RDA-PSO: A computational method to quantify the diffusive dispersal of insects

TL;DR

This work tackles the challenge of quantifying diffusive dispersal of insects from mark-release-recapture data by estimating the diffusion coefficient $D$. It introduces the Recapture of Diffusive Agents–Particle Swarm Optimization (RDA-PSO) method, an agent-based forward model combined with grid search and PSO to infer diffusion parameters from temporal and spatial recapture ratios, proving robustness to low recapture rates and uneven trap layouts. The study compares RDA-PSO against MDT-based, time-corrected (TC), and area-and-time-corrected (ATC) approaches, showing RDA-PSO yields more accurate $D$ estimates on synthetic data and field datasets, with k estimates normally distributed and trap-parameter interdependencies not compromising $D_{RDA}$. The results highlight the value of a discrete, optimization-based diffusion framework for informing vector-dynamics models and disease-risk assessments, especially in settings with sparse and nonuniform sampling. The method offers practical potential for guiding vector-control strategies and can be extended to incorporate wind, spatial heterogeneity, and more complex attractor landscapes.

Abstract

This article introduces a computational method, called "Recapture of Diffusive Agents & Particle Swarm Optimization" (RDA-PSO), designed to estimate the dispersal parameter of diffusive insects in mark-release-recapture (MRR) field experiments. In addition to describing the method, its properties are discussed, with particular focus on robustness in estimating the observed diffusion coefficient in the presence of uncertainty. It is shown that RDA-PSO provides a simple and reliable approach to quantify insect dispersal that can handle low recapture rates and uneven capture site distributions without the need for area corrections. Tests on synthetic data, for which the actual diffusion coefficient is known, show the method outperforms three techniques based on the solution of the diffusion equation, which are also introduced in this work. Examples of application to real field data for the yellow fever mosquito are provided.

Figures (15)

• Figure 1: Results of the RDA-PSO method with tables \ref{['tab:capture-table-temporal']} and \ref{['tab:capture-table-spatial']} as input. Each returned optimal parameter 4-tuple, $({\tt k}, {\tt q}, {\tt p}, {\tt s}_{\tt e})$, is represented as a set of 3 points, $({\tt k}, {\tt q})$ (blue circles), $({\tt k}, {\tt p})$ (red squares), and $({\tt k}, {\tt s}_{\tt e})$ (yellow multiplication signs). The corresponding error is also plotted as a function of k (purple dots). Out of 500 parameter tuples obtained, those associated with an error one half standard deviation (Cairns) or one standard deviation (Hainan) above the mean are considered outliers and were removed. Left panel: Parameter estimation for the Hainan MRR experiment with release point at the center of the village. About 14.8% of the returned 4-tuples were considered outliers and are not plotted. Middle panel: Parameter estimation for the Hainan MRR experiment with release point at the periphery of the village (percentage of not-plotted outliers: 14.2%). Right panel: Parameter estimation for the Cairns MRR experiment (percentage of not-plotted outliers: 29.4%)
• Figure 2: Empirical distributions of the k values obtained in Figure \ref{['fig:PSO-Hainan-Cairns-Parameters-4-nRuns-500-nPart-36-nGens-12-par']}. The top row shows the normalized histogram of k along with the normal distribution curve (in red) with the same mean and standard deviation as the k data. The bottom row shows the quantiles of k versus the theoretical quantile values from a normal distribution. Left: Hainan, center; middle: Hainan, edge; right: Cairns
• Figure 3: Left panel: Plot of d/$\zeta$ (see Equation \ref{['eq:step_length']}) as a function of $\phi$ for a walker located at $(x, y) = (2,0)$, assuming the trap center is at $(x_0, y_0) = (0,0)$. We let $\alpha = 0.2$, which leads to dBase = 0.0247. Top right panel: Range of the step sizes d as a function of the distance $r$ between the walker location and the center of a capture site. The vertical segment at OR/3 shows the range with largest extent. The exact value of d depends on the angle $\phi$. Bottom right panel: Possible steps taken within a trap of outer radius OR = 10. The red dots represent a walker's current location. The blue circles around each red dot visualize how far the walker would move if it were to head in that specific direction
• Figure 4: Left panel: Virtual map with 5 capture sites per region of size 100 m $\times$ 100 m. Margins equal to 150 m are shown on all sides. Right panel: Concentric zones of width 50 m superimposed on the capture sites shown in the left panel. In this example, there are 5, 9, 22, 25, and 39 capture sites in zones 1 through 5, respectively
• Figure 5: Left panel: Error landscape produced by the grid search for the synthetic data of Table \ref{['tab:capture-table-virtual']}. The error $E$ is calculated over a uniform mesh of size $51 \times 21$, with values of k in the interval $[50, 150]$ and values of q in the interval $[10, 50]$. Note that the surface is plotted using cubic interpolation over the actual data. Right panel: Contour plot of $E$ showing the estimated minimizer (red star) near k = 100 and q = 30. Here, the parameter p is set at ${\tt p} = 0$ and the trap efficiency at ${\tt s}_{\tt e} = 100$ %