title: Formulating spread of species with habitat dependent growth and dispersal in heterogeneous landscapes.
abstract: Habitat heterogeneity can have profound effects on the spreading dynamics of invasive species. Using integro-difference equations, we investigate the spreading dynamics in a one-dimensional heterogeneous landscape comprising alternating favourable and unfavourable habitat patches or randomly generated habitat patches with given spatial autocorrelation. We assume that population growth and dispersal (including emigration probability and dispersal distance) are dependent on habitat quality. We derived an approximation of the rate of spread in such heterogeneous landscapes, suggesting the sensitivity of spread to the periodic length of the alternating favourable and unfavourable patches, as well as their spatial autocorrelation. A dispersal-limited population tends to spread faster in landscapes with shorter periodic length. The spreading dynamics in a heterogeneous landscape was found to be not only dependent on the availability of favourable habitats, but also the dispersal strategy. Estimates of time lag before detection and the condition for boom-and-bust spreading dynamics were explained. Furthermore, rates of spread in heterogeneous landscapes and corresponding homogeneous landscapes were compared, using weighted sums of vital rates.
authors.affiliation: Centre for Invasion Biology, Department of Mathematical Sciences, Stellenbosch University, Matieland 7602, South Africa; Mathematical and Physical Biosciences, African Institute for Mathematical Sciences, Cape Town 7945, South Africa. Electronic address: mihataims@gmail.com.
authors.forename: Andriamihaja
authors.initials: A
authors.lastname: Ramanantoanina
authors.affiliation: Centre for Invasion Biology, Department of Mathematical Sciences, Stellenbosch University, Matieland 7602, South Africa; Mathematical and Physical Biosciences, African Institute for Mathematical Sciences, Cape Town 7945, South Africa.
authors.forename: Cang
authors.initials: C
authors.lastname: Hui
mesh_terms: D000818:Animals; D003198:Computer Simulation; D017753:Ecosystem; D058865:Introduced Species; D055641:Mathematical Concepts; D008954:Models, Biological; D011157:Population Dynamics; D011158:Population Growth
keywords: Biological invasion; Boom-and-bust; Dispersal strategy; Habitat heterogeneity; Lag phase; Range expansion