Nicholson's blowflies revisited

Abstract

A simple time-delay model of laboratory insect populations which postulates a ‘humped’ relationship between future adult recruitment and current adult population gives good quantitative agreement with Nicholson's classic blowfly data and explains the appearance of narrow ‘discrete’ generations in cycling populations

Global Exponential Stability of Periodic Solutions for a Nicholson’s Blowflies Model with a Linear Harvesting Term

“…It is well known that the Nicholson's blowflies equation has been introduced by Gurney et al [1] to describe the population of the Australian sheep-blowfly and to agree with the experimental data obtained in [2]. Later, the theory of Nicholson's blowflies equation has been made a remarkable progress in the past many years.…”

Perverse Consequences of Infrequently Culling a Pest

“…If this is so, then the pattern just described may repeat indefinitely (stable oscillations have been observed in the model (1), as mentioned in [20]) or the oscillations may die down as the population tends to a fixed point (see figure 1 and corollary 9.3 on page 163 of [28]). …”

“…A commonly used form for a birth function is b(N ) = λ 1 N e −λ 2 N for positive constants λ 1 , λ 2 . Certain blowfly population experiments by Nicholson [18,19] inspired Gurney et al [20] to consider a birth function of this form, which motivated Terry [13] to label such a function as being of Nicholson-type. However, notice that a function of the form N e r−kN , for positive constants r, k, is sometimes referred to as a Ricker functional form, descending from fisheries research by Ricker [21,22].…”

Diffusive and nondiffusive population models

“…More precisely, if aT < π/2, u = a/b is still a stable steady state, which becomes unstable if aT > π/2. When the time lag is not constant, one may employ the distributed delay equation The model of May was generalized and applied to the modeling of Australian sheep-blowfly populations by Gurney et al [57]. Diffusive versions can be found in [138,148].…”