Time delays in density dependence are often not destabilizing

A new model with delay for mosquito population dynamics

In this paper, we formulate a new model with maturation delay for mosquito population incorporating the impact of blood meal resource for mosquito reproduction. Our results suggest that except for the usual crowded effect for adult mosquitoes, the impact of blood meal resource in a given region determines the mosquito abundance, it is also important for the population dynamics of mosquito which may induce Hopf bifurcation. The existence of a stable periodic solution is proved both analytically and numerically. The new model for mosquito also suggests that the resources for mosquito reproduction should not be ignored or mixed with the impact of blood meal resources for mosquito survival and both impacts should be considered in the model of mosquito population. The impact of maturation delay is also analyzed.

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

Aedes aegypti L. (Diptera: Culicidae) is a common pantropical urban mosquito, vector of dengue, Yellow Fever and chikungunya viruses. Studies have shown Ae. aegypti abundance to be associated with environmental fluctuations, revealing patterns such as the occurrence of delayed mosquito outbreaks, i.e., sudden extraordinary increases in mosquito abundance following transient extreme high temperatures. Here, we use a two-stage (larvae and adults) matrix model to propose a mechanism for environmental signal canalization into demographic parameters of Ae. aegypti that could explain delayed high temperature induced mosquito outbreaks. We performed model simulations using parameters estimated from a weekly time series from Thailand, assuming either independent or autocorrelated environments. For autocorrelated environments, we found that long delays in the association between the onset of "hot" environments and mosquito outbreaks (10 weeks, as observed in Thailand) can be generated when "hot" environments sequentially trigger a larval survival decrease and over-compensatory fecundity increase, which lasts for the whole "hot" period, in conjunction with a larval survival increase followed by a fecundity decrease when the environment returns to "normal". This result was not observed for independent environments. Finally, we discuss our results implications for prospective entomological research and vector management under changing environments.

An alternative formulation for a delayed logistic equation

We derive an alternative expression for a delayed logistic equation, assuming that the rate of change of the population depends on three components: growth, death, and intraspecific competition, with the delay in the growth component. In our formulation, we incorporate the delay in the growth term in a manner consistent with the rate of instantaneous decline in the population given by the model. We provide a complete global analysis, showing that, unlike the dynamics of the classical logistic delay differential equation (DDE) model, no sustained oscillations are possible. Just as for the classical logistic ordinary differential equation (ODE) growth model, all solutions approach a globally asymptotically stable equilibrium. However, unlike both the logistic ODE and DDE growth models, the value of this equilibrium depends on all of the parameters, including the delay, and there is a threshold that determines whether the population survives or dies out. In particular, if the delay is too long, the population dies out. When the population survives, i.e., the attracting equilibrium has a positive value, we explore how this value depends on the parameters. When this value is positive, solutions of our DDE model seem to be well approximated by solutions of the logistic ODE growth model with this carrying capacity and an appropriate choice for the intrinsic growth rate that is independent of the initial conditions.

Reinterpreting space, time lags, and functional responses in ecological models

Natural enemy-victim interactions are of major applied importance and of fundamental interest to ecologists. A key question is what stabilizes these interactions, allowing the long-term coexistence of the two species. Three main theoretical explanations have been proposed: behavioral responses, time-dependent factors such as delayed density dependence, and spatial heterogeneity. Here, using the powerful moment-closure technique, we show a fundamental equivalence between these three elements. Limited movement by organisms is a ubiquitous feature of ecological systems, allowing spatial structure to develop; we show that the effects of this can be naturally described in terms of time lags or within-generation functional responses.