Ideal Free Distributions, Evolutionary Games, and Population Dynamics in Multiple-Species Environments

In this article, we develop population game theory, a theory that combines the dynamics of animal behavior with population dynamics. In particular, we study interaction and distribution of two species in a two-patch environment assuming that individuals behave adaptively (i.e., they maximize Darwinian fitness). Either the two species are competing for resources or they are in a predator-prey relationship. Using some recent advances in evolutionary game theory, we extend the classical ideal free distribution (IFD) concept for single species to two interacting species. We study population dynamical consequences of two-species IFD by comparing two systems: one where individuals cannot migrate between habitats and one where migration is possible. For single species, predator-prey interactions, and competing species, we show that these two types of behavior lead to the same population equilibria and corresponding species spatial distributions, provided interspecific competition is patch independent. However, if differences between patches are such that competition is patch dependent, then our predictions strongly depend on whether animals can migrate or not. In particular, we show that when species are settled at their equilibrium population densities in both habitats in the environment where migration between habitats is blocked, then the corresponding species spatial distribution need not be an IFD. Thus, when species are given the opportunity to migrate, they will redistribute to reach an IFD (e.g., under which the two species can completely segregate), and this redistribution will also influence species population equilibrial densities. Alternatively, we also show that when two species are distributed according to the IFD, the corresponding population equilibrium can be unstable

Stabilitási vizsgálatok az evolúcióökológia területén = Stability in Evolutionary Ecology

Többfajos evolúcióökológiai modellt dolgoztunk ki, amely alkalmas az invazív fajok és a paleontológia „szakaszos egyensúlyi” fogalmának vizsgálatára. Megmutattuk, hogy az adaptív dinamikai stabilitás speciális esetként adódik az általunk bevezetett dinamikus stabilitásból. Kimutattuk, hogy a nem kooperáló egyedek kellően hatásos büntetésével stabilizálható a kooperáció. Igazoltuk, hogy a természetes szelekció folyamán az „optimalizáló” (saját bevételét maximalizáló) típust kiszelektálja a „versengőt” (aki relatív előnyét maximalizálja). Egy evolúciós játékelméleti modellel kimutattuk, hogy kis csoportlétszám mellett az altruista segítség többszöri ragadozótámadás esetén ESS. Igazoltuk, hogy mind a Ewens-féle parciális rátermettség, mind a relatív előny növekedési rátája egyaránt arányos a rátermettségek varianciájával. Példát adtunk olyan paraméterekre, amelyek esetén a méhek optimális nektárgyűjtési viselkedése nem garantálja a koegzisztenciát, ha két növényfaj nektárjáért két méhfaj versenyez. Megmutattuk, hogy nem opportunista (célprédát kereső és csak azt üldöző) ragadozó esetén kevert ESS, míg opportunista (alkalmanként nem célprédára is támadó) ragadozó esetén általában tiszta ESS alakul ki. Megmutattuk, hogy két külön-külön stabilizáló hatás (menedékhasználat és látszólagos versengés) együttesen destabilizálhat egy ragadozó-zsákmány rendszert. A pályázat a célkitűzései között nem szereplő problémákról további csatlakozó cikkeket publikáltunk | We have set up a multi-species evolutionary-ecological model, appropriate for the study of invasive species and the concept of punctuated equilibrium of paleontology. We have shown that adaptive dynamic stability can be obtained as a special case of the dynamic stability introduced by us. We have proved that cooperation can be stabilized by sufficiently efficient punishment of non-cooperative individuals. We have demonstrated that in natural selection the “optimizer” type (maximizing its own revenue) selects out the competitor type (maximizing its relative advantage). Using an evolutionary game-theoretic model, we have shown that, for small groups, altruism is ESS in multi-attack games. We have proved that both partial fitness of Ewens and relative advantage have a growth rate proportional to the fitness variance. We have found parameter values, for which, the optimal nectar collection doesn’t guarantee coexistence, if two bee species compete for the nectar of two plant species. We have shown that in the case of a non-opportunistic predator (seeking a focal prey and chasing only that) a mixed ESS is formed, while in the case of an opportunistic predator (occasionally also attacking a non-focal prey), a pure ESS is developed. We have proved that different stabilizing factors (refuge use and apparent competition), applied together, may destabilize a predator-prey system. We have also published papers on related problems not figuring among the original objectives of the project

