Wolves at Memphis: Soul to Squeeze?
The Timberwolves (11-12) take on the Memphis Grizzlies (10-12) today in Memphis. The game is at 5 P.M Central and can be seen on FSN (you), LP (me), or listened to on 830 WCCO.
The Wolves have won two of their last three. They're coming off of a tough loss at San Antonio on Friday, in which Kevin Love was the main attraction. Love put up 42 & 14 whilst shooting 8-9 from downtown in the Wolves 117-110 loss to San Antonio. Kevin Martin had his second straight sub-par game. He scored 14 but shot only 4-12 and played bad defense.
Tonight, the style of play is likely to look very different. Memphis is a grind-it-out, defensive-minded team that will try to stop the Wolves uptempo game.
Memphis is without its best player, Marc Gasol. Kosta Koufos should get the starting nod at center. Nikola Pekovic and Kevin Love should be able to exploit mismatches on the frontline as they arise. And they will.
Tony Allen is probably the best defender in the NBA, and he'll presumably be putting the shackles on Kevin Martin. Martin's mini-slump could continue with Allen checking him. The Wolves tend not to play well when Martin doesn't play well.
Anyway, it wasn't that long ago that Kevin Durant was calling Z-Bo the best PF in the League. He's still a joy to watch.
And here's Hayes' Shaft Theme set to the original movie.
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Communities and Social Networks in Spain
What to see in Spain
Sport and nature
Natural Parks of Spain
Golf Courses in Spain
Gofio escaldado recipe, the Canarian accompaniment that comes from the Guanches
The recipe for gofio escaldado is typical of the Canary Islands. Gofio is the name given to a variety of flour that is made from toasted cereals, mainly corn (millo). This food has a lot of history in the Canary Islands, as it was consumed by the Guanches, the indigenous people who inhabited the island since pre-Hispanic times. In fact, since 2014 Gofio Canario has been recognised as a geographical indication with a protected designation of origin.
In this case, the gofio mixed with fish stock results in the well-known gofio escaldado; a recipe that is served as an accompaniment or appetizer. It is usually served with chopped onions (which are used as spoons to eat it) and accompanied by the typical papas arrugadas con mojo picón. An ideal menu to explore the Canarian cuisine.
Ingredients for the gofio escaldado recipe:
200 g of gofio de millo (toasted corn flour)
900 ml fish stock or fumet
1 sprig of peppermint
A quarter of red onion
How to make gofio escaldado:
Put the fish stock or fumet in a saucepan to cook and, when it boils, turn off the heat. Then, add the sprig of peppermint and leave it in the broth for two minutes so that it acquires flavour. Do not forget to remove it afterwards.
In a bowl, add the gofio (toasted corn flour) and, gradually, add the fish stock; stirring constantly so that no lumps are formed. The gofio escaldado has to be dense, so you can add more gofio if you need it.
When your gofio escaldado is ready, serve it in a bowl and decorate it with chopped onions and a couple of peppermint leaves.
You can use any kind of broth (vegetable, chicken, meat, fish, etc.) and any kind of gofio (wheat, corn, barley, spelt, legumes, etc.) for the recipe; so it is a dish that you can adapt to your taste.
fish, Spanish traditional cuisine, vegetables
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Our Work in CER
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Antony Iton
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George Kaplan, PhD
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Steve Woolf
Chris D'Adamo
Carley Riley
George Kaplan
Brian Berman, MD
Susan Hartnoll Berman
Kirstin Aschbacher, PhD
Wendy Bohdel
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Christopher D'Adamo, PhD
Director of Research, Center for Integrative Medicine
Assistant Professor, Department of Family & Community Medicine
Dr. D'Adamo's presentation for the Building Bridge forum:
Programs that Influence Youth Health: The Challenges of Outcomes Evaluations
Chris D'Adamo, PhD, is an epidemiologist with research interests in the synergistic effects of healthy lifestyle practices and genetics on human health as well as outcomes evaluations of multi-modality, whole-practice integrative health interventions and programs.
Dr. D'Adamo received his PhD in Epidemiology from the University of Maryland, School of Medicine, and is currently an Assistant Professor with dual appointments in the Center for Integrative Medicine within the Department of Family & Community Medicine, as well as in the Department of Epidemiology & Public Health. Dr. D'Adamo serves as the Director of Research at the University of Maryland Center for Integrative Medicine and holds an adjunct faculty position in the multi-campus Gerontology Doctoral Program of the University of Maryland. He also serves as Senior Program Advisor to the Institute for Integrative Health, a Baltimore-based non-profit with expertise in health programming for underserved communities.
Dr. D'Adamo has served as Principal Investigator on a wide variety of studies including a large outcomes evaluation conducted across a national collaborative of integrative medicine clinics, exercise as a treatment for chronic disease, the efficacy of dietary supplements in promoting overall health and wellness, therapeutic music for improvement in cancer outcomes, and outcomes evaluations of nutrition, physical activity, and mindfulness meditation programs in urban communities.
Prior to joining the faculty at the University of Maryland School of Medicine, Dr. D'Adamo held positions in the federal government as a Research Analyst at the Centers for Medicare and Medicaid Services (CMS) and in industry as a healthcare management consultant.
In addition to his current academic work, Dr. D'Adamo is a Certified Personal Trainer through the American Council on Exercise (ACE), a Certified Sports Nutrition Consultant through the International Sports Medicine Association (ISMA), and he has received advanced training in Mind-Body Medicine and Ayurvedic Medicine from the Institute for Integrative Health. Dr. D'Adamo regularly lectures and conducts workshops on the topic of health lifestyles to both public and healthcare audiences and manages a small exercise and nutritional consulting practice incorporating the latest research findings into program development and support for his clients.


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Future of Privacy Forum and ConnectSafely Release Educator's Guide to Student Data Privacy
May 23, 2016 | Melanie E. Bates
Contact: Melanie Bates, Director of Communications, [email protected]
Contact: Hani Khan, Outreach Manager, [email protected]
FUTURE OF PRIVACY FORUM AND CONNECTSAFELY RELEASE
EDUCATOR'S GUIDE TO STUDENT DATA PRIVACY
Washington, DC – Today, the Future of Privacy Forum (FPF) and ConnectSafely are releasing the Educator's Guide to Student Data Privacy. Technology tools and applications are changing the way schools and teachers educate students across the country. New resources are making it easier for teachers and students to communicate in and outside of the classroom making learning a 24/7 activity. When schools use technology, a student's personal information is often collected and shared for the purpose of furthering their education. The Educator's Guide will help teachers utilize technology in the classroom responsibly and protect their students' privacy, explaining among other things:
Why student privacy matters, including legal requirements;
Teachers options for vetting an app for privacy considerations; and
Available resources, including a quick reference checklist for teachers to use as they continue to incorporate technology.
The Educator's Guide follows the success of the Parent's Guide to Student Data Privacy, which was jointly developed by ConnectSafely and FPF to help parents understand the laws and regulations in place to protect their child's personally identifiable information. The Educator's Guide will help teachers understand their role in protecting students' information and ensuring students use classroom technology in a responsible way.
"Schools across the country are rapidly integrating new technologies meant to deliver a quality education to students in more effective and efficient manner. The Educator's Guide will be a vital new resource for teachers when helping students use educational applications and technology in a safe way that protects their data privacy," said Kobie Pruitt, Education Policy Manager, FPF.
"As a teacher who knows first-hand how technology tools have helped my students feel empowered to find the resources they need, collaborate with one another and with me, and create professional quality work I know we are in the midst of a transformational time for education. Teachers want to both inspire and protect their students, and this guide will help them feel confident they are doing both when using technology," said Kerry Gallagher, Director of K-12 Education for ConnectSafely.
FPF and ConnectSafely are proud to help educators implement new technologies responsibly in order to promote successful student outcomes. To view and download the Educator's Guide to Student Data Privacy and many other online privacy and safety resources, please visit FERPA|SHERPA andConnectSafely.
The Future of Privacy Forum (FPF) is a Washington, DC based think tank that seeks to advance responsible data practices. Learn more about FPF.
ConnectSafely.org is a Silicon Valley, Calif.-based nonprofit organization dedicated to educating users of connected technology about safety, privacy and security with research-based safety tips, parents' guidebooks, advice, news and commentary on all aspects of tech use and policy.
Tags: education, Top Story
K-12 Education Archive
November 25, 2019 | FPF Staff
FPF Welcomes New Members to the Youth & Education Privacy Project
October 31, 2019 | FPF Staff
What They're Saying: Stakeholders Warn Senate Surveillance Bill Could Harm Students, Communities
October 29, 2019 | Amelia Vance
ICYMI: New Senate Legislation Mandates "Pervasive Surveillance" in Attempt to Improve School Safety
August 28, 2019 | Amelia Vance
ICYMI: FPF's Amelia Vance Raises Concerns about School Surveillance Technologies on WOSU
July 9, 2019 | Amelia Vance
Education, Privacy, Disability Rights, and Civil Rights Groups Send Letter to Florida Governor About Discriminatory Student Database
March 27, 2019 | FPF Staff
40 Organizations Release Principles For School Safety, Privacy, and Equity
January 23, 2019 | editor
FPF's Amelia Vance on the Future of Student Privacy


