Evolution of Predator and Prey Movement into Sink Habitats

Mathematical models of predator‐prey interactions in a patchy landscape are used to explore the evolution of dispersal into sink habitats. When evolution proceeds at a single trophic level (i.e., either prey or predator disperses), three evolutionary outcomes are observed. If predator‐prey dynamics are stable in source habitats, then there is an evolutionarily stable strategy (ESS) corresponding to sedentary phenotypes residing in source habitats. If predator‐prey dynamics are sufficiently unstable, then either an ESS corresponding to dispersive phenotypes or an evolutionarily stable coalition (ESC) between dispersive and sedentary phenotypes emerges. Dispersive phenotypes playing an ESS persist despite exhibiting, on average, a negative per capita growth rate in all habitats. ESCs occur if dispersal into sink habitats can stabilize the predator‐prey interactions. When evolution proceeds at both trophic levels, any combination of monomorphic or dimorphic phenotypes at one or both trophic levels is observed. Coevolution is largely top‐down driven. At low predator mortality rates in sink habitats, evolution of predator movement into sink habitats forestalls evolution of prey movement into sink habitats. Only at intermediate mortality rates is there selection for predator and prey movement. Our results also illustrate an evolutionary paradox of enrichment, in which enriching source habitats can reduce phenotypic diversity

When everything is not everywhere but species evolve: an alternative method to model adaptive properties of marine ecosystems

The functional and taxonomic biogeography of marine microbial systems reflects the current state of an evolving system. Current models of marine microbial systems and biogeochemical cycles do not reflect this fundamental organizing principle. Here, we investigate the evolutionary adaptive potential of marine microbial systems under environmental change and introduce explicit Darwinian adaptation into an ocean modelling framework, simulating evolving phytoplankton communities in space and time. To this end, we adopt tools from adaptive dynamics theory, evaluating the fitness of invading mutants over annual timescales, replacing the resident if a fitter mutant arises. Using the evolutionary framework, we examine how community assembly, specifically the emergence of phytoplankton cell size diversity, reflects the combined effects of bottom-up and top-down controls. When compared with a species-selection approach, based on the paradigm that “Everything is everywhere, but the environment selects”, we show that (i) the selected optimal trait values are similar; (ii) the patterns emerging from the adaptive model are more robust, but (iii) the two methods lead to different predictions in terms of emergent diversity. We demonstrate that explicitly evolutionary approaches to modelling marine microbial populations and functionality are feasible and practical in time-varying, space-resolving settings and provide a new tool for exploring evolutionary interactions on a range of timescales in the ocean.France. Agence nationale de la recherche (grant PHYTBACK (ANR-10-BLAN-7109))European Union (EU Micro B3 project)European Research Council (ERC Diatomite project)Gordon and Betty Moore Foundation (Grant #3778

Evolution of host resistance towards pathogen exclusion: the role of predators

Question: Can increased host resistance drive a pathogen to extinction? Do more complex ecosystems lead to significantly different evolutionary behaviour and new potential extinctions? Mathematical method: Merging host-parasite models with predator-prey models. Analytically studying evolution using adaptive dynamics and trade-off and invasion plots, and carrying out numerical simulations. Key assumptions: Mass action (general mixing). All individuals of a given phenotype are identical. Only prey vulnerable to infection. Mutations are small and rare (however, the assumption on the size of mutation is relaxed later). In simulations, very small (negligible) populations are at risk of extinction. Conclusions: The presence of the predator can significantly change evolutionary outcomes for host resistance to a pathogen and can create branching points where none occurred previously. The pathogen (and sometimes the predator) is protected from exclusion if we take mutations to be arbitrarily small; however, relaxing the assumption on mutation size can lead to its exclusion. Increased resistance can drive the predator and/or pathogen to extinction depending on inter-species dynamics, such as the predator's preference for infected prey. Predator co-evolution can move exclusion boundaries and prevent the predator's own extinction if its rate of mutation is high enough (with respect to that of the prey)

The Predator's Numerical and Functional Responses Derived from First Principles : Population Dynamical and Evolutionary Consequences

