A stochastic simulation model for <em>Anelosimus studiosus</em> during prey capture: A case study for determination of optimal spacing

Abstract

In this paper, we develop a stochastic differential equation model to simulate the movement of a social/subsocial spider species, Anelosimus studiosus, during prey capture using experimental data collected in a structured environment. In a subsocial species, females and their maturing offspring share a web and cooperate in web maintenance and prey capture. Furthermore, observations indicate these colonies change their positioning throughout the day, clustered during certain times of the day while spaced out at other times. One key question was whether or not the spiders spaced out ``optimally'' to cooperate in prey capture. In this paper, we first show the derivation of the model where experimental data is used to determine key parameters within the model. We then use this model to test the success of prey capture under a variety of different spatial configurations for varying colony sizes to determine the best spatial configuration for prey capture.

Spatio-temporal analysis of foraging behaviors of Anelosimus studiosus utilizing mathematical modeling of multiple spider interaction on a cooperative web

“…[22] using stochastic differential equations and computational algorithms. In [2], the trajectory of the spider is determined by dr(t) = µ{r(t), t} dt + Σ{r(t), t} dW(t)…”

“…represents the location of the spider at time t, dt is an incremental change in time, µ is the directional component, Σ is a diffusion parameter, and W is assumed to be a brownian process [2]. The diffusion parameter is given by…”

“…al. [2], was that spiders must stay close to the retreat when the threat of predators is high; however, they spread out to optimize prey capture during other parts of the day. The model in [2] was a more simplistic model for predation in which it was assumed that spiders acted immediately upon detection of a prey in the web and moved in a similar manner to each other with no interaction between the spiders of the web.…”

“…[2], was that spiders must stay close to the retreat when the threat of predators is high; however, they spread out to optimize prey capture during other parts of the day. The model in [2] was a more simplistic model for predation in which it was assumed that spiders acted immediately upon detection of a prey in the web and moved in a similar manner to each other with no interaction between the spiders of the web. Under these assumptions, they concluded that the "model predictions generally support the hypothesis that these spiders can improve their communal prey capture success employing regular or random distributions, thus increasing their collective foraging area.…”

“…The model also predicted that if the spiders position themselves around the perimeter of the web they are more successful at capturing prey" [2].…”