A User’s Guide to Integrodifference Models for Invasive Spread

Abstract

This chapter focuses on connecting integrodifference models to biological data, so theoreticians can readily calculate spreading speeds for an invader based on available data. We investigate the use of a nonparametric estimator, which avoids the need to specify a functional form for the dispersal kernel. This approach is extended to include a histogram estimator, which can be applied to the case where data are binned into distance classes. We show how calculations differ slightly for different types of one-dimensional data (radial dispersal distances versus linear, one-dimensional dispersal distances), and we provide explicit formulae for each case. In some situations, dispersal distances come not from data but from complex computer simulations. In this case, Monte Carlo simulations can provide data for the nonparametric estimator, which in turn yields a straightforward estimate for spreading speed. Finally, the complexity of stage structure can be included in the integrodifference equation, yielding spreading speeds for stage-structured integrodifference models. Applications of the theory in this chapter are made to spreading speeds for Drosophila and teasel.