If you're looking for high-quality vehicle inventory, professional service, or expert financing, then you will discover that our dealership offers everything that you're looking for and then some. We provide our customers with additional services and resources that you won't find at your typical dealership. Whether it's money-saving deals, financial tools, and research information.
You will find that it isn't hard to take advantage of everything that we have to offer since we are conveniently located on Route 77, also known as N Oracle Rd. Come to our location to have all your automotive needs met.
One landmark to keep an eye out for is the Jack in the Box located on W River Rd that tells you to head south on Route 77. If you're coming from the south up Route 77, you will find our location past Planet Fitness and across the bridge on the left. If you're traveling from further away, our dealership is just a short drive off of Interstate 10 in the northern area of Tucson.
Our dealership is open between 8 am - 8 pm, Monday through Saturday. With these hours, you will find that we are available when you need us. Whether you want to visit us after work or on your Saturday, our staff is ready to help you with whatever services that you need.
We even offer a night drop service for those that need to drop off their vehicle at later times. Just drop off your vehicle and your keys in the black drop box, and our service team will contact you the next morning to confirm your vehicle and address your concerns.
If you're ready for us to address all your automotive needs, then come to Tucson Subaru for exceptional services and inventory!
Tucson Subaru proudly serves our surrounding neighbors of Oro Valley, Sahuarita, Sierra Vista, Marana and Green Valley, AZ. Please stop by or give us a call. Our Professionals are here to help.


Make plans now to be at The Bristol Campground, 100 Sportsway Drive, Bristol, TN 37620 from Thursday, March 13th through Saturday, March 15th to enjoy great music from Southern Edge, Adelee & Gentry, and Charee White. NASCAR driver, Reed Sorenson, will have a time of "meet and greet". There will be entertainment for the whole family including games, surprises, and inspiring messages from Steve Wingfield. In addition, there will also be a special program paying tribute to veterans, active duty personnel, and local first responders. It's all FREE! Come out and enjoy!


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The 1937 Ladies Open Championships was held at the Queen's Club, West Kensington in London from 25–31 January 1937. Margot Lumb won her third consecutive title defeating Mrs Sheila McKechnie in the final.

Seeds

Draw and results

First round

Second round

Third round

Quarter-finals

Semi-finals

Final

References

Women's British Open Squash Championships
Women's British Open Squash Championships
Women's British Open Squash Championships
Women's British Open Squash Championships
Squash competitions in London
British Open Championships

redpajama_set_name: RedPajamaWikipedia


Spring is a bittersweet time of year in Telluride, Colorado. Locals celebrate the season heartily, basking in long days of sunshine and booking adventures to exotic locales. Beach time is just around the corner, and our toes are ready to trade the ski boots for sand. But there's the rub: While our feet might be anxious for the break, it's hard to give up skiing and snowboarding now—these are some of the best days of the year.
On Friday, Telluride got lucky. We received 22 inches of snow in 24 hours, the most snowfall during that period anywhere in North America. To say the least, Saturday was memorable. We found fresh tracks and face shots in every cranny of the Telluride Ski Resort, and my ski posse logged over seven hours of turns. On Sunday, it warmed into the 50s. The snow compacted into a creamy soft butter under our skis while a bluebird sky hung overhead. Put simply: The weekend was two days of absolute alpine perfection.
Telluride Ski Resort closes at 5 p.m. on Easter (April 4), so there're only a few more days to savor. The summer festival line-up looks great, but I'm reluctant to let go of ski season. Another storm is forecasted for Thursday. Maybe we'll get lucky again. Either way, I aim to make the most of these last days of lift-served access.