Technical review on derivation methods for behavior dependent functional responses

Abstract Functional responses measure the trophic interactions between species, taking into account the density and behavior of the interacting species. In predator-prey interactions, the prey preference of the predator and the antipredator behavior of the prey together determine the feeding rate of the predator and the survival rate of the prey. Consequently, the behavior dependent functional responses make it possible to establish dynamic ecological models providing insight, among others, into the coexistence of predator and prey species and the efficiency of agents in biological pest control. In this paper the derivation methods of functional responses are reviewed. Basically, there are three classes of such methods: heuristic, stochastic and deterministic ones. All of them can take account of the behavior of the predator and prey. There are three main stochastic methods for the derivation of functional responses: renewal theory, Markov chain and the Wald equality-based method. All these methods assume that during the foraging process the prey densities do not change, which provides a mathematical basis for heuristic derivation. There are two deterministic methods using differential equations. The first one also assumes that during the foraging process the prey densities do not change, while the second one does not use that assumption. These derivation methods are appropriate to handle the behavior dependent functional responses, which is essential in the derivation of ecological games, when the payoff of prey and predator depends on the strategies of the prey and predator at the same time

Kooperáció és kommunikáció az állatvilágban: játékelméleti vizsgálatok = Cooperation and communication in biology: game theoretical studies

Pályázatunk elsősorban a kooperáció eredetének számos aspektusát, továbbá a komunikációs rendszerek őszinteségét fenntartó mechanizmusok tanulmányozta. Az elméleti munkák mellett e témakörben humán és állatkísérleteket is elindítottunk. Rámutattunk az olcsó vagy költségmentes kommunikáció őszinteségét fenntartó ökológiai tényezőkre. Megmutattuk például, hogy az emberi kooperáció és az őszinte kommunikáció evolúciója szoros kapcsolatban lehet, illetve állati társadalmakban a kommunikácó őszinteségét a kompetíció erőssége is befolyásolhatja. Vizsgáltuk az ember és a kutya kooperációjának kommunikációs sajátságait. Megmutattuk, hogy a préda-perdátor vagy gazda-parazita kölcsönhatások ismerete szükséges számos kooperatív viselkedés evolúciójának értelmezéséhez. Például a predációs nyomás okozhatja a prédák altruista viselkedését, vagy a kasztrációs parazitát éppen a mutualista társ jelenléte szabályozza. Számos tanulmányban az egyedek térbeli elhelyezkedésének és korlátozott mozgásának a kooperáció evolúciójára kifejtett hatását vizsgáltuk. Több olyan munkánk is született, ahol a humán kommunikáció illetve kooperáció sajátságait a többszintű szelekciós modellek segítségével értelmeztük. Sikerült kiépítsünk egy számítógépes labort, mellyel a jövőben s humán etológiai kísérleteket tudunk végezni. A kutatás legfontosabb eszközének számító evolúciós játékelméletben számos alapkutatás jellegű eredményünk is született, a sztochasztikus elmélet fejlesztésétől a többfajos elméletig. | Our project mainly focused on several aspects of the evolution of cooperation and of the mechanisms maintaining honesty in communicating systems. Beside theoretical works we started animal and human experiments as well. We reveal ecological backgrounds maintaining honesty of cheap or costless communication in numerous systems. It is shown for example that the origin of human cooperation and reliable information processing can be in close connection to each other, and that strength of competition modifies the level of honesty in animal communities. We studied the characteristics of communication in the case of human-dog cooperation. We have shown that characteristics of predator-prey or host-parasite interactions are required to explain evolution of cooperative behaviour in numerous cases. For example, predation load can cause altruistic predator defence among preys, or a mutualistic competitor can control castrating parasites. Several papers focused on the spatial aspects and limited migration of individuals on the evolution of cooperation. Other works emphasized that characteristics of human cooperation can be explained by multilevel selection. We set up a computer lab, which could be a basis of a series of human behavior experiment in the near future. We have significant purely theoretical results in the field of our primary mathematical method, that is of evolutionary game theory; from the development of stochastic theory to the multi-species theory

