Predicting the time to colonization of the parasitoid Diadegma semiclausum: The importance of the shape of spatial dispersal kernels for biological control

The time at which natural enemies colonize crop fields is an important determinant of their ability to suppress pest populations. This timing depends on the distance between source and sink habitats in the landscape. Here we estimate the time to colonization of sink habitats from a distant source habitat, using empirical mark-capture data of Diadegma semiclausum in Broccoli. The data originated from experiments conducted at two locations and dispersal was quantified by suction sampling before and after a major disturbance. Three dispersal kernels were fitted to the dispersal data: a normal, a negative exponential, and a square root negative exponential kernel. These kernels are characterized by a thin, intermediate and a fat tail, respectively. The dispersal kernels were included in an integro-difference equation model for parasitoid population redistribution to generate estimates of time to colonization of D. semiclausum in sink habitats at distances between 100 and 2000 m from a source. We show that the three dispersal kernels receive similar support from the data, but can produce a wide range of outcomes. The estimated arrival time of 1% of the D. semiclausum population at a distance 2000 m from the source ranges from 12 days to a length of time greatly exceeding the life span of the parasitoid. The square root negative exponential function, having the thickest tail among the tested functions, gave the fastest spread and colonization in three of the four data sets, but it gave the slowest redistribution in the fourth. In all four data sets, the rate of accumulation at the target increased with the mean dispersal distance of the fitted kernel model, irrespective of the fatness of the tail. This study underscores the importance of selecting a proper dispersal kernel for modelling spread and colonization time of organisms, and of the collection of pertinent data that enable kernel estimation and that can discriminate between different kernel shapes.