Ideal Cost-Free Distributions in Structured Populations for General Payoff Functions

Abstract

The important biological problem of how groups of animals should allocate themselves between different habitats has been modelled extensively. Such habitat selection models have usually involved infinite well-mixed populations. In particular, the model of allocation over a number of food patches when movement is not costly, the ideal free distribution (IFD) model, is well developed. Here we generalize (and solve) a habitat selection game for a finite structured population. We show that habitat selection in such a structured population can have multiple stable solutions (in contrast to the equivalent IFD model where the solution is unique). We also define and study a "predator dilution game" where unlike in the habitat selection game, individuals prefer to aggregate (to avoid being caught by predators due to the dilution effect) and show that this model has a unique solution when movement is unrestricted.

Evolutionary dynamics and the evolution of multiplayer cooperation in a subdivided population

“…In [10] a new framework for the flexible modelling of structured populations using multiplayer interactions was introduced, see also [8,13,11]. This work built on classical evolutionary graph theory, but was limited in terms of the dynamics used.…”

“…Following our assumptions, the population evolves following a succession of invasions of subpopulations either of cooperators by defectors or of defectors by cooperators. The probability that the next such event will be the invasion of a subpopulation of defectors by a cooperator is simply 11) where…”

“…More recently a general framework has been developed [10,13,8,11] which considers the interaction of populations in a more flexible way, where groups of any size can form, with different propensity potentially depending upon a number of factors, including the history of the process. Crucially, the key elements of evolutionary graph theory of population structure, game and evolutionary dynamics occur for this new framework too; this makes it capable of analysing different spatial structures whilst providing the flexibility for different multiplayer interactions.…”

Evolving multiplayer networks: Modelling the evolution of cooperation in a mobile population

“…A more general framework that can be used is that of [11] where it is possible to consider multiplayer interactions in groups of any size, depending upon various factors like the population's history, whilst keeping the beneficial aspects of evolutionary graph theory. More recently this framework has been used to model different kinds of multiplayer behaviour [13,9,12]. In this paper, we extend this work to consider a population of mobile individuals, focusing on a specific multiplayer game, a public goods game [6,7,25,55].…”

Models and measures of animal aggregation and dispersal

“…In particular, the utility value is independent of conditions in other patches within the landscape. Broom and Rychtář (2018) applied this local aggregation assumption to structured population models. This assumption is reasonable if there is not some direct in uence of one patch on another, such as if our individuals have a highly mobile predator who can observe more than one patch, so that its choice to hunt on one patch depends upon what it observes on another.…”