text:
Hot Stuff & Cold
HOT STUFF. Our blog about the Dushane v. CCSD lawsuit generated a firestorm of comebacks, which are still igniting. If you can stand the heat, scroll down to our 10/25 entry The Secret Lawsuit. If the comments are not immediately visible, click on the word Commentary at the bottom of the text.
IMMINENT *Tonight+: Festival of Trees. Fortnightly Club's annual event, this one dubbed "A Nautical Christmas" and held at Elks Lodge, 45 N. Jefferson Avenue, Catskill. Opening gala from 7 pm. ($25 per person, tickets required in advance). Continuing Saturday and Sunday, daytime ($3 admission). Information: 943-2044, 943-5616 or 943-6242. *Tonight+. "Balzac and the Little Chinese Seamstress" at Catskill Mountain Foundation's movie theater in Hunter, from 8 pm. Also Saturday and Sunday night, and Sunday at 3. *Saturday & Sunday. "Chilly Willy" tours of Bronck family houses near Coxsackie, by Historical Society members, with tales about living in GreeneLand in the 1600's. Info: 731-6490. *Saturday from 6 pm.: "No Place Like Home" exhibition ("Petals, Photograms, Photographs…") opens at BRIK Gallery, 473 Main St, Catskill. Runs to December 4. *Saturday, from 5 pm: Opening of exhibition of works by Gabe Brown and John Lippert at Wilder Gallery, 375 Main St, Catskill. Information: wilderstudios@msn.com; 578-3464.
BUSTED, for stealing $6586 from her dentist employer: former receptionist Christine Maddaloni, 39, of High Hill Road, Catskill. Her method consisted of accepting cash payments made by patients of Drs Catalano, Liefer & Bruno, recording the payments, then erasing the entries. She was caught and made a partial confession after, among other things, patients complained of being billed for payments they'd already made. Faced with a 49-count indictment for grand larceny and falsifying business records, she entered a plea of guilty to GL and is due on November 22d for sentencing by judge Daniel Lalor to a prison term of 3.5-7 years. The impending sentence comes in the wake of prior convictions for similar offenses.
BULLY RATES. The incidence of domestic violence in GreeneLand evidently is growing. According to Barbara Palmateer of Community Action, new cases handled by the Domestic Violence program during this year's first nine months matched the load handled all of last year. And of course, the frequency of assaults against women and children is far greater than what gets reported. Have a nice day.
NEW CHEF at Stewart House, Jeffrey E. Marquise, 46, was not a student at the highly esteemed Culinary Institute of America. He taught there.
DAILY MAUL. "…brought down the house Saturday night performing at the Historic Catskill Point Saturday." "…Rick Surrano has been chosen by the Athens Republican Committee to run for town supervisor in the November election two-term incumbent Albert Salvino" (8/24). "Every library in the county will be received some assistance, Seward noted" (11/2). "According to Ulscht, economic development is what is needed to bring tax relief and that a lack of business means higher taxes for residents" (11/4). 2=number of articles, in addition to the Calendar of Events, published Oct. 31 on the "Greene County" page. 0=number of articles on that page that pertained to Greene County. 4=number of articles appearing on 11/6 the "Neighbors" page. 0=number of articles that were not about Greene County. 7=number of articles on Monday (11/10) "Neighbors" page. 1=number of articles not about Greene County. 3=articles on Nov. 9th "Greene County" page. 0=articles about Greene County (while on "Neighbors" page, all 7 articles pertained to Greene County).
MYSTERY SOLVED. Among oddities in the late GreeneLand elections was a billboard facing eastbound motorists at the fork in Catskill of West Bridge Street and Route 9W. The billboard urged voters to elect Louis O'Connor to the Town Board and not Robert Antonelli. But O'Connor and Antonelli are fellow Republicans, they are pals, and they were standing for two vacant seats on the Board. The third candidate on the ballot, Evan Ulscht, is a Democrat and is not part of The Club. The key to solving the mystery is Sol Ferro, who paid for the billboard. He has a grudge against Antonelli.
RHETORIC DISSECTED. Also noteworthy about that billboard are the terms of Mr Ferro's pitch. Preceding his endorsement of Mr O'Connor were three questions: "Are you sick of high taxes? Are you sick of being told how to live? Are you sick of being told what to do with your property?" Invited by those questions, in the context of a Town Council contest, is belief that electing the endorsed candidate will bring about, or will increase substantially the prospects of, cuts in taxes and in regulation. Invited too are inferences that your taxes are high, that you ought to be sick of same, that you are incessantly being thwarted, that you ought to be sick of same, that the pushing and prodding emanate from governmental agencies such as the Town Council, and that (consequently?) the election of O'Connor would alleviate the illness. With regard to property, the suggestion then must be that you have been bugged by regulatory constraints, that you should be sick of same, and that the election of O'Connor would be a liberating event. For sophisticated respondents, moreover, the message would be, specifically, that O'Connor would free you from the shackles of planning, zoning, permits and inspections. The blather was Ferro's, not O'Connors.
"DEAR KIWANIS. Thank you for the dictionary… It has all the words I need." "I like using it for hard words." "It is very usfull for our whole entire class!" "I can't wait to meet the whole Kiwanis club. You help us get what we need. I really corrected correcting on this paper." "They work really good. I like to use my dictionary because they have a lot of words in my dictionary." "I'll also use it for I think isn't right." "We also have been using them for when we don't know to spell a really hard word." "We like the realy much." "Thanck you for the dictionary's. I you's mine for vocabulary. I you's mine for spelling words correctly… " "I've used it for reading and for looking up words I don't know." "I like to use it for when I don't know how to spell a wourd." "When we use them we use them with care." "Dictionarys make you smart." "They really come in handy! You are very nice to children. I just want to tell you." "You are my favorite one who would give us dictionarys to the whole school. Please visit us another time." "P.S. Thank you for coming all the way just to give us a dictionary." ---from Abagail, Ada, Austin, Caden, Caitlin, Chase, Connor, David, Deborah, Glage, Joey, Kenneth, Megan, Meghan, Mike, Rachel, Seaver, Stephanie,Tyler and Victoria, of Mrs Brown's 3d grade at Coxsackie Elementary School.
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Why no comment on Dr. Kosich double billing the county and the $500,000 shortage?
Rationality-Hunting


MISTAKE MONDAY for March 5: Can YOU spot what's wrong?
MISTAKE MONDAY for March 4: Can YOU spot what's wrong?
MISTAKE MONDAY for March 19: Can YOU spot what's wrong?
https://www.investmentwriting.com/newsite/wp-content/uploads/2018/01/Mistake-Monday-2.png 404 440 Susan Weiner, CFA https://www.investmentwriting.com/newsite/wp-content/uploads/2016/12/investmentwriting_logo_2016.png Susan Weiner, CFA2019-03-25 05:30:152018-11-07 19:45:02MISTAKE MONDAY for March 25: Can YOU spot what's wrong?


text:
Kevin Hart Insists He Won't Host Oscars: 'I Can't Do That Right Now'
Entertainment 12:43 PM PST, January 9, 2019 - Inside Edition Staff
12:43 PM PST, January 9, 2019 - Inside Edition Staff
Kevin Hart has made it official that he will not host the Oscars this year.
The actor told "Good Morning America" co-host Michael Strahan that with the Oscars weeks away, it's too late for him to change his mind.
"Right now, from a time perspective, I don't have the time. You're talking about two weeks that I would really have to prepare, I start filming 'Jumanji' in February," he said.
He added: "I would like to call myself a perfectionist, so if I do something I'd like to be able to give it my all, make sure the production is a great representation of me and my talent. I can't do that right now."
Strahan pressed Hart about those controversial homophobic remarks from past years that led him to back out of the hosting gig.
"Here's what I'm trying to say. I've over it," he said. "That's what I'm trying to say. I'm done with it. I want everybody to know that I'm done with it. It's a choice that I've personally made to say I'm not addressing it anymore.
"And that's not from an angry place, it's just from a place of, it's never going to really end."
The interview comes five days after his sit down with Ellen DeGeneres aired on her show Friday.
She begged him to reconsider hosting the show and told her that he is not homophobic.
"I know I don't have a homophobic bone in my body," Hart said. "I know that I've addressed it; I know that I've apologized. ... I've taken 10 years to put my apology to work. I have yet to go back to that version of the immature comedian that once was."
Hart's appearances on both "Ellen" and "GMA" have sparked outrage from some including "Queer Eye" star Jonathan Van Ness, who is urging the Academy to find an LGBTQ host.
Nothing like enabling someone to mansplain why they're homophobic past comments paired w defensive irritated half apologies are totally fabulous! Gay Men of color in this country face HUGE STIGMA caused by this behavior. Ellen gurl. Not cool. https://t.co/ns9OGABoVX
— Jonathan Van Ness (@jvn) January 9, 2019
There are so many amazing queer comedians especially of color who are much better suited for this job and actually... funny. https://t.co/iC5E8UFfTs
Kevin Hart's Ex-Wife Insists He's Not Homophobic: Today on Inside Edition
Kevin Hart's Ex Defends Him Amid Backlash Over Tweets: 'He Was Just Making a Joke'
Kevin Hart Quits Oscars Hosting Gig After Outcry Over Homophobic Tweets
Original 'Queer Eye' Cast Tries to Make Over Inside Edition's Interview Room


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text:
\section{Introduction}
\label{S:1}

Animals differ from plants by their ability to move actively and choose an optimal environment. Animals move for many reasons: to acquire resources; to avoid predators and other agents of mortality; to avoid competition (e.g. natal dispersal); and to be near conspecifics for mating and other social interactions (conspecific attraction). Clearly, the various functions of movement are related to survival and reproduction, and the parameters that govern movement are therefore subject to natural selection.

One of the most interesting types of animals' movements are the so-called ``long-distance movements'' of individuals from the places of their birth or release. During such movements an organism can disperse far beyond the region of its origin through a variety of landscapes and then either return back or settle in a very new environment. Long-distance movements or long-distance dispersal (LDD) has gained most attention in the studies of passive dispersal of plants (\cite{Nathan2008movement}). A number of reports has been presented for invertebrates and birds (\cite{Earl2016Characteristics}). Recent advances in satellite-tracking techniques increased the number of such reports for mammals (\cite{Fuglei2019Arctic,Hindell2000Long, Weller2016First}). Studies of ungulates' behavior have shown that despite rare long-distance movements have been observed for many species. For example, for wild boar ({it Sus scrofa}) most of animals dispersed not more than 20 km from their place of birth, but some individuals moved more than 60 or even more than 80 km (\cite{Truve2004Dispersal}).

