Turbulent transport of suspended particles and dispersing benthic organisms: the hitting-distance problem for the local exchange model.

The local exchange model developed by McNair et al. (1997) provides a stochastic diffusion approximation to the random-like motion of fine particles suspended in turbulent water. Based on this model, McNair (2000) derived equations governing the probability distribution and moments of the hitting time, which is the time until a particle hits the bottom for the first time from a given initial elevation. In the present paper, we derive the corresponding equations for the probability distribution and moments of the hitting distance, which is the longitudinal distance a particle has traveled when it hits the bottom for the first time. We study the dependence of the distribution and moments on a particle's initial elevation and on two dimensionless parameters: an inverse Reynolds number M (a measure of the importance of viscous mixing compared to turbulent mixing of water) and the Rouse number s(a measure of the importance of deterministic gravitational sinking compared to stochastic turbulent mixing in governing the vertical motion of a particle). We also compute predicted hitting-distance distributions for two published data sets. The results show that for fine particles suspended in moderately to highly turbulent water, the hitting-distance distribution is strongly skewed to the right, with mode

Turbulent transport of suspended particles and dispersing benthic organisms: the hitting-time distribution for the local exchange model.

Fine particles suspended in turbulent water exhibit highly irregular trajectories as they are buffeted by fluid eddies. The Local Exchange Model provides a stochastic diffusion approximation to the randomlike motion of such particles (e.g. dispersing benthic organisms in a stream). McNair et al. (1997, J. theor. Biol.188, 29) used this model to derive equations governing the mean hitting time, which is the expected time until a particle hits bottom for the first time from a given initial elevation. The present paper derives equations governing the probability distribution of the hitting time, then studies the distribution's dependence on a particle's initial elevation and two dimensionless parameters. The results show that for fine particles suspended in moderately to highly turbulent water, the hitting-time distribution is strongly skewed to the right, with mode

Stability effects of a juvenile period in age-structured populations.

Prior theoretical studies have shown that the juvenile period's length is an important determinant of local stability in age-structured population dynamics. For example, both short and long periods produce stability, but intermediate lengths can cause instability. Short juvenile periods significantly increase stability (compared to no juvenile period) if fecundity is independent of adult age. Here I re-examine these and other patterns, using a model which includes a variable juvenile period, juvenile mortality, density-dependent fecundity and adult mortality, and age-dependence is adult fecundity. Among other things, the results confirm the stable-unstable-stable pattern with increasing juvenile period length, but show that the stabilizing effect of short periods disappears when fecundity varies with adult age. Broadly speaking, the results suggest that age-dependence in adult fecundity has important dynamical consequences, and that models assuming that fecundity is independent of adult age may be unreliable guides to the dynamics of populations for which this assumption is not reasonably accurate.

The effects of refuges on predator-prey interactions: a reconsideration.

Prey refuges are widely believed to prevent prey extinction and damp predator-prey oscillations. A review of the empirical evidence suggests that refuges are indeed capable of playing the former role. But the conditions under which they do so are not understood, nor is there any solid evidence for an effect on population fluctuations. The intuitive view that refuges act to stabilize equilibria and damp predator-prey oscillations is based in several theoretical studies of extremely simple models. Using a more realistic model, I show that several kinds of refuges can exert a locally destabilizing effect and create stable, large-amplitude oscillations which would damp out if no refuge was present. This finding contrasts sharply with the usual view. I argue that current evidence is tol weak, and the range of theoretically possible effects is too broad, to justify any simple characterization of refuge effects in nature. Manipulative empirical studies are an important first step toward correcting this situation, and I discuss some important factors to consider in their design.