American Institute of Mathematical Sciences

Advanced
2007, 4(1): 67-84. doi: 10.3934/mbe.2007.4.67

An individual, stochastic model of growth incorporating state-dependent risk and random foraging and climate

William Wolesensky 1, and  J. David Logan 2,

1. 

Program in Mathematics, College of St. Mary, Omaha, NE 68134
2. 

Department of Mathematics, University of Nebraska, Lincoln, NE 68588-0130

Received  January 2006 Revised  March 2006 Published  November 2006

We model the effects of both stochastic and deterministic temperature variations on arthropod predator-prey systems. Specifically, we study the stochastic dynamics of arthropod predator-prey interactions under a varying temperature regime, and we develop an individual model of a prey under pressure from a predator, with vigilance (or foraging effort), search rates, attack rates, and other predation parameters dependent on daily temperature variations. Simulations suggest that an increase in the daily average temperature may benefit both predator and prey. Furthermore, simulations show that anti-predator behavior may indeed decrease predation but at the expense of reduced prey survivorship because of a greater increase in other types of mortality.
Keywords: vigilance, temperature, grasshoppers., foraging, nutritional state, stochastic.
Mathematics Subject Classification: 92D25, 92D40, 92D5.
Citation: William Wolesensky, J. David Logan. An individual, stochastic model of growth incorporating state-dependent risk and random foraging and climate. Mathematical Biosciences & Engineering, 2007, 4 (1) : 67-84. doi: 10.3934/mbe.2007.4.67
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