Scale of dispersal in varying environments and its implications for life histories of marine invertebrates.

We present several models concerning the short term consequences of spreading offspring in varying environments. Our goal is to determine what patterns of spatial and temporal variation yield an advantage to increasing scale of dispersal. Of necessity, the models are somewhat artificial but we feel they are a reasonable approximation of and hence generalizable to natural systems. With these models we examine consequences of dispersal arising from environmental variation: increased environmental variance, different degrees of spatial and temporal correlation, some arbitrary spatial patterns of favorability and finally some patterns derived from long-term, large-scale weather data collected along a contiguous stretch of coastline from southern Oregon to northern Washington (USA). We examine the costs and benefits of increasing sclae of dispersal in both density dependent and density independent models.Several conclusions may be drawn from the results of these models. In the absence of any spatial or temporal order to favorability (where favorability is directly proportional to either fitness or carrying capacity) increasing scale of spread produces a higher tate of population increase. At larger scales, though, an asymptote of maximum relative advantage is approached, so each added increment of spread has a smaller contribution to fitness. This asymptote is higher and the approach to it relatively slower with increasing environmental variance. For a given environmental variance, increasing spatial correlation results in a slower approach to the same asymptote. In density independent models, increasing temporal correlation of fitness selects against increased dispersal if expected differences between sites are sufficiently great relative to variation within sites; but in this instance, density dependence yields a somewhat different result: dispersers have a refuge at sites of low carrying capacity or sites lacking non-dispersers. Finally, optimum intermediate scales of dispersal can occur where differences in expected fitness increase with increasing distance from the parental site, such as in a gradient, but where the environmental variation at a given site is fairly large relative to differences in expected fitness between adjacent sites.The foregoing results are extended for the following predictions. When greater longevity in a resistant phase of the life cycle reduces temporal variation in survival and fecundity, increased generation time should decrease the benefits of spreading offspring in an environment that would otherwise favor spread and could either increase or decrease the costs of spreading offspring in an environment selecting against spread. We speculate that if large scale patterns of varying survival and fecundity are similar to the variation in the physical environment which we examined with weather data, there should be little or no short term advantage to large scale spread of offspring (on the order of 50 kilometers or more) because expected differences increase and seldom if ever decrease with increasing distance between sites.This suggests that feeding larvae of benthic invertebrates with their concomitant long planktonic period, receive little if any advantage from increased scale of dispersal, and consequently that the advantages to planktotrophy over lecithotrophy must lie in other life history aspects, such as the ability to produce a greater number of smaller eggs.