How population control of pests is modulated by density dependence: The perspective of genetic biocontrol

Abstract

Managing pest species relies critically on mechanisms that regulate population dynamics, particularly those factors that change with population size. These density-dependent factors can help or hinder control efforts and are especially relevant considering recent advances in genetic techniques that allow for precise manipulation of the timing and sex-specificity of a control. Despite this importance, density dependence is often poorly characterized owing to limited data and an incomplete understanding of developmental ecology. To address this issue, we construct and analyze a mathematical model of a pest population with a general control under a wide range of density dependence scenarios. Using this model, we investigate how control performance is affected by the strength of density dependence. By modifying the timing and sex-specificity of the control, we tailor our analysis to simulate different pest control strategies, including conventional and genetic biocontrol methods. We pay particular attention to the latter as case studies by extending the baseline model to include genetic dynamics. Finally, we clarify past work on the dynamics of mechanistic models with density dependence. As expected, we find substantial differences in control performance for differing strengths of density dependence, with populations exhibiting strong density dependence being most resilient to suppression. However, these results change with the size and timing of the control load, as well as the target sex. Interestingly, we also find that population invasion by certain genetic biocontrol strategies is affected by the strength of density dependence. While the model is parameterized using the life history traits of the yellow fever mosquito, Aedes aegypti, the principles developed here apply to many pest species. We conclude by discussing what this means for pest population suppression moving forward.

Figure 1:

One way to characterize the strength of density dependence is by measuring the time it takes for a perturbed population to return to equilibrium; stronger density dependence produces a shorter return time, while weaker density dependence produces a longer return time. The plot above shows this for different forms of $f(J)$, or density-dependent juvenile mortality. The generalized logistic case for $\beta =0.5$ is given by the solid line, $\beta =1$ by the dashed line, $\beta =1.5$ by the dash-dotted line, and the logarithmic case by the dotted line.

Figure 2:

The adult female population at the control equilibrium for various levels of an early-acting control load when it is (a) female-sex and (b) bi-sex targeting. Line types indicate the per capita DD juvenile mortality function. The solid line denotes the generalized logistic case for $\beta =0.5$, the dashed line corresponds to the $\beta =1$ case, the dot-dashed line is $\beta =1.5$, and the dotted line corresponds to the logarithmic case, $f(x)=\mathrm{l}\mathrm{o}\mathrm{g}(1+(\alpha x{)}^{\beta })$.

Figure 3:

The adult female population at the control equilibrium relative to the pre-control population versus a late-acting control load. Results are equivalent for female- and bi-sex control loads. Line types indicate the functional form of per capita DD juvenile mortality. The solid line denotes the generalized logistic case for $\beta =0.5$, the dashed line corresponds to the $\beta =1$ case, the dot-dashed line is $\beta =1.5$, and the dotted line corresponds to the logarithmic case, $f(x)=\mathrm{l}\mathrm{o}\mathrm{g}(1+(\alpha x{)}^{\beta })$.

Figure 4:

Comparison of the relative adult female population at the control equilibrium [(a) and (b)] and invasion threshold [(c) and (d)] for a female-sex (left column) and bi-sex targeting (right column) transgene for the one-locus EU drive as the ambient fitness cost $\left(c_a\right)$ is varied. The adult female population at equilibrium is equivalent between female- and bi-sex targeting cases, while the invasion threshold is lower for the latter. The density dependence functions studied are the generalized logistic case for $\beta =0.5$ (solid line), $\beta =1$ (dashed line), $\beta =1.5$ (dot-dashed line), and the logarithmic case $f(X)=\mathrm{l}\mathrm{o}\mathrm{g}(1+(\alpha X{)}^{\beta })$ (dotted line).

Figure 5:

Comparison of the relative adult female population at the control equilibrium [(a) and (b)] and invasion threshold [(c) and (d)] for a female-sex (left column) and bi-sex targeting (right column) transgene for the two-locus EU gene drive. We assume that the toxin is lethal without the complementary allele ($c_t=1$). The density dependence functions studied are the generalized logistic case for $\beta =0.5$ (solid line), $\beta =1$ (dashed line), $\beta =1.5$ (dot-dashed line), and the logarithmic case $f(X)=\mathrm{l}\mathrm{o}\mathrm{g}(1+(\alpha X{)}^{\beta })$ (dotted line).

Figure 6:

A comparison of the number of surviving organisms at $t=1$ for the (a) discrete system in Eqtn. (10) and the (b) continuous-time system in Eqtn. (9) for $\mu (N)=\mathrm{l}\mathrm{o}\mathrm{g}(1+(\alpha N{)}^{\beta })$ for variable initial densities. The different parameter values used are: $\alpha =0.01$, $\beta =1$ (dashed), $\alpha =0.01$, $\beta =5$ (dot-dashed), and $\alpha =0.02$, $\beta =5$ (solid). The discrete system in (a) exhibits overcompensatory density dependence, or scramble competition, while the continuous-time differential equation in (b) does not.