Modeling diffusive spread in a heterogeneous population: A movement study with stream fish

Using a mark-recapture technique in a small temperate stream, we described the movement of four fish species over a five-month period and developed a mathematical model that described the observed movement patterns. The movement distributions were generally leptokurtic, and two of the four species demonstrated some degree of upstream bias. There was little difference in movement among species or through time. There were no temporal correlations in probability of movement, movement direction, or distance moved. The spatial spread of the most abundant species, bluehead chubs, over a four-month period was characterized by upstream bias, diffusion-like spread, and persistent leptokurtosis. Bluehead chubs demonstrated complex relationships between probability of movement and size and growth, while creek chubs showed only an effect of size on probability of movement. Further, growth of individual bluehead chubs was correlated through time. These empirical results suggest the hypothesis that heterogeneity in phenotypic attributes, such as size and growth, is related to heterogeneity in movement behavior. A diffusion-advection model of bluehead chub movement, structured with two subgroups that dispersed at different rates (fast fish and slow fish), was parameterized and validated with the field data. This model with heterogeneity in movement rates generated the leptokurtic pattern observed in the field data, in contrast to the classic diffusion model without population heterogeneity, which produces a normal distribution. The results from this work suggest that heterogeneity in fitness-influencing attributes such as size and growth could explain heterogeneity in individual-level movement behavior and might underlie the leptokurtic patterns that have been observed at the population level in numerous field studies.