Approaches to study LDD were classified in \cite{Nathan2003Methods} and mathematical modeling was listed as one of the possible ways to understand this phenomenon together with a set of observational methods. Generally, model-based studies of animals' movements address the following main problems:

1. Approximation of the empirical movement (presumably telemetry) data with mathematically defined processes, like random (correlated or uncorrelated, biased or unbiased) walk or Levy walk (e.g. reviews \cite{Hawkes2009Linking,Lewis2015Mathematics});

2. Using mathematical approaches (like, for example, partial differential equations) to model population dynamics accounting for dispersal and range shifts, particularly during biological invasions (reviewed in \cite{Lewis2015Mathematics});

3. Effect of habitat heterogeneity and population dynamics on the process of dispersal and patterns of animals' movements (\cite{Hawkes2009Linking, Barton2009evolution, Hiebeler2004Competition});

4. Habitat selection during dispersal and the factors affecting it (\cite{Davis2004effect, Stamps2005Search, Stamps2007Someplace}).

Thus the models of animals' movements study the behavior under the assumptions of some movement strategy, but none of them (to our knowledge) address the problem of comparing the efficiency of different strategies. \cite{Lewis2015Mathematics} wrote ``long-distance dispersal can be the driving force for population spread if populations introduced at low densities thrive and do not go extinct''. But what is the chance for a population not to extinct if it implements LDD? -- that is the question! On one hand the wide distribution of this phenomenon among living organisms (\cite{Nathan2005Long-distance, Sutherland2000Scaling, Teitelbaum2015How}) indicates that this could be (under certain conditions) an important part of species' life history. On the other hand the relative rarity of such events (in compare with short distance dispersal) (\cite{Wilson2009Something}) shows that animals moving long distances most probably are subject to higher mortality and thus the selection against long-distance dispersal could take place.

In this study we hypothesize that 1) dispersal success could result from some evolutionary stable strategy (ESS) of maximizing the population fitness and 2) that this strategy could be based on deferred gain, when animals invest in travel to reach some high-quality habitat (``habitat of dream''). The last hypothesis is rooted in the concept of natal habitat preference induction (\cite{Davis2004effect}) which states that the experience with the natal habitat shapes the habitat preferences of the individuals that disperse particularly after releases in new areas (\cite{Stamps2007Someplace}).

Checking these hypotheses using observational methods is practically impossible since we always have to guess what animals have in their minds while choosing one or another way of expansion: e.g., is it a random choice or it is pre-determined by some ESS. We address this problem via programming individuals search strategies. In other words, we tell the modeled animals (animats) (\cite{Wilson1991animat}) how to behave and then check which behavior would result in higher fitness of the whole population.

We compare the ecological (short-term) success of three strategies:

-- ``Smart'' -- choosing the locally optimal cell (a cell with the highest quality among the neighboring units);

-- ``Random''  -- random movement between cells without taking into account the quality of the environment;

-- ``Dreamer'' -- movements aims to find ``a cell of dream'' with  quality much higher than that of the initial and neighboring cells.

Comparing the strategies, we address three main questions:

1) What is the relative success of each strategy in bad, medium and good habitat?

2) How the success of each strategy could be affected by the harshness of environment (particularly, environmental seasonality)?

3) Could the ``Dreamer'' strategy provide sufficient fitness for the population implementing this strategy?

\section{Model}

We modeled the movements of organisms taken  from optimal habitat and released  in a new environment where the spatial distribution of habitat patches and quality of habitat is not known by them. There is a number of examples of such (intentional or non-intentional) translocations of animals by humans, which resulted in extinction or successful expansion of newly established populations (\cite{Bertolero2007Assessing,Bremner-Harrison2004Behavioural,Lodge2003Biological}).

\subsection{Map}

The map in the experiments is a square divided into $100\times100$ square cells. Each cell belongs to one of three strata: ``bad'', ``medium'' or ``good''. For the details on the process of map construction see Algorithm 1 in \ref{alg_sec_map} and a map example in Fig.\ref{fig:map_example}. Note that Algorithm 1 allows to produce maps with any given area ratio $S_{bad}/S_{medium}/S_{good}$ and different ``pathchness''. In our experiments we used three types of map: ``bad'' -- with $S_{bad}/S_{medium}/S_{good} = 0.67/0.3/0.03$, ``medium'' -- with $S_{bad}/S_{medium}/S_{good} = 0.22/0.56/0.22$ and ``good'' -- with $S_{bad}/S_{medium}/S_{good} = 0.03/0.3/0.67$.

\begin{figure}
    \centering
    \includegraphics[width=0.35\textwidth]{pics/map_example.png}\\
    \vspace{3mm}
    \includegraphics[width=0.5\textwidth]{pics/strata_energy.pdf}
    \caption{An example of the $100\times100$ experiment maps  generated by Algorithm 1. All three strata occupy equal area: $S_{bad}/S_{norm}/S_{good}=1/1/1$ (dark-brown is for ``bad'', light-brown -- for ``medium'' and green -- for ``good''), ``patchness'' is equal to 5. The scale shows the connection between cell types (strata) and energy (attractiveness)}
    \label{fig:map_example}
\end{figure}

\subsection{Energy}

There are two types of energy in the model: energy of the animats (which positive level is necessary for each animat to live and to move) and energy (or attractiveness) of the cells on the map (which serves as a source of energy for the animats). The latter one plays the role of food for the animats; it does not deplete but can change over time depending on season.

\subsubsection{Energy of cells}

Each cell is assigned a random energy value (attractiveness) according to its strata: from 1 to 20 for ``bad'', from 40 to 60 for ``medium'', and from 80 to 100 for ``good''.

The energy of the cells follow a ``weather conditions'' sine wave during a 1000 steps cycle: first getting worse to model ``autumn'' and ``winter'' and then recover to ``spring'' and ``summer''. At the worst time (in the middle of winter) the attractiveness of each cell drops to the lowest value $q/w$, where $q$ is the initial attractiveness of this cell and $w$ is the experiment parameter -- ``winter harshness''. The formal expression for the attractiveness (energy) of a cell with the initial energy $q$ at the step $j$ (varying from 1 to 1000) is
\begin{equation}
\label{eq:weather_sine}
    \frac{q-\tfrac{q}{w}}{2}\cdot cos\left(\frac{2\pi j}{1000}\right)+\frac{q+\tfrac{q}{w}}{2},
\end{equation}
(see examples of these waves for different $q$ in Fig. \ref{fig:energy_sine_example}).
\begin{figure}
    \centering
    \includegraphics[width=0.35\textwidth]{pics/energy_sine_example.pdf}
    \caption{An example of ``seasonal'' variation of the cells' energy (attractiveness) during a 1000 steps experiment cycle. The variation is presented for 3 cells with initial energies 100, 50, 20 and ``winter harshness'' equal to 2}
    \label{fig:energy_sine_example}
\end{figure}

\subsubsection{Energy of animats}

Each animat constantly acquires energy from the cells it visits  and spends it for metabolism and movements. In our experiments, we assume that an animat spends $E^m=25$ units of energy for each shift to a neighbor cell
(half as much as the average initial energy of the cells in the ``medium'' strata). If an animat cannot make a move at the current step, it spends $E^m/2=12.5$ units of energy for just keeping homeostasis (twice as low as the energy for a move).
Each newly created animat is provided with $E^0=10E^m$ units of energy (so in can make 10 moves without any energy input). After arriving at a new cell an animat receives the amount of energy given by \eqref{eq:weather_sine} for this cell at the current step of the ``weather'' sine wave. If the energy balance of an animat drops below zero, the animat dies.

