Spreading speeds for stage structured plant populations in fragmented landscapes

Landscape fragmentation has huge ecological and economic implications and affects the spatial dynamics of many plant species. Determining the speed of population spread in fragmented/heterogeneous landscapes is therefore of utmost importance to ecologists. Stage-structured integrodifference equations (IDEs) are deterministic models which accurately reflect the life cycles and dispersal patterns for numerous species. Existing approximations to wave-speeds consider only particular kernels, or landscapes in which the scale of variation is much smaller than the dispersal scale. We propose an analytical approximation to the wave-speeds of IDE solutions with periodic landscapes of alternating good and bad patches, where the dispersal scale is greater than the extent of each good patch and where the ratio of the demographic rates in the good and bad patches is given by a small parameter, denoted as ε. We formulate this approximation for the Gaussian and Laplace dispersal kernels and for stage structured and non-stage structured populations, and compare the results against numerical simulations. We find that the approximation is accurate for the landscapes considered, and that the type of dispersal kernel affects the relationship between landscape structure, as classified by landscape period and good patch size, and the spreading speed. This indicates that accurately fitting a kernel to data is important in determining the relationship between landscape structure and spreading speed.