This article-based dissertation uses mathematical models to study predator-prey interactions and their population dynamical and evolutionary consequences. The focus is on the predator's numerical and functional response which I derive from first principles, i.e., from the interactions between prey and predator individuals. The aim is to connect population-level phenomena and the long-term evolution of the prey or the predator to processes on the level of the individuals. The dissertation consists of a general introductory part and three research articles with general results as well as applications to specific models. The first two articles have already been published in the Journal of Mathematical Biology and in the Journal of Theoretical Biology, respectively. The third article is under review for publication. In the first research article, I introduce a formal method for the derivation of a predator's functional and numerical response from the interactions between the individual prey and predators. Such derivation permits an explicit interpretation of the parameters and structure of the functional and numerical responses in terms of individual behaviour. The general method is illustrated with several concrete examples. Some examples give novel derivations of already well-known functional responses. Other examples give derivations for responses that have not been used before and lead to a rich population dynamical behaviour including Allee effects as well as simultaneous existence of multiple positive population-dynamical attractors. In the second research article, I model a stand-off between a predator and a prey individual when the prey is hiding and the predator is waiting for the prey to come out from its refuge, or when the two are locked in a situation of mutual threat of injury or even death. The stand-off is resolved when the predator gives up or when the prey tries to escape. Using the methods of the first article, this individual-level model leads to the well-known Rosenzweig-MacArthur model but now with parameters that directly connect to the behaviour of the individuals, in particular the giving-up rates of the prey and the predator. I use the model to study the coevolution of the giving-up rates using the mathematical theory of adaptive dynamics. New and different evolutionary results emerge in comparison with the asymmetric war of attrition in evolutionary game theory which is the more traditional way of modelling a stand-off. In the third research article, I study the evolution of density dependent handling times (i.e., the processing time of captured prey) and the related functional and numerical responses. It is a well-established theoretical result that coexistence of two predator species feeding on one and the same prey is possible, but only if the system exhibits non-equilibrium dynamics. Coexistence is possible because the two predator species occupy different temporal niches: the one with the longer handling time has the advantage when the prey is rare so that holding on to the same catch is the better option, while the species with the shorter handling time has the advantage when the prey is common and easy to catch. Using the adaptive dynamics approach, I show that a predator species with a non-constant handling time that decreases with the prey density is selectively superior regardless of whether the prey is rare or common. The reason is that such generalist predator can occupy both temporal niches all by itself. By means of these examples, the dissertation demonstrates the strengths of deriving population models from first principles as it enables us to connect population-level phenomena and long-term evolution to the behaviour of the individuals that make up the population.Tämä artikkelipohjainen väitöskirja tutkii matemaattisten mallien avulla petoeläimen ja saaliin välistä vuorovaikutusta ja niiden populaation dynaamisia ja evolutiivisia seurauksia. Työn painopiste on petoeläimen numeerisessa ja toiminnallisessa vasteessa, jonka johdan ensimmäisistä periaatteista eli saaliin ja petoeläinten välisistä vuorovaikutuksista. Tavoitteena on yhdistää populaatiotason ilmiöt ja saaliin tai petoeläimen pitkäaikainen kehitys yksilötason prosesseihin. Väitöskirja koostuu yleisestä johdanto-osasta ja kolmesta tutkimusartikkelista, joissa on yleisiä tuloksia sekä sovelluksia tiettyihin malleihin. Kaksi ensimmäistä artikkelia on jo julkaistu Journal of Mathematical Biology ja Journal of Theoretical Biology -lehdissä. Kolmatta artikkelia tarkastellaan julkaisua varten. Ensimmäisessä tutkimusartikkelissa esittelen muodollisen menetelmän saalistajan toiminnallisen ja numeerisen vasteen johtamiseksi yksittäisen saaliin ja petoeläinten välisistä vuorovaikutuksista. Tällainen johtaminen mahdollistaa funktionaalinen vaste ja numeeristen vasteiden parametrien ja rakenteen eksplisiittisen tulkinnan yksilön käyttäytymisen kannalta. Yleistä menetelmää havainnollistetaan useilla konkreettisilla esimerkeillä. Jotkut esimerkit antavat uusia johdannaisia jo hyvin tunnetuista toiminnallisista vasteista. Muut esimerkit antavat johdannaisia vastauksista, joita ei ole käytetty aiemmin ja jotka johtavat runsaaseen populaation dynaamiseen käyttäytymiseen, mukaan lukien Allee-vaikutukset sekä useiden useampien dynaamisten attraktorien samanaikainen olemassaolo samanaikainen olemassaolo. Toisessa tutkimusartikkelissa mallinnan eroa saalistajan ja saalisyksilön välillä, kun saalis on piilossa ja saalistaja odottaa saaliin tulevan ulos turvapaikastaan tai kun nämä kaksi ovat lukittuina tilanteeseen, jossa on molemminpuolinen loukkaantumisen tai jopa kuoleman uhka. Vastakkainasettelu ratkeaa, kun saalistaja luovuttaa tai kun saalis yrittää paeta. Ensimmäisen artikkelin menetelmiä käyttäen tämä yksilötason malli johtaa hyvin tunnettuun Rosenzweig-MacArthurin -malliin, mutta nyt parametreillä, jotka liittyvät suoraan yksilöiden käyttäytymiseen, erityisesti saaliin ja saalistajan luopumisasteeseen. Mallin avulla tutkin pedon ja saaliin välisen luovuttamisen yhteisevoluutiota adaptiivisen dynamiikan viitekehyksen avulla. Minun mallini tuottamat uudet evolutiiviset tulokset poikkeavat merkittävästi evoluutiopeliteorian tutkimuksessa tyypillisesti käytetyn näännytyssodan mallin tuloksista. Kolmannessa tutkimusartikkelissa tutkin saalispopulaatioiden tiheyksistä riippuvien käsittelyaikojen (eli pyydystetyn saaliin käsittelyajan) evoluutiota ja niihin liittyviä funktionaalisia ja numeerisia vasteita. Vakiintunut teoreettinen tulos kertoo kahden samaa saalista syövän saalislajin rinnakkaiselon olevan mahdollista vain, jos populaatiodynaaminen tila on epätasapainossa. Rinnakkaiselo on mahdollista, koska kaudella saalislajilla voi olla erilainen ekologinen lokero: pidemmän käsittelyajan omaavalla on etulyöntiasema, kun saalis on harvinainen, jolloin pyydystetyn saaliin syömisessä pitäytyminen on parempi vaihtoehto, kun taas lyhyemmän käsittelyajan omaavalla lajilla on etulyöntiasema, kun saalis on yleinen ja helppo pyydystää. Adaptiivisen dynamiikan viitekehystä käyttämällä osoitan, että saalistajalaji, jonka käsittelyaika ei ole vakio ja joka pienenee saalistiheyden mukana, on valikoivasti parempi riippumatta siitä, onko saalis harvinainen vai yleinen. Syynä on, että tällainen yleispetoeläin voi varata molemmat ekologiset lokerot itselleen. Väitöskirja osoittaa näillä esimerkeillä populaatiomallien johtamisen vahvuuksia ensimmäisistä periaatteista, koska se mahdollistaa populaatiotason ilmiöiden ja pitkän aikavälin evoluution yhdistämisen populaation muodostavien yksilöiden käyttäytymiseen

