Predator Equation Research Articles

STOCHASTIC PREDATION MODEL WITH DEPLETION

AbstractA stochastic model is developed for the expected number of prey taken by a single predator when prey depletion is apparent. The so-called “random predator equation” with prey exploitation of Royama and Rogers is compared with the stochastic model. The numerical comparisons illustrate situations where the deterministic model provides adequate and inadequate approximations.

On some Markov models of certain interacting populations.

We give a stochastic foundation to the Volterra prey-predator population in the following case. We take Volterra's predator equations and let a free host birth and death process support the evolution of the predator population. The purpose of this article is to present a rigorous population sample path construction of this interacted predator process and study the properties of this interacted process. The constructions yields a strong Markov process. The existence of steady-state distribution for the interacted predator process means the existence of equilibrium population level. We find a necessary and sufficient condition for the existence of a steady-state distribution. Next we see that if the host process possesses a steady-state distribution, so does the interacted predator process and this distribution satisfies a difference equation. For special choices of the auto death and interaction parametersa andb of the predator, whenever the host process visits the particular statea *=a/b the predator takes rest (saturates) from its evolution. We find the probability of asymptotic saturating of the predator.

Functional response of <i>Phytoseiulus persimilis</i> Athias-Henriot to Tetranychus urticae Koch: effects of prey life stages and temperature

This paper examines the effect of density and temperature on the functional response of adult female Phytoseiulus persimilis to different life stages of the spider mite, Tetranychus urticae. The functional response was determined using functional response assay technique with plant leaf discs an arena. We conducted a logistic regression of the proportion of prey consumed as a function of initial prey density to identify functional response types, and used nonlinear least-squares regression and the random predator equation to estimate attack rates and handling times. In all the cases number of adult male prey attacked by female predator were greater than adult female prey. P. persimilis consumed more eggs and larvae than other stages of prey. Female predator consumed adult prey at each temperature which generally increased with prey density initially but leveled off at higher prey densities. The highest number of eggs, larvae and nymphs consumed by predator in 24 hours was 16.3 ± 0.42, 9.9 ± 0.59 and 9.5 ± 0.40 respectively whereas the highest number of eggs, larvae and nymphs consumed by a single female in 48 hours was 19.5 ± 1.15, 18.6 ± 0.62 and 13.3 ± 0.65 respectively. Handling time generally decreased with temperature whereas successful attack rate increased with temperature except at 30º C. Judging by a/Th values, P. persimilis was most efficient against T. urticae at 30-35ºC, about half as efficient at 25 ºC and performed poorly at 20º C. Again, from a/Th values, P. persimilis was most efficient against T. urticae in egg stage, about half as efficient at larva and nymph stages and performed poorly at adult stage. Key words: Phytoseiulus persimilis; Tetranychus urticae; functional response; predation; temperature.DOI: http://dx.doi.org/10.3329/ujzru.v29i1.9458 UJZRU 2010; 29(1): 1-8