To understand a species’ population dynamics, we require at minimum a model of how individuals interact locally with their neighbours, and a model for the density of neighbours an individual can face. Theoretical work on spatial dynamics typically assumes independent dispersal of individuals, which allows deriving the local density of interacting individuals by summing the probability of each organism reaching a neighbourhood from its source. This assumption breaks down if physical or biological mechanisms cause individuals to cluster in space as they move. Currently, we lack an integrated theoretical framework to determine when and how a given clustering mechanism will cause growth rates to deviate from that predicted from independent dispersal.
In this talk, we develop such a framework from two components: a micro-scale model of how clusters of individuals are created, destroyed, and change in size, and a macro-scale model of the resulting density fields affecting population dynamics. We integrate existing modelling frameworks to model both levels, in the form of fragmentation/coagulation models for micro behaviour and cluster-point processes for macro patterns. We illustrate the utility of this approach by developing a stock-recruitment model with clustered settlement, where recruitment is driven by local competition between propagules.
Results/Conclusions
Our results demonstrate that the key parameters determining how strongly the observed stock-recruitment relationship should deviate from the equivalent unclustered model are:
the maximum distance over which individuals compete (scale of competition)
the radius of a typical cluster (scale of clustering)
the ratio between the variance and the mean number of individuals in a cluster (overdispersion)
The greater the mismatch between the scale of competition and scale of clustering, the less effect clustering has on population dynamics. However, for any given scale of clustering and competition, increasing overdispersion will increase the effect clustering has on dynamics. We use numerical simulations of our stock-recruitment model under different assumptions of competitive mechanism to determine to what extend our analytic model of cluster dynamics and distribution predicts recruitment outcomes.