\subsection{Movement}

We test 3 search strategies using the movement tactics based on Levy-walk. In our variant of the Levy-walk model, the animats choose
each next direction randomly but restricted to the forward semiplane with respect to the vector of the previous run (the first direction is selected without any restrictions). This peculiarity brings an element of the correlated random walk to our model. The number of successive steps in each direction is chosen in accordance with the Levy-walk model with $\mu=2$ (\cite{Viswanathan1999Optimizing}), but does not exceed 50 (the expectation of the animat's position is the map's center, which lies 50 or little more cells away from the edges in any direction). Reaching an edge of the map naturally leads to a re-initialization of the Levy-walk without the ``semiplane restriction''.

The movements include a concept of memory: the animats do not shift to the cells they visited during the previous $r$ steps. For example, if $r=3$ and an animat starts from the cell $A$, shifts to $B$ then to $C$ and remains there, then the memory queue goes through the following states: $AAA$ -- $AAB$ -- $ABC$ -- $BCC$ -- $CCC$; after the first step the animat is not allowed to return to $A$, after the second -- to both $A$ and $B$, after the third -- to $A$, $B$, and $C$, after the fourth -- only to $B$ and $C$. In our experiments, the memory size was chosen equal to 10: little more than the number of neighbors of each inner cell in a square grid.

It is important to note that in our model a moving animat can recognize strata (good, medium or bad) without entering it (so the animat may refuse to enter a cell of a worse type), but the animats cannot distinguish ``by eye'' the energy attractiveness of two cells belonging to one strata.

The three search strategies studied in the experiments were:

1. ``Random'' or ``no determination by environment''.
In this strategy each animat randomly chooses a direction and a length from a Levy-walk distribution and follows the chosen direction until the chosen length is achieved or until it comes to an edge of the map. The ``Random'' animats do not take into account the strata or energy of the cells they pass through: for example, an animat can move from a cell with quality 5 to a cell with quality 1 (for the details on the movement of ``Randoms'' see Algorithm 2 in \ref{sec:b_algorithms}). We hypothesize that in a completely new environment such behavior could occur due to partial inability of organisms to analyze efficiently the whole volume of incoming information.

2. ``Smart'' or ``full determination''. While following the same Levy-walk movement pattern a ``Smart'' animat shifts to the cell proposed by its current movement tactics only if the type of this new cell is not worse than the type of the current cell (see Algorithm 3 in \ref{sec:b_algorithms} for the details). For example, a ``Smart'' animat cannot move from a ``good'' habitat to a ``medium'' one, but it can move from a cell with energy 55 to a cell with energy 45 (within the category ``medium'').
If the next step in the Levy-walk movement model leads to the decrease of the habitat quality, the successive Levy walk is stopped and reinitialized (with the choice of a new direction and ``flight'' length). From mathematical point of view this strategy is a {\it greedy local search} heuristic (\cite{metaheuristics2010handbook}) which is a well-known and extensively used instrument in the field of optimization.

3. "Dreamer" or "partial determination". Each ``Dreamer'' animat has an idea of ``dream habitat'': a cell with enough attractiveness to stop the search and to rest contently.
Together with remembering the attractiveness of its dream, a ``Dreamer'' estimates the expectation to achieve it: this expectation starts with 100\% and reduces with each step where the dream is not found (see the details in \ref{sec:b_algorithms} after Algorithm 3). A ``Dreamer'' stops when the attractiveness of the ``dream'' multiplied by the expectation to achieve it becomes less than the attractiveness (energy) of the current cell (given that the probability to achieve the current cell is evidently 1) (see Algorithm 4 in \ref{sec:b_algorithms} for the formal expression of the stop condition).
Note that due to the changing ``weather conditions'' a ``dreamer''  that has already taken the decision to rest content with the current cell can continue moving since the current cell attractiveness (energy) becomes too small to trump its dream.
This strategy as well has a clear analogue in the theory of optimization – {\it simulated annealing} technique (\cite{metaheuristics2010handbook}), where the intention of an agent to explore the space of the problem states gradually decreases in time until the agent finally satisfies with its current achievements.

\subsection{Metrics}
\label{sec:metrics_general}
The following parameters were assessed in each experiment:

-- proportion of the survived individuals (S);

-- dispersal from the starting points (D) (Euclidean distance between the initial and final cells);

-- energy accumulated by the animats during the experiment (E);

-- quality of the cells occupied at the end of the experiment (Q);

-- the product of the accumulated energy and cell quality further denoted as {\it Fitness} showing the ability of an individual not just to survive but to occupy good habitat and to accumulate energy for the future (EQ).

These metrics aimed at the characterization of homogeneous 100-animat groups or ``populations'' (where each member follows the same search strategy) at the end of the 1000-step experiment cycles. Each metric was computed in two variants: average over the individuals that managed to survive until the end of experiment and sum over all the members of the population (including those who died). While the former variant describes the survivors only, the latter one characterizes the populations as wholes (note that it is proportional to the average over {\it all} the members of the population). All the metrics were additionally normalized into $[0,1]$ to compare their relative manifestation within different strategies. The rigorous expressions for the metrics are given in \ref{sec:b_metrics}, see equations \eqref{b_aver_n}--\eqref{eq:normalized2} for the details).

\subsection{Experiment}

The 1000 step experiment cycle was repeated 30 times for each of the three types of 100-animat groups (``Randoms'', ``Smarts'' and ``Dreamers''), each of the three types of map (``bad'', ``medium'', ``good''), and each of the five types of winter harshness ($w=2,4,6,8,10$). Thus, the final data set consisted of 30 independent estimates of the metrics (S,D,E,Q,EQ) for each combination of terms (search strategy, map and winter harshness) (see  \ref{sec:b_metrics} for the details).
A new map was generated every time after ``Randoms'', ``Smarts'' and ``Dreamers'' had used it each once in the same experiment conditions. Constant and variable parameters of the experiments are summarized in Table \ref{tab:all_parameters}.
The computational experiments were conducted using Python3, the code is available at GitHub (\cite{software}).

\begingroup
\setlength{\tabcolsep}{10pt}
\renewcommand{\arraystretch}{1.3}
\begin{table}
    \centering
    \vspace{5mm}
    \small
    \begin{tabular}{c|c}
       {\bf Terms in the model}  & {\bf Value} \\
        \hline\multicolumn{2}{c}{Constants}\\\hline
        Map size & $100\times 100$\\
        Energy of cells in good habitat & 80-100\\
        Energy  of  cells in medium habitat	& 40-60\\
        Energy  of  cells in bad habitat & 0-20\\
        Energy of ``dream habitat'' & 10000\\
        Initial energy of animat & 250\\
        Cost of animat movement & 25\\
        Cost of animat staying	& 12.5\\
        Duration of cycle & 1000 steps\\
        Animat memory size	& 10 steps\\
        \hline\multicolumn{2}{c}{Variables}\\\hline
        Proportions of habitat in: & (bad/medium/good) \\
        -- ``bad'' map & 0.67/0.3/0.03\\
        -- ``medium'' map & 0.22/0.56/0.22\\
        -- ``good'' map & 0.03/0.3/0.67\\
        Winter harshness & 2, 4, 6, 8, 10\\
        Search strategy & ``Random'', ``Smart'', ``Dreamer''
    \end{tabular}
    \caption{Constant and variable terms of the model}
    \label{tab:all_parameters}
\end{table}
\endgroup

\section{Results}

\subsection{``Bad'' map (model of bad habitat  prevalence)}

(Fig.\ref{fig:2d_aver}a,d,g,j and Fig.\ref{fig:2d_sum}a,d,g,j)

On the ``bad'' maps, ``Smarts'' considered as a whole population (i.e. using the summary metrics),  perform much better than the other strategies. All their metrics are the highest and almost independent of the winter harshness except for E, which decreases in a non-linear manner with the increase of the winter harshness. The ``Smart'' strategy animats tend to find locally optimal habitat patches quickly and are able to withstand the ``seasonal'' changes in cells quality by moving (or staying) within the discovered favorable habitat patches (thus maximizing the energy accumulation and survival). The comparison of "Smarts" with the other strategies basing on the average metrics on the ``bad'' maps makes sense only in the case of mild winters: in harsh winters the low survival rate of "Dreamers" and "Randoms" increases the bias of the corresponding average values.
 Though in mild winters the average metrics of the ``Smarts'' generally repeat the corresponding summary metrics, there are two exceptions: 1) the average dispersal of both ``Dreamer'' and ``Random'' survivors is considerably larger than the one of ``Smarts''; 2) ``Dreamers'' and ``Smarts'' settle the habitat of almost the same quality.

