Fig 1.
Mosquito life history and spatial structure.
In the lumped age-class model, mosquitoes are divided into four life stages: egg, larva, pupa and adult (A). The durations of the sub-adult stages are TE, TL and TP for eggs, larvae and pupae, respectively. Sex is modeled at the adult stage, with half of pupae developing into females and half developing into males. Daily mortality rates vary by life stage - ,
,
and
for eggs, larvae, pupae and adults, respectively. Density-dependent mortality occurs at the larval stage and is a function of the total number of larvae, NL. Females mate once upon emergence, and retain the genetic material from that mating event for the remainder of their lives. Males mate at a rate equal to the female emergence rate. Females lay eggs at a rate, β. In the spatial extension of the lumped age-class model, mosquito populations are distributed in space, with movement between them defined by an exponential (solid line) or zero-inflated exponential dispersal kernel (dashed lines) (B). The daily probability of remaining in the same population, p0, is varied while preserving the mean dispersal distance. This value is trimmed from the plot, but specified in the key. Mosquito populations are distributed according to a 19-by-19 grid of households (circles), with mosquito traps distributed in select households (black circles) according to the sampling scheme (C). In some simulations and analyses, a barrier to movement is included (solid line) (D).
Table 1.
Demographic, life history and dispersal parameters for Aedes aegypti mosquitoes.
Table 2.
Kinship categories, sampled life stages, sampling times, locations, and probability symbols used in spatial close-kin mark-recapture analysis.
Fig 2.
Schematic representation of spatial mother-larval offspring kinship probability.
Parameters and state variables are as defined in Table 1 and Sect 2.1. Subscript 1 refers to the parent, and subscript 2 refers to the offspring (the perspective from which probabilities are calculated). Circles represent living individuals, squares represent sampled individuals, and colors represent their locations: blue for the sampled parent, x1, and purple for the sampled offspring, x2. Parents are sampled on day t1, eggs are laid on day y2, and offspring are sampled on day t2. Offspring kinship probabilities are the ratio of the expected number of surviving offspring from a given adult at location x2 on day t2, and the expected number of surviving offspring from all adult females for this location and day. Calculating the expected number of surviving larval offspring at location x2 on day t2 from an adult female requires considering days of egg-laying, y2, consistent with maternal ages at sampling in the range [0,TA), and larval offspring ages at sampling in the range [0,TL). The only movement to consider is that of the mother (orange arrow).
Fig 3.
Schematic representation of spatial adult-adult full-sibling kinship probabilities.
Parameters and state variables are as defined in Table 1 and Sect 2.2. Subscript 1 refers to the reference sibling, and subscript 2 refers to the sibling from whose perspective the probabilities are calculated. Circles represent living individuals, squares represent sampled individuals, and colors represent their locations: blue for sibling 1, x1, purple for sibling 2, x2, grey for the location of egg-laying for sibling 1, and pink for the location of egg-laying for sibling 2. The location of egg-laying for the firstborn sibling (here, sibling 1) is denoted by x*, and denotes the egg-laying location for the other sibling. Sibling 1 is sampled on day t1 and laid on day y1. Sibling 2 is sampled on day t2 and laid on day y2. Sibling kinship probabilities are the ratio of the expected number of surviving siblings of a given individual at location x2 on day t2, and the expected number of surviving offspring from all adult females for this location and day. Calculating the expected number of surviving full-siblings at location x2 on day t2 requires considering days of egg-laying, y1 and y2, consistent with adult ages at sampling in the range [0,TA). There are three movements to consider: those of the mother and two adult siblings (orange arrows). Movement probabilities consider both orders of egg-laying.
Fig 4.
Sampling schemes to estimate for Ae. aegypti.
Violin plots depict estimates of for sampling scenarios described in Sect 3.1. The default simulated metapopulation consists of a 19-by-19 grid of households each inhabited by 25 adult Ae. aegypti at equilibrium with bionomic parameters listed in Table 1. Boxes depict median and interquartile ranges of 100 simulation-and-analysis replicates for each scenario, thin lines represent 5% and 95% quantiles, points represent outliers, and kernel density plots are superimposed. The initial sampling scheme consists of a total of 2,000 adult females sampled as ca. 2 individuals collected twice weekly over a three-month period for each trap node, considering a 6-by-6 array of trap nodes with one population node separating each trap node (Fig 1C). In panel (A), the number and spacing of trap nodes is varied (arranged in 4-by-4, 5-by-5 or 6-by-6 grids with zero, one or two population nodes separating each trap node). In panel (B), trap nodes are arranged in a 5-by-5 grid with two population nodes separating each trap node (Fig 1D), and total sample sizes of 1,500, 2,000, 2,500 and 3,000 are explored. In panel (C), a sample size of 2,500 is adopted, and three life stage proportions are explored: all larvae, all adult females, and half larvae/half adult females. The optimal sampling scheme consists of 2,500 adult females collected biweekly over a three-month period spread over a 5-by-5 grid of trap nodes with two population nodes separating each trap node. In panel (D), the optimal sampling scheme is adopted and a larger metapopulation consisting of a 37-by-37 grid of households is used to evaluate how far apart trap nodes may be placed (separated by 0-7 household nodes) while still obtaining reasonable estimates of
.
Fig 5.
Influence of false negative and false positive kinship pairs on estimation of .
Violin plots depict estimates of mean daily dispersal distance, , obtained using the spatial CKMR approach for the optimal sampling scheme determined in Sect 3.1. Two scenarios are explored: (A) in which 0-20% of mother-offspring and full-sibling pairs were decoupled at random (i.e., introducing false negatives), and (B) in which 0-20% of individuals without sampled mothers or full-siblings were assigned them at random (i.e., introducing false positives). The simulated metapopulation consists of a 19-by-19 grid of households each inhabited by 25 adult Ae. aegypti at equilibrium with bionomic parameters listed in Table 1. Boxes depict median and interquartile ranges of 100 simulation-and-analysis replicates for each scenario, thin lines represent 5% and 95% quantiles, points represent outliers, and kernel density plots are superimposed. The true value of
is depicted by a dotted line.
Fig 6.
Estimates of barrier strength and daily staying probability using spatial CKMR methods.
In the first (left) analysis, violin plots depict estimates of mean daily dispersal distance, (A), and barrier strength, δ (C), obtained using the spatial CKMR approach for the optimal sampling scheme determined in Sect 3.1, and considering a barrier to movement as depicted in Fig 1D whereby movement to the other side of the barrier is reduced by a factor, δ, in the range [0,0.9]. In the second (right) analysis, violin plots depict estimates of mean daily dispersal distance conditional upon movement,
(B), and daily staying probability, p0 (D), in the range [0.1,0.9], again obtained using the spatial CKMR approach for the optimal sampling scheme determined in Sect 3.1, and considering a zero-inflated dispersal kernel as described in Eq 2 and depicted in Fig 1B. The simulated metapopulation consists of a 19-by-19 grid of households each inhabited by 25 adult Ae. aegypti at equilibrium with bionomic parameters listed in Table 1. Boxes depict median and interquartile ranges of 100 simulation-and-analysis replicates for each scenario, thin lines represent 5% and 95% quantiles, points represent outliers, and kernel density plots are superimposed. True parameter values are depicted by triangles, or by a dotted line when they are consistent across all cases.