Functional response and population dynamics for fighting predator, based on activity distribution

The classical Holling type II functional response, describing the per capita predation as function of prey density, was modified by Beddington and DeAngelis to include interference of predators that increases with predator density and decreases the number of killed prey. In the present paper we further generalize the Beddington–DeAngelis functional response, considering that all predator activities (searching and handling prey, fight and recovery) have time duration, the probabilities of predator activities depend on the encounter probabilities, and hence on the prey and predator abundance, too. Under these conditions, the aim of the study is to introduce a functional response for fighting predator and analyse the corresponding dynamics, when predator-predator-prey encounters also occur. From this general approach, the Holling type functional responses can be also obtained as particular cases. In terms of the activity distribution, we give biologically interpretable sufficient conditions for stable coexistence. We consider two-individual (predator-prey) and three-individual (predator-predator-prey) encounters. In the three-individual encounter model there is a relatively higher fighting rate and a lower killing rate. Using numerical simulation, we surprisingly found that when the intrinsic prey growth rate and the conversion rate are small enough, the equilibrium predator abundance is higher in the three-individual encounter case. The above means that, when the equilibrium abundance of the predator is small, coexistence appears first in the three-individual encounter model

Optimal Forager Against Ideal Free Distributed Prey

The introduced dispersal-foraging game is a combination of prey habi2 tat selection among two patch types and optimal foraging approaches. Prey’s patch 3 preference and forager behavior determine the prey’s survival rate. The forager’s 4 energy gain depends on local prey density in both types of exhaustible patches and 5 on leaving time. 6 We introduce two game solution concepts. The static solution combines the ideal 7 free distribution of the prey with optimal foraging theory. The dynamical solution 8 is given by a game dynamics, describing the behavioral changes of prey and forager. 9 We show that (a) each stable equilibrium dynamical solution is always a static 10 solution, but not conversely; (b) at an equilibrium dynamical solution, the forager 11 can stabilize prey mixed patch use strategy in cases where ideal free distribution 12 theory predicts that prey will use only one patch type; (c) when the equilibrium 13 dynamical solution is unstable at fixed prey density, stable behavior cycles occur 14 where neither forager nor prey keep a fixed behavior

The impacts of the global financial and economic crisis on the agro-food sector of Central and Eastern European and Central Asian countries

This paper assesses the impacts of the global financial and economic crisis on the agro-food sector of Central and Eastern European, Caucasus and Central Asian countries on the basis of research conducted in Hungary, Ukraine, Armenia and Kyrgyzstan. The objective of the study was to propose policy options to the Food and Agriculture Organisation of the United Nations and other public authorities which can be applied to lessen the undesirable effects of the current or future crises in the sector. Results of interviews of stakeholders were analysed in the context of primary economic data and sixteen policy recommendations were formulated

Szexuális és aszexuális populációkban zajló frekvencia-, illetve denzitásfüggő evolúció vizsgálata = Investigation of frequency- and density-dependent evolution in sexual and asexual populations