``Randoms'' are the worst in the bad habitat -- they demonstrate the lowest values of all metrics (both summary and averaged, except for the dispersal in the mildest winter $w=2$). Their survival does not exceed 10\% and the average quality of the cells occupied by a few survivors at the end of the experiments does not exceed 20. The strategy of random movements does not allow the animats to find patches of good or medium habitat in the ``bad'' map and they die quickly due to high cost/gain energy ratios. The increase of winter harshness from 2 to 4 results in almost zero survival rate thus the further increase of $w$ does not significantly affect the metrics.

``Dreamers'' demonstrate an intermediate performance but in the summary metrics are closer to ``Randoms'' than to ``Smarts''.  "Dreamers" metrics decrease with the increase of winter harshness, possibly due to the strong decrease of survival in harsh winters. According to the values of average cell quality the few survivors are those who managed to reach good and medium habitat.

\subsection{``Medium'' map (model of medium habitat prevalence)}

(Fig.\ref{fig:2d_aver}b,e,h,k and Fig.\ref{fig:2d_sum}b,e,h,k)

In medium habitat  ``Smarts'' show almost no mortality (S above 0.9), E and Q values (both average and sums) are the highest, and D is the lowest observed among the three strategies. The effect of winter harshness is insignificant for all metrics except for E, which is negatively correlated with the winter conditions.

``Randoms'' perform almost as good as the other strategies in mild winters in terms of survival. Also in mild winters their dispersal is the highest. Their E and Q metrics are however the lowest ones. All metrics except dispersal decrease linearly with the increase of winter harshness. Thus the strategy of random movement allows the animats to survive well in the medium habitats which quality does not change strongly within the season. Even in very harsh winters their survival does not fall below 40\% which shows that this strategy could theoretically help animals to survive and to establish viable populations in suboptimal environment, however the probability of it stays much lower than for ``Dreamers'' and ``Smarts''.

In differ with the ``bad'' maps, in the ``medium'' maps ``Dreamers'' perform much better than ``Randoms'' in terms of S, E and Q. Their values of the summary population D are higher than for the other strategies (except for ``Randoms'' at $w$=2) and this index does not change significantly with winter harshness, while the average D of the survivors almost reaches the ``Randoms'' level. The effect of winter on the ``Dreamers'' S and Q metrics is not very high (about 20\%) but noticeable. The E index decreases twice with the 5-fold increase in winter harshness. Thus in medium habitats the implementation of the ``Dreamer'' strategy results in relatively high population success in terms of survival, expansion and occupation of good habitat.

\subsection{``Good'' map (model of good habitat prevalence)}

(Fig.\ref{fig:2d_aver}c,f,i,l and Fig.\ref{fig:2d_sum}c,f,i,l)

In good habitat the survival of ``Smarts'', ``Dreamers'' and ``Randoms'' is above 98\% showing almost no mortality. In this case the survival rate does not affect the average metrics and they are equal to the corresponding summary ones.

``Randoms'' are the most successful in dispersal (which is not a surprise given their dispersal is not intermitted by any decisions), but least successful in energy accumulation and the quality of habitat occupied by the animats at the end of the experiments.

``Dreamers'' perform better than the other strategies in terms of Q, they are as good as ``Smarts'' in energy accumulation (E). Their dispersal D strongly increases with winter harshness approaching the values typical for ``Randoms''. The dispersal of ``Randoms'' and ``Smarts'' is in fact not affected by the winter harshness. For all the strategies, the E index decreases with winter harshness, while the slight decrease in Q was observed for ``Randoms'' and ``Dreamers'' but not for ``Smarts''. Thus in favorable environment all the strategies are almost equally successful.

\begingroup
\setlength{\tabcolsep}{5pt}

\begin{figure}[H]
    \centering

\begin{tabular}{cccc}
& {\footnotesize``bad'' map} & {\footnotesize``medium'' map} & {\footnotesize``good'' map} \\
\rotatebox[origin=c]{90}{\footnotesize \qquad survival ($\mathbf{S}$)\qquad } &
\makecell{(a)\\\includegraphics[align=c,width=0.3\textwidth]{pics/av_survival_bad1.pdf}}
     &
\makecell{(b)\\\includegraphics[align=c,width=0.3\textwidth]{pics/av_survival_medium1.pdf}}
     &
\makecell{(c)\\\includegraphics[align=c,width=0.31\textwidth]{pics/av_survival_good1.pdf}}\\
\rotatebox[origin=c]{90}{\footnotesize \qquad dispersal ($\mathbf{D}_A$)\qquad } &
\makecell{(d)\\\includegraphics[align=c,width=0.3\textwidth]{pics/av_disp_bad1.pdf}}
     &
\makecell{(e)\\\includegraphics[align=c,width=0.3\textwidth]{pics/av_disp_medium1.pdf}}
     &
\makecell{(f)\\\includegraphics[align=c,width=0.3\textwidth]{pics/av_disp_good1.pdf}}\\
\rotatebox[origin=c]{90}{\footnotesize \qquad  energy ($\mathbf{E}_A$)\qquad } &
\makecell{(g)\\\includegraphics[align=c,width=0.31\textwidth]{pics/av_energy_bad1.pdf}}
     &
\makecell{(h)\\\includegraphics[align=c,width=0.31\textwidth]{pics/av_energy_medium1.pdf}}
     &
\makecell{(i)\\\includegraphics[align=c,width=0.31\textwidth]{pics/av_energy_good1.pdf}}\\
\rotatebox[origin=c]{90}{\footnotesize \quad\enskip cell quality ($\mathbf{Q}_A$)\quad\enskip } &
\makecell{(j)\\\includegraphics[align=c,width=0.3\textwidth]{pics/av_cellquality_bad1.pdf}}
     &
\makecell{(k)\\\includegraphics[align=c,width=0.3\textwidth]{pics/av_cellquality_medium1.pdf}}
     &
\makecell{(l)\\\includegraphics[align=c,width=0.3\textwidth]{pics/av_cellquality_good1.pdf}}
\end{tabular}

    \caption{Performance of different search strategies (average and its standard deviation in 30 experiments) along average metrics in relation to the proportions of bad, medium and good habitat (``map type'') and winter harshness. Red, green and blue lines represent respectively ``Smart'', ``Random'' and ``Dreamer'' strategies. X-axis indicates winter harshness, Y-axis - the values of the respective metrics (see \eqref{b_aver_n}\eqref{b_aver_all} for the explicit expressions of the shown metrics)}
    \label{fig:2d_aver}
\end{figure}
\endgroup