Modeling the ecology and evolution of communities: A review of past achievements, current efforts, and future promises

Background: The complexity and dynamical nature of community interactions make modeling a useful tool for understanding how communities develop over time and how they respond to external perturbations. Large community-evolution models (LCEMs) are particularly promising, since they can address both ecological and evolutionary questions, and can give rise to richly structured and diverse model communities. Questions: Which types of models have been used to study community structure and what are their key features and limitations? How do adaptations and/or invasions affect community formation? Which mechanisms promote diverse and table communities? What are the implications of LCEMs for management and conservation? What are the key challenges for future research? Models considered: Static models of community structure, demographic community models, and small and large community- evolution models. Conclusions: LCEMs encompass a variety of modeled traits and interactions, demographic dynamics, and evolutionary dynamics. They are able to reproduce empirical community structures. Already, they have generated new insights, such as the dual role of competition, which limits diversity through competitive exclusion, yet facilitates diversity through speciation. Other critical factors determining eventual community structure are the shape of trade-off functions, inclusion of adaptive foraging, and energy availability. A particularly interesting feature of LCEMs is that these models not only help to contrast outcomes of community formation via species assembly with those of community formation via gradual evolution and speciation, but that they can furthermore unify the underlying invasion processes and evolutionary processes into a single framework

Understanding the role of eco-evolutionary feedbacks in host-parasite coevolution

It is widely recognised that eco-evolutionary feedbacks can have important implications for evolution. However, many models of host-parasite coevolution omit eco-evolutionary feedbacks for the sake of simplicity, typically by assuming the population sizes of both species are constant. It is often difficult to determine whether the results of these models are qualitatively robust if eco-evolutionary feedbacks are included. Here, by allowing interspecific encounter probabilities to depend on population densities without otherwise varying the structure of the models, we provide a simple method that can test whether eco-evolutionary feedbacks per se affect evolutionary outcomes. Applying this approach to explicit genetic and quantitative trait models from the literature, our framework shows that qualitative changes to the outcome can be directly attributable to eco-evolutionary feedbacks. For example, shifting the dynamics between stable monomorphism or polymorphism and cycling, as well as changing the nature of the cycles. Our approach, which can be readily applied to many different models of host-parasite coevolution, offers a straightforward method for testing whether eco-evolutionary feedbacks qualitatively change coevolutionary outcomes