Főbb eredmények Több, egymással kölcsönható aszexuális fajra vonatkozóan megadtunk egy monomorf evolúciós stabilitási fogalmat az ökológiai szelekcióra, és alkalmaztuk egyrészt az "ideal free distribution" koncepció két kölcsönható fajra való kiterjesztésére, másrészt diszkrét tulajdonságok evolválódásának leírására. Végül kimutattuk, hogy az adaptív dinamika evolúciós stabilitási fogalma speciális esetként adódik a mi stabilitási fogalmunkból. Két méhfaj és két növényfaj közötti kölcsönhatás estén megmutattuk, hogy a méhek optimális nektárgyűjtése akkor és csak akkor stabilis, ha a hosszú távú morfológiai koevolúció divergens. Megmutattuk, hogy a domináns-recessziv öröklődés esetén a szexuális és az aszexuális populációban zajló frekvenciafüggő szelekció végállapota fenotipikusan azonos. Az általános replikátordinamikára nézve beláttuk, hogy a replikátorok marginális fitneszének varianciája egy egyensúlyi pont környezetében akkor és csak akkor fogy, ha ez az egyensúlyi állapot egyúttal ESS is. A matematikai rendszerelmélet eszközeivel különböző biológiai szituációkban biológiailag interpretálható elégséges feltételeket adtunk meg frekvenciafüggő evolúciós és denzitásfüggő ökológiai modellekben a rendszer megzavart egyensúlya adott idő alatt visszaállítható legyen. E modellekhez ún. megfigyelő rendszert konstruáltunk, amely lehetővé teszi bizonyos indikátor fenotípusok vagy fajok megfigyeléséből a rendszer teljes állapotfolyamatának rekonstruálását. | Main results For several interacting asexual species, we introduced a concept of monomorphic evolutionary stability for ecological selection and applied to the extension of the 'ideal free distribution' approach to the case of two interacting species, and also gave a description of the evolution of discrete traits. Finally we proved that the evolutionary stability concept of adaptive dynamics can be obtained as a particular case of our stability concept. For the interaction of two bee and two plant populations, we have shown that the optimal nectar collection of the bees is stable if and only if the long-term morphological coevolution is divergent. We proved that in case of a dominant-recessive inheritance, the terminal state of frequency-dependent selection in sexual and asexual populations phenotypically coincide. For general replicator dynamics we demonstrated that the variance of the marginal fitness of the replicators decreases near an equilibrium if and only if the equilibrium is also an ESS. Using mathematical systems theory, for different biological situations, in both frequency-dependent evolutionary and density-dependent ecological models, we found biologically interpretable sufficient conditions to guarantee that a disturbed system can be controlled back to the equilibrium. For such systems we constructed a so-called observer system that, from the observation of certain indicator phenotypes or species, the whole state process can be reconstructed

To save or not to save your family member’s life? Evolutionary stability of self-sacrificing life history strategy in monogamous sexual populations

Abstract Background For the understanding of human nature, the evolutionary roots of human moral behaviour are a key precondition. Our question is as follows: Can the altruistic moral rule “Risk your life to save your family members, if you want them to save your life” be evolutionary stable? There are three research approaches to investigate this problem: kin selection, group selection and population genetics modelling. The present study is strictly based on the last approach. Results We consider monogamous and exogamous families, where at an autosomal locus, dominant-recessive alleles determine the phenotypes in a sexual population. Since all individuals’ survival rate is determined by their altruistic family members, we introduce a new population genetics model based on the mating table approach and adapt the verbal definition of evolutionary stability to genotypes. In general, when the resident is recessive, a homozygote is an evolutionarily stable genotype (ESG), if the number of survivors of the resident genotype of the resident homozygote family is greater than that of non-resident heterozygote survivors of the family of the resident homozygote and mutant heterozygote genotypes. Using the introduced genotype dynamics we proved that in the recessive case ESG implies local stability of the altruistic genotype. We apply our general ESG conditions for self-sacrificing life history strategy when the number of new-born offspring does not depend on interactions within the family and the interactions are additive. We find that in this case our ESG conditions give back Hamilton’s rule for evolutionary stability of the self-sacrificing life history strategy. Conclusions In spite of the fact that the kidney transplantations was not a selection factor during the earlier human evolution, nowadays “self-sacrificing” can be observed in the live donor kidney transplantations, when the donor is one of the family members. It seems that selection for self-sacrificing in family produced an innate moral tendency in modulating social cognition in human brain