\newpage

\begingroup
\setlength{\tabcolsep}{5pt}

\begin{figure}[H]
    \centering

\begin{tabular}{cccc}
& {\footnotesize``bad'' map} & {\footnotesize``medium'' map} & {\footnotesize``good'' map} \\
\rotatebox[origin=c]{90}{\footnotesize \qquad survival ($\mathbf{S}$)\qquad} & \makecell{(a)\\
\includegraphics[align=c,width=0.3\textwidth]{pics/av_survival_bad1.pdf}}
     &
\makecell{(b)\\\includegraphics[align=c,width=0.3\textwidth]{pics/av_survival_medium1.pdf}}
     &
\makecell{(c)\\\includegraphics[align=c,width=0.3\textwidth]{pics/av_survival_good1.pdf}}\\
\rotatebox[origin=c]{90}{\footnotesize \qquad dispersal ($\mathbf{D}_S$)\qquad} &
\makecell{(d)\\\includegraphics[align=c,width=0.3\textwidth]{pics/sum_disp_bad1.pdf}}
     &
\makecell{(e)\\\includegraphics[align=c,width=0.3\textwidth]{pics/sum_disp_medium1.pdf}}
     &
\makecell{(f)\\\includegraphics[align=c,width=0.3\textwidth]{pics/sum_disp_good1.pdf}}\\
\rotatebox[origin=c]{90}{\footnotesize \qquad energy ($\mathbf{E}_S$)\qquad} &
\makecell{(g)\\\includegraphics[align=c,width=0.3\textwidth]{pics/sum_energy_bad1.pdf}}
     &
\makecell{(h)\\\includegraphics[align=c,width=0.3\textwidth]{pics/sum_energy_medium1.pdf}}
     &
\makecell{(i)\\\includegraphics[align=c,width=0.3\textwidth]{pics/sum_energy_good1.pdf}}\\
\rotatebox[origin=c]{90}{\footnotesize \quad\enskip cell quality ($\mathbf{Q}_S$)\quad\enskip } &
\makecell{(j)\\\includegraphics[align=c,width=0.3\textwidth]{pics/sum_cellquality_bad1.pdf}}
     &
\makecell{(k)\\\includegraphics[align=c,width=0.3\textwidth]{pics/sum_cellquality_medium1.pdf}}
     &
\makecell{(l)\\\includegraphics[align=c,width=0.3\textwidth]{pics/sum_cellquality_good1.pdf}}
\end{tabular}

    \caption{Performance of different search strategies along summary metrics (sum and its standard deviation in 30 experiments)in relation to the proportions of bad, medium and good habitat (``map type'') and winter harshness. Red, green and blue lines represent respectively ``Smart'', ``Random'' and ``Dreamer'' strategies. X-axis indicates winter harshness, Y-axis -- the values of the respective metrics (see \eqref{b_aver_n}\eqref{eq:b_sum_all} for the explicit expressions of the shown metrics)}
    \label{fig:2d_sum}
\end{figure}

\endgroup

\subsection{Multivariate portrays of the strategies}

In Sections 3.1 - 3.3 we demonstrated that the relative success of a strategy may consist of different components: e.g., one strategy may win in dispersal, another -- in energy or cell quality. To compare the relative performance of the considered search strategies along different metrics we use radar charts (Fig.\ref{fig:averaged_radars}) with all the metrics normalized into [0,1] (see equations \eqref{eq:normalized1},\eqref{eq:normalized2} in \ref{sec:algorithms}). For the detailed portrays considering the winter harshness see Fig.\ref{fig:radar_aver},\ref{fig:radar_sum} in \ref{sec:pictures}.

\begingroup
\setlength{\tabcolsep}{10pt}
\begin{figure}[H]
    \centering
\begin{tabular}{cccc}
\qquad & {\footnotesize``bad'' map} & {\footnotesize``medium'' map} & {\footnotesize``good'' map} \\
\rotatebox[origin=c]{90}{\footnotesize \quad\qquad Summary\qquad\quad} &
\scalebox{0.7}{\raisebox{-.5\height}{\footnotesize\input{pics/radar_all_sum_bad.pdf_tex}}}
     &
\scalebox{0.7}{\raisebox{-.5\height}{\footnotesize\input{pics/radar_all_sum_norm.pdf_tex}}}
     &
\scalebox{0.7}{\raisebox{-.5\height}{\footnotesize\input{pics/radar_all_sum_good.pdf_tex}}}
\\
\rotatebox[origin=c]{90}{\footnotesize \quad\qquad Average \qquad\quad} &
\scalebox{0.7}{\raisebox{-.5\height}{\footnotesize\input{pics/radar_all_aver_bad.pdf_tex}}}
     &
\scalebox{0.7}{\raisebox{-.5\height}{\footnotesize\input{pics/radar_all_aver_norm.pdf_tex}}}
     &
\scalebox{0.7}{\raisebox{-.5\height}{\footnotesize\input{pics/radar_all_aver_good.pdf_tex}}}

\end{tabular}

    \caption{Portrays of relative performance of the search strategies along different normalized metrics
    averaged by the winter harshness $w$.
    Color is used to mark off the strategies: green for ``Random'', red for ``Smart'' and blue for ``Dreamer''. All the axes run from 0 to 1
    \label{fig:averaged_radars}
\end{figure}

\endgroup

In Fig.\ref{fig:pareto} we compare different strategies along two general dimensions of success -- {\it Dispersal} D and {\it Fitness} EQ (see \ref{sec:metrics_general}) -- with the survival rate S playing the role of ``significance'' for each entry (all the metrics are again normalized into [0,1], see \eqref{eq:normalized1},\eqref{eq:normalized2} in \ref{sec:algorithms}). In all the cases, except for the summary metrics on ``bad'' maps, ``Dreamers'' clearly belong to the Pareto frontier (\cite{pareto}) (so that no other strategy could outperform it in both D and EQ).

\begingroup
\setlength{\tabcolsep}{10pt}

\begin{figure}[H]
    \centering
\begin{tabular}{ccc}
\qquad & Summary &  Average \\
\rotatebox[origin=c]{90}{\qquad\qquad``bad'' map\qquad\qquad} &
\makecell{(a)\\\scalebox{1.2}{\raisebox{-.5\height}{\footnotesize\input{pics/pareto_sum_bad.pdf_tex}}}}
     &
\makecell{(b)\\\scalebox{1.2}{\raisebox{-.5\height}{\footnotesize\input{pics/pareto_aver_bad.pdf_tex}}}}
\\
\rotatebox[origin=c]{90}{\quad\qquad``medium'' map\qquad\quad} &
\makecell{(c)\\\scalebox{1.2}{\raisebox{-.5\height}{\footnotesize\input{pics/pareto_sum_norm.pdf_tex}}}}
     &
\makecell{(d)\\\scalebox{1.2}{\raisebox{-.5\height}{\footnotesize\input{pics/pareto_aver_norm.pdf_tex}}}}
\\
\rotatebox[origin=c]{90}{\qquad\qquad``good'' map\qquad\qquad} &
\makecell{(e)\\\scalebox{1.2}{\raisebox{-.5\height}{\footnotesize\input{pics/pareto_sum_good.pdf_tex}}}}
     &
\makecell{(f)\\\scalebox{1.2}{\raisebox{-.5\height}{\footnotesize\input{pics/pareto_aver_good.pdf_tex}}}}

\end{tabular}
    \vspace{1mm}
    \caption{Success of different strategies in {\it Dispersal} $\times$ {\it Fitness} space. Here red color corresponds to ``Smarts'', blue -- to ``Dreamers'' and orange -- to ``Randoms''. Color intensity indicates the harshness of winter $w$: the higher intensity -- the milder winter. The size of the circle is directly proportional to the corresponding survival rate $\mathbf{S}$. All the axes run from 0 to 1 (see \eqref{eq:normalized1}\eqref{eq:normalized2} for the details)
    \label{fig:pareto}
\end{figure}

\endgroup

\section{Discussion}

As mentioned in \cite{Bowler2005Causes}, how the organism integrates the information from different environmental cues and thereby reaches its decision has largely been overlooked in previous studies and this makes it difficult to compare our results with other models of animals' dispersal.

