The Mechanistic Basis of Discrete-Time Population Models: The Role of Resource Partitioning and Spatial Aggregation

Anazawa, Masahiro. “The Mechanistic Basis of Discrete-Time Population Models: The Role of Resource Partitioning and Spatial Aggregation.” Theoretical Population Biology 77, no. 3 (May 2010): 213–18. doi:10.1016/j.tpb.2010.02.005.

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Anazawa (2010) expands on the coupled lattice model, or “site-based framework”, of population growth in Brannstrom & Sumpter (2005) to include multiple types of competition and spatial aggregation amongst sites. While the initial model included scramble competition, and further studies have adjusted the model to include contest competition, the model goes further to explicitly model resource partitioning amongst individuals, allowing for a range of intermediate competition types. It also expands on previous models by controlling for aggregation of individuals across sites.

The model crated is a discrete time, site-based model. It is not spatially explicitly in the way that CLMs are, although there is a dispersal step where individuals redisperse amongst sites according to a negative binomial distribution. Spatial dynamics are incorporated similar to Chesson’s scale transition theory, in that dynamics of the whole population are obtained by averaging local dynamics in a way that conserves variation across local sites. Competition is incorporated through the use of resource partitioning. Each individual receives an equal amount of resources, and the remaining resources are partitioned according to competitive ability, with only those individuals receiving above a set threshold amount of resources reproducing in that time step. At each time step, individuals disperse across the sites, compete, reproduce, and then die, allowing the next generation of offspring to disperse at time t+1.

This study focused on how changes in competition and spatial aggregation affected the population density and and stability of the whole system (i.e. across all sites). As competition becomes closer to scramble, density dependence within a site becomes stronger and overcompensates, and the model is similar to a Ricker population model. When the model shifts towards contest competition, the resulting dynamics are similar to logistic growth with a carrying capacity, caused by exact compensating density dependence. Interestingly, the effect of spatial autocorrelation is dependent on the competition. When competition is that of the ideal contest, the effect of density dependence is independent of spatial autocorrelation. As spatial autocorrelation decreases, the variance between site population densities becomes greater. When put in the framework of scale-transition theory, this shifts the peak of the curve in n(t) and n(t+1) space downward, and leads to stabilizing dynamics.

Unlike coupled lattice models which can rely on approximations, this method of modeling site-based population dynamics allows for a first-principle derivation of population dynamics in discrete-time. This model was relatively simple, but could be expanded upon by incorporating further biological realisms, such as Allee effects (which the author does in a later paper), and provides a starting point for incorporating the analytical solutions of scale transition theory with the spatial framework of coupled lattice models.