A general modeling framework for describing spatially structured population dynamics

Abstract

Variation in movement across time and space fundamentally shapes the abundance and distribution of populations. Although a variety of approaches model structured population dynamics, they are limited to specific types of spatially structured populations and lack a unifying framework. Here, we propose a unified network‐based framework sufficiently novel in its flexibility to capture a wide variety of spatiotemporal processes including metapopulations and a range of migratory patterns. It can accommodate different kinds of age structures, forms of population growth, dispersal, nomadism and migration, and alternative life‐history strategies. Our objective was to link three general elements common to all spatially structured populations (space, time and movement) under a single mathematical framework. To do this, we adopt a network modeling approach. The spatial structure of a population is represented by a weighted and directed network. Each node and each edge has a set of attributes which vary through time. The dynamics of our network‐based population is modeled with discrete time steps. Using both theoretical and real‐world examples, we show how common elements recur across species with disparate movement strategies and how they can be combined under a unified mathematical framework. We illustrate how metapopulations, various migratory patterns, and nomadism can be represented with this modeling approach. We also apply our network‐based framework to four organisms spanning a wide range of life histories, movement patterns, and carrying capacities. General computer code to implement our framework is provided, which can be applied to almost any spatially structured population. This framework contributes to our theoretical understanding of population dynamics and has practical management applications, including understanding the impact of perturbations on population size, distribution, and movement patterns. By working within a common framework, there is less chance that comparative analyses are colored by model details rather than general principles.

Population and evolutionary dynamics in spatially structured seasonally varying environments

“…Taylor & Norris, ). Indeed, network models provide a flexible approach that can in principle encompass any spatial structure and form of seasonality, and hence model any desired combination of non‐migratory, fully migratory and partially migratory sub‐populations (Sample et al, ).…”

“…Such frameworks would, in principle, allow system‐specific forecasting of PMMP dynamics and persistence given any real or hypothetical landscape and postulated scenario of spatio‐temporal seasonal environmental change. In contrast to network models (Sample et al, ), such IBMs do not necessarily require focal populations to inhabit landscapes where discrete habitat patches can be clearly defined.…”

Quantifying the Contribution of Habitats and Pathways to a Spatially Structured Population Facing Environmental Change

“…Symbols used throughout this article are given in table 1. We consider a network in which habitats are nodes and movement pathways are edges (Taylor and Norris 2010;Sample et al 2018). We consider a population of c classes (or life stages) in a network of n nodes and s seasons.…”

A guide to calculating habitat‐quality metrics to inform conservation of highly mobile species

“…Each of these three functions could include densitydependent effects or other forms of spatiotemporal variation in vital rates. An extensive description of this modeling approach can be found in Sample et al (2017). Sensitivity is defined as the change in an output variable (e.g., network-level growth rate) when one or more system parameters (e.g., habitat-specific survival rate) is changed.…”