For example, in differ with the studies that question the dynamics of dispersing as a function of some external factors (like habitat quality, habitat matrix, climate, and other factors that affect dispersal costs) (\cite{Kubisch2014Where}), we suggest that dispersal success depends on the "built-in" behavioral strategy which could be more or less successful according to the particular external factors. In differ with the studies that also base on some behavioral strategy, e.g. implying a-priori differences between short-distance and long-distance dispersers (\cite{Ramanantoanina2014Spatial}), the probability to perform a long movement is equal for all the animats and drawn from the Levy-walk model.  The habitat preferences are in fact also the same for all animats (as could be expected for the individuals belonging to one species) and base on the potential energy gain from the cell.   Thus the model populations are different rather in behavioral than ecological traits and their success in survival is affected by the decision-making process. The strategies (``Random'', ``Smart'', ``Dreamer'') are the examples of search strategies previously implemented in a number of studies (e.g. \cite{Stamps2005Search, Zollner1999Search}), but they have not been compared. The classical study \cite{Zollner1999Search} also compares the success of dispersal in habitat of low, medium and high habitat quality, but they address differences related rather to the shape of movements than to decision-making process underlying these movements. In our study we do not pre-define the shape of movements though all the strategies perform the correlated Levy walk.

Our model is pretty simple: it does not take into account possible interactions between population members and habitat depletion. We assume that animals are released in a region previously non-inhabited by the species. In such new environment both intra-species competition (and other types of intra-population interactions) is negligible and the resources of the habitat do not limit animals' abundance. An important part of our model is that all the individuals following a particular strategy are exactly the same, while animals' personality is an important factor shaping their movements (\cite{Hawkes2009Linking}). We believe that more complex models that take into account the variability of movement behavior could be the subject of future research.

``Random'' is a strategy with no habitat selection. It could be implemented when animals cannot correctly assess habitat quality. In reality, errors in the estimation of habitat quality could result in ``ecological trap'' (\cite{Kokko2001Ecological}) while random search theoretically could help to escape these traps and provide higher fitness in compare with more specific strategies of habitat selection. However such scenario was not included in our model: ``Smarts'' and ``Dreamers'' correctly assess the habitat quality (at the strata level -- ``good'', ``medium'' or ``bad'') and thus random search predictably performed worse than the other strategies (in terms of survival, accumulated energy and the quality of habitat) in marginal (``bad'') and suboptimal (``medium'') environment. This is in agreement with other studies that compare random search with different search strategies (\cite{Conradt2003Foray}). Interestingly, in favorable environment (``good'') survival and fitness of ``Randoms'' stays as high as in the other strategies, while being accompanied with the highest dispersal ability. Thus random search strategy could explain very fast expansion and establishment of viable populations in good environment (for example, when species relax the effect of competitors, parasites and diseases) which is the classic case of biological invasion (\cite{Lewis2015Mathematics} and references therein).

``Smarts'' are the best dispersers only in bad habitat and mainly due to low survival of ``Randoms'' and ``Dreamers''. In medium and good habitat the ``Smart'' strategy provides high survival and high fitness combined with relatively low dispersal distances -- organisms sequentially inhabit the best patches close to the place of origin. We suspect that this strategy could underlie the wave front expansion (type I expansion in terms of \cite{Shigesada2002Invasion}) which is slow expansion with constant speed. Though the speed of population expansion in our model has  not yet been studied, the independence of dispersal from winter conditions allows to assume the independence from temporal climatic variation and thus to support the suggestion of constancy of the expansion rate. Fast discovery of locally optimal habitat, demonstrated by ``Smarts'', could suggest the familiarity of the dispersers with the habitat, thus it could be expected for the populations introduced in the environment which is ecologically close to that in the place of origin (\cite{Davis2004effect}). A practical way to make animals familiar to a new environment during re-introduction is keeping them in enclosures for some time before release. It is well known by conservation biologists and called `` soft release'' (\cite{Jung2017Observations}).

``Dreamers'' settled the best possible habitat in the middle and far distance from the place of release, demonstrating high survival and high energy accumulation by dispersing individuals. Similar effect has been previously reported in \cite{Stamps2005Search} where the likelihood that a disperser would settle in a high-quality rather than in a low-quality habitat is positively related to both selectivity of habitat and time of search. Dreamers are indeed highly selective due to high difference between the available habitat and the ``habitat of dream'' and this strategy could illustrate the dispersal associated with the habitat selection based on natal habitat preference induction (NHPI) (\cite{Davis2004effect,Stamps2007Someplace}). Extending the result of \cite{Stamps2005Search}, we show how this pattern is affected by habitat composition, seasonal variation in habitat quality and compare it with the success of the other strategies. Our results indicate that ``Dreamers'' are quite successful in finding good habitat at a significant distance from the place of origin, especially on ``medium'' and ``good'' maps, though the success of dispersal remains relatively low in bad habitat depending in addition on winter harshness. Populations implementing the ``Dreamer'' strategy thus expands with successfully dispersing propagules rather than with a wave front.

In the above paragraphs we tried to assign the results of our experiments to the real ecological situations and types of population expansion. However, in reality it is most probable that the expansion of a population results from a mixed strategy, where different individuals use different strategies. In the studies of animals' personality, researchers most often distinguish ``bold'' and ``shy'' individuals, but more specifically to dispersal they are placed in the ``exploration-avoidance'' continuum, illustrating the animals' reaction to novel environment (\cite{Reale2007Integrating}). Populations with high dispersal rates have been shown to be composed of bold, exploratory, and aggressive individuals, which is being found in different taxons and habitat (\cite{Malange2016Personality} and references therein). These better dispersers in terms of our model could be assigned to the ``Random'' and ``Dreamer'' strategies. High mortality, which is often observed for bold and explorative individuals (\cite{Bremner-Harrison2004Behavioural}), put them closer to ``Randoms'' than to ``Dreamers'', since the latter are those who used their high dispersal ability to successfully settle an optimal habitat. `Shy'' individuals could follow the ``Smart'' strategy.

\section{Conclusions and future work}

Answering the questions formulated in the Introduction we conclude that

1) In good and medium habitat the ``Dreamer'' strategy performs better than the others since it provides higher dispersal in compare with the ``Smart'' strategy and higher quality of habitat in the place of settlement in compare with the ``Random'' strategy. In bad habitat only ``Smarts'' provides a reasonable level of survival and population fitness. The ``Random'' strategy is appropriate only in good habitat;

2) The performance of the "Smart" strategy does not depend strongly on winter harshness, while for the two other strategies most metrics decrease with winter harshness. The only metrics that clearly increased with winter harshness is the dispersal rate of ``Dreamers''in good habitat;

3) The ``Dreamer'' strategy or the strategy of deferred gain belongs to the Pareto frontier in the {\it Fitness$\times$Dispersal} space but only in optimal and suboptimal habitat and in the relatively mild climate.

The most general conclusion is that while survival and wealth of the population is affected presumably by overall habitat quality, the dispersal depends mainly on the behavioral strategy. In the future work, it would be interesting to model the population expansion for several generations checking the scenarios of random and non-random inheritance of the search strategies.

\section*{Author's contributions}

N.I. Markov: Conceptualization, Methodology, Formal analysis, Investigation, Writing - Review \& Editing; E.E. Ivanko: Methodology, Software, Formal analysis, Investigation, Resources, Data Curation, Writing -- Original Draft, Visualization, Funding acquisition.

\section*{Funding information}

The research was supported by Russian Foundation for Basic Research (RFBR), project No 18-07-00637а.

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