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Module BIO-‐M1-‐S06 “Evolu3onary ecology” The struggle for existence David Claessen! Institut de Biologie de l’ENS! Equipe Eco-Evolution Mathématique Thomas Robert Malthus • The increase of popula0on is necessarily limited by the means of subsistence; • The popula0on does invariably increase when the means of subsistence increase; • The superior power of popula0on is repressed, and the actual popula0on kept equal to the means of subsistence, by misery and vice. Logistic growth Mathéma0cien, inspiré par le « principe de popula0on » de Malthus, il proposa en 1838 ce modèle pour la dynamique des popula0ons animales grâce à un modèle qui ne soit pas exponen0el. K = capacité de charge r = taux intrinsèque de croissance Redecouvert en 1920 par Raymond Pearl et Lowell Reed, depuis très répandu en écologie Charles Darwin (1859) identified the « struggle for existence »," in combination with heritable variation," as the driving force of evolutionary change. 4 5 6 7 The origin of this struggle (« It is the doctrine of Malthus applied with manifold force to the whole animal and vegetable kingdoms ») Two basic observations: 1. All populations tend to grow exponentially" 2. Exponentially growing populations are kept in check by regulatory mechanisms – Food depletion, predation, disease, competition, etc 8 Struggle for existence • As a population grows exponentially, its impact on the environment is such that conditions get less favorable for population growth" • This results in population regulation • In combination with heritable variation, this also results in natural selection " (or: survival of the fittest) 9 Resource Time Time 10 Population Population Resource Time Struggle for existence Time 11 Feedback loop • The struggle for existence corresponds to a feedback loop: – The environmental " conditions determine the " population growth rate" – The population size " determines the " environmental conditions" 12 A very simple model example Exponential growth with Constant mortality Food-dependent reproduction Population impact on the environment 13 The « Environment » formulation • Why use such a complicated model formulation, if we can write the same model like this: with • Answers: – to obtain a linear model for the population dynamics – to make the feedback loop explicit – to use a generic model formulation for modelling density-dependence 14 The environmental feedback loop Individual (realised life history, behaviour) Environment (resources, ecological interactions, physical environment) Population (dynamics, structure, demography) 15 The environmental feedback loop Individual (realised life history, behaviour) ics m a n y on d i t a l u y the b Pop d e vern are go graphic demo ies of rt prope , such as als u d i v i ival, v r ind u s ity, fecund al growth, du indivi tion rate. migra Environment (resources, ecological interactions, physical environment) Population (dynamics, structure, demography) 16 Indi The environmental feedback loop part vid , on ual prop th er (food e state o ties dep e f pred density the env nd, in ,a ir ators , tem bundan onment c pera ture, e of etc). Individual (realised life history, behaviour) Environment (resources, ecological interactions, physical environment) Population (dynamics, structure, demography) 17 The environmental feedback loop Individual (realised life history, behaviour) Environment (resources, ecological interactions, physical environment) Population (dynamics, structure, demography) Colle ct indiv ively, id influe uals nce th envir e o thoug nment, e.g ., h exp l o i ta of res ource tion18 s How can we use the idea of the environmental feedback loop to model evolutionary dynamics? It provides us with a ‘‘free’’ fitness definition 19 Adaptive dynamics • The starting point is to consider the fate of a rare mutant that arrives in an established resident population – Can the mutant invade? (increase) – Can the mutant replace the resident? Trait u → • Use these questions to determine the path of evolution Evolu0onary 0me → 20 The environmental feedback loop Individual (realised life history, behaviour) Environment (resources, ecological interactions, physical environment) Population (dynamics, structure, demography) 21 The environmental feedback loop Individual (realised life history, behaviour) Individual Environment (realised life history, behaviour) (resources, ecological interactions, physical environment) Population Population (dynamics, structure, demography) (dynamics, structure, demography) 22 Fitness • The mutant initially does not impact the environment • Hence its population growth is exponential: • And its invasion fitness is given by the exponential growth rate r that we now write as 23 Fitness Adaptive dynamics The fitness landscape changes after each successive mutant invasion & replacement 0 Trait 0 The resident always has fitness=0 (The struggle for existence) Metz et al (1992, 1996), Geritz et al (1998), etc… Evolutionarily stable strategy (CSS) 0 24 Fitness Adaptive dynamics Evolution towards disruptive selection 0 Trait 0 Evolutionarily branching point (EBP) 0 Metz et al (1992, 1996), Geritz et al (1998), etc… 25 Fitness Adaptive dynamics Evolution towards disruptive selection 0 Trait 0 Evolutionarily branching point (EBP) « If Muhammed will not go to the mountain pass, the mountain pass will come to Muhammed »" 0 " (Francis Bacon paraphrased) Metz et al (1992, 1996), Geritz et al (1998), etc… 26