The struggle for existence

Transcription

1 Module BIO- M1- S06 Evolu3onary ecology The struggle for existence David Claessen! Institut de Biologie de l ENS! Equipe Eco-Evolution Mathématique

2 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.

3 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

4 Charles Darwin (1859) identified the «struggle for existence»," in combination with heritable variation," as the driving force of evolutionary change. 4

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8 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

9 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

10 Time Resource Population Time 10

11 Population Time Resource Struggle for existence Time 11

12 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

13 A very simple model example Exponential growth with Constant mortality Food-dependent reproduction Population impact on the environment 13

14 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

15 The environmental feedback loop Individual (realised life history, behaviour) Environment (resources, ecological interactions, physical environment) Population (dynamics, structure, demography) 15

16 The environmental feedback loop Population dynamics are governed by the demographic properties of individuals, such as fecundity, survival, individual growth, migration rate. Individual (realised life history, behaviour) Population (dynamics, structure, demography) Environment (resources, ecological interactions, physical environment) 16

17 Individual properties depend, in part, on the state of the environment (food density, abundance of predators, temperature, etc). The environmental feedback loop Individual (realised life history, behaviour) Environment (resources, ecological interactions, physical environment) Population (dynamics, structure, demography) 17

18 The environmental feedback loop Individual (realised life history, behaviour) Environment (resources, ecological interactions, physical environment) Population (dynamics, structure, demography) Collectively, individuals influence the environment, e.g., though exploitation of resources 18

19 How can we use the idea of the environmental feedback loop to model evolutionary dynamics? It provides us with a free fitness definition 19

20 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? Use these questions to determine the path of evolution Trait u Evolu0onary 0me 20

21 The environmental feedback loop Individual (realised life history, behaviour) Environment (resources, ecological interactions, physical environment) Population (dynamics, structure, demography) 21

22 The environmental feedback loop Individual (realised life history, behaviour) Environment (resources, ecological interactions, physical environment) Individual (realised life history, behaviour) Population (dynamics, structure, demography) Population (dynamics, structure, demography) 22

23 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

24 Adaptive dynamics Fitness 0 The fitness landscape changes after each successive mutant invasion & replacement Trait 0 Evolutionarily stable strategy (CSS) The resident always has fitness=0 (The struggle for existence) 0 Metz et al (1992, 1996), Geritz et al (1998), etc 24

25 Adaptive dynamics Fitness 0 Evolution towards disruptive selection Trait 0 Evolutionarily branching point (EBP) 0 Metz et al (1992, 1996), Geritz et al (1998), etc 25

26 Adaptive dynamics Fitness 0 Evolution towards disruptive selection Trait 0 Evolutionarily branching point (EBP) «If Muhammed will not go to the mountain pass, the mountain pass will come to Muhammed»" " (Francis Bacon paraphrased) 0 Metz et al (1992, 1996), Geritz et al (1998), etc 26