DEMOGRAPHY AND DISPERSAL: CALCULATION AND SENSITIVITY ANALYSIS OF INVASION SPEED FOR STRUCTURED POPULATIONS

TLDR

Invasion speed, a key feature of biological range expansion, depends on population growth and dispersal and is comparable to the sensitivity of population growth rate. The study constructs a discrete‑time model coupling matrix population models with integrodifference equations to analyze biological invasions. The model incorporates age‑ or size‑dependent vital rates and dispersal, and is illustrated with data from teasel and Calathea ovandensis. The authors derive asymptotic invasion speed formulas and sensitivities, show these metrics correlate strongly with population growth sensitivity, and demonstrate that long‑distance dispersal dominates invasion speed even when rare.

Abstract

A fundamental characteristic of any biological invasion is the speed at which the geographic range of the population expands. This invasion speed is determined by both population growth and dispersal. We construct a discrete-time model for biological invasions that couples matrix population models (for population growth) with integrodifference equations (for dispersal). This model captures the important facts that individuals differ both in their vital rates and in their dispersal abilities, and that these differences are often determined by age, size, or developmental stage. For an important class of these equations, we demonstrate how to calculate the population's asymptotic invasion speed. We also derive formulas for the sensitivity and elasticity of the invasion speed to changes in demographic and dispersal parameters. These results are directly comparable to the familiar sensitivity and elasticity of population growth rate. We present illustrative examples, using published data on two plants: teasel (Dipsacus sylvestris) and Calathea ovandensis. Sensitivity and elasticity of invasion speed is highly correlated with the sensitivity and elasticity of population growth rate in both populations. We also find that, when dispersal contains both long- and short-distance components, it is the long-distance component that governs the invasion speed—even when long-distance dispersal is rare.