Modification of the random-search type II functional response equation for incorporation into simulation models

Because of the assumptions implicit in the Royama-Rogersʹ Type II Random Search Parasitoid Equation (RSPE), the estimates of parameters are valid only within an area unit equal to the experimental area used to estimate them. This assumption was tested using different values of Nt (host density) and Pt (parasitoid density), while maintaining the host: parasitoid ratio constant at 10:1. If the RSPE is valid at any area unit, then the value of F(Nt, Pt) (probability of being parasitized) should be constant at all values of Nt and Pt provided that the Nt:Pt ratio remains constant. Instead, the value of F(Nt, Pt) showed an asymptotic rise to a plateau. This result supports the assumption that the RSPE validity is limited by the area unit in which its parameters are estimated. Such a limitation precludes the incorporation of this Type II equation into an age-structured simulation model. A modification to the RSPE which lacks these space-dependence limitations is proposed. The modification consisted of the division of the coefficient aʹ by parasitoid density (t). This modification transforms the instantaneous rate of discovery into a per capita basis.