Invasion speeds for structured populations in fluctuating environments

TL;DR

This paper develops analytical methods to estimate invasion speeds in fluctuating environments using stochastic structured population models, revealing how variability and autocorrelation affect invasion rates and their uncertainty.

Contribution

It introduces a novel analytical framework for invasion speed estimation in stochastic, structured populations, accounting for environmental variability and autocorrelation effects.

Findings

Increased environmental variability slows invasion speeds.

Variability increases uncertainty in invasion rate estimates.

Autocorrelation effects on invasion speed depend on life history traits.

Abstract

We live in a time where climate models predict future increases in environmental variability and biological invasions are becoming increasingly frequent. A key to developing effective responses to biological invasions in increasingly variable environments will be estimates of their rates of spatial spread and the associated uncertainty of these estimates. Using stochastic, stage-structured, integro-difference equation models, we show analytically that invasion speeds are asymptotically normally distributed with a variance that decreases in time. We apply our methods to a simple juvenile-adult model with stochastic variation in reproduction and an illustrative example with published data for the perennial herb, \emph{Calathea ovandensis}. These examples buttressed by additional analysis reveal that increased variability in vital rates simultaneously slow down invasions yet generate greater uncertainty about rates of spatial spread. Moreover, while temporal autocorrelations in vital rates inflate variability in invasion speeds, the effect of these autocorrelations on the average invasion speed can be positive or negative depending on life history traits and how well vital rates ``remember'' the past.