Formulating spread of species with habitat dependent growth and dispersal in heterogeneous landscapes.

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.

Spatial assortment of mixed propagules explains the acceleration of range expansion.

Range expansion of spreading organisms has been found to follow three types: (i) linear expansion with a constant rate of spread; (ii) bi-phase expansion with a faster linear expansion following a slower linear expansion; and (iii) accelerating expansion with a continuously increasing rate of spread. To date, no overarching formula exists that can be applied to all three types of range expansion. We investigated how propagule pressure, i.