Density-dependent intraspecific competition in the larval stage of Aedes aegypti (Diptera: Culicidae): revisiting the current paradigm

Abstract

Density-dependent intraspecific competition has been considered an important determinant of the dynamics of larval stages of Aedes aegypti. A model was published in 1984 providing a mathematical description of this density dependence, based on field data, that has since been widely used. This description, however, is based on the strong assumption that all mortality is density-dependent. We re-examine the data without this premise and find a reduced importance of density dependence, as well as a different functional form. Based on these discrepancies, we emphasize that the characterization of density dependence in the larval stages of Ae. aegypti should be based on a more complete dataset, and we use artificially generated data to explore how such additional information could help developing a better description of this density dependence. We review other empirical studies on larval competition, discuss the need for further dedicated studies, and provide a few simple guidelines for the design of such studies.

Fig. 1

k₁₂ mortality from the Southwood et al. (1972) dataset (symbols), together with best-fitting functional forms for the dependence of k₁₂ on egg density (N) obtained using two assumptions about the density-independent parameter λ. Dotted lines: assuming no density independence (λ = 1), the curve is forced to go through (k₁₂ = 0, N = 0), showing strong density dependence with α₁₂ = 0.229 ± 0.251 and β₁₂ = 0.302 ± 0.129 (Dye 1984b). Dashed lines: first step of the two-step approach, assuming a linear relationship between k and N to estimate λ = 0.126 ± 0.052. Solid lines: second step using the value of λ = 0.126 to estimate α₁₂ = 3.518 ×10⁻⁴ ± 14.36 × 10⁻⁴ and β₁₂ = 0.922 ± 0.474, showing weaker (nonsignificant) density dependence. (Top) k₁₂ plotted against N. (Bottom) k₁₂ plotted against ln(N). On the bottom panel, density dependence is undercompensatory if the slope of the curve is <1, exactly compensatory if the slope = 1, and overcompensatory if the slope is >1.

Fig. 2

Estimating the parameters describing density dependence in k₁₂ mortality with 500 additional artificial data points (see text). + signs mark the original nine points from the study of Southwood et al. × signs mark the artificial added points. Dot-dashed lines are the best-fit curves based on the original nine points, from which the artificial points are generated. Solid lines are the new fits based on all 509 points. (A) Artificial points are generated using the parameter values in equation 5, assuming λ₁₂ = 1. (B) Artificial points are generated using the parameter values in equations 6 and 7, based on the two-step method and assuming λ₁₂ = 0.126. Note that the dot-dashed line in A corresponds to the dotted line in Fig. 1, and the dot-dashed line in B corresponds to the solid line in Fig. 1.

Fig. 3

Sensitivity of the goodness-of-fit (sum of squared error [SSE]) to the parameters α and β, when the model in equation 1 is fitted to the artificial 509-point datasets. (A) Using the dataset in which artificial points are generated according to equation 5, assuming no density-independent mortality (λ = 1). (B) Using the dataset in which artificial points are generated according to equations 6 and 7, assuming some level of density-independent mortality (λ = 0.126). Note that the scale of the SSE axis is the same in both panels. Regression analysis involves finding the lowest point on this surface, that is, the set of parameters that minimizes SSE.