Demography and dispersal: Calculation and sensitivity analysis of invasionspeed for structured populations

A fundamental characteristic of any biological invasion is the speed at whi ch the geographic range of the population expands. This invasion speed is d etermined 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). Th is model captures the important facts that individuals differ both in their vital rates and in their dispersal abilities, and that these differences a re 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 pa rameters. 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 Cala thea ovandensis. Sensitivity and elasticity of invasion speed is highly cor related with the sensitivity and elasticity of population growth rate in bo th populations. We also find that, when dispersal contains both long- and s hort-distance components, it is the long-distance component that governs th e invasion speed-even when long-distance dispersal is rare.