If only the resource was manipulated, then this pattern
would indicate that removal of that resource increased loss rate, but only in a density‐independent fashion. See Hixon and
Jones for a more complete list of possible experimental outcomes and interpretations.