Resonant Population Cycles in Temporally Fluctuating Habitats

Abstract

Experiments with the flour beetle Tribolium have revealed that animal numbers were larger in cultures grown in a periodically fluctuating volume of medium than in cultures grown in a constant volume of the same average size. In this paper we derive and analyze a discrete stage-structured mathematical model that explains this phenomenon as a kind of resonance effect. Habitat volume is incorporated into the model by the assumption that all rates of cannibalism (larvae on eggs, adults on eggs and pupae) are inversely proportional to the volume of the culture medium. We tested this modeling assumption by conducting and statistically analyzing laboratory experiments. For parameter estimates derived from experimental data, our model indeed predicts, under certain circumstances, a larger * Corresponding author.

Hot temperatures can force delayed mosquito outbreaks via sequential changes in Aedes aegypti demographic parameters in autocorrelated environments

“…This feature is common to other insects, where variable environments can lead to larger average population size when compared with stable environments (Costantino et al 1998). In that sense, forecasts concerning unusual temperature increases could help to temporally target interventions of highly productive larval developmental containers (Maciel-de-Freitas & Lourenco-de-Oliveira 2011) and other refugia that potentially promote mosquito outbreaks (Wallner 1987).…”

“…The introduction of sequential and over-compensatory changes in the life history of Ae aegypti could lengthen the delay of the association beyond what can be attributed to a reactive response, with an average of 4 to 5 weeks ( Figure 3C & 3D). These environmentally forced "cycles" can then be amplified if they coincide with reactive response in the model, a result independently derived for matrix models (Costantino et al 1998;Tuljapurkar 1985) and ordinary differential equations (Nisbet & Gurney 1976). In fact, the 5 week cycles can resonate and generate association delays of sub-harmonic length (i.e., a multiple of 4 or 5 weeks), for example 10 weeks.…”

Multiple Attractors, Saddles, and Population Dynamics in Periodic Habitats

“…The LPA model has been validated by means of a number of experiments, and has been used successfully to predict transitions between equilibria, periodic cy-cles, invariant loops, and chaos, as well as saddle phenomena and phase switching in population cycles (see Costantino et al, 1995Costantino et al, , 1997Costantino et al, , 1998Cushing et al, 1996Cushing et al, , 1998Dennis et al, 1995Dennis et al, , 1997Desharnais et al, 1997;Beniot et al, 1998;Henson et al, 1998). Henson and Cushing (1997) and Costantino et al (1998) modified the autonomous LPA model (1) to account for the periodic flour volume.…”

“…An exception is the laboratory experiment conducted by Jillson (1980) and the subsequent model-based explanation proposed by Costantino et al (1998). For a different interpretation of the Jillson experiment see Nisbet and Gurney (1981) and Renshaw (1991).…”

“…To explain this phenomenon, the discrete LPA Tribolium model of Dennis et al (1995Dennis et al ( , 1997 and Costantino et al (1995Costantino et al ( , 1997 was modified by Henson and Cushing (1997) and Costantino et al (1998) to account for the periodic flour volume. Cannibalism between life cycle stages is the nonlinear mechanism driving flour beetle dynamics in these experiments (Park et al, 1970).…”