Fig 1.
Experimental data on development time and survival.
(A) Development time, in days, of mosquitoes across all experiments, categorized by (left) sex and (right) density treatment. (B) Development time by mass group and density treatment. Box plots of each mass group emerging under (left) low density and (right) high density treatments. This includes mass data, but excludes stage data. In (A)-(B) red lines represent the median of the data; the blue box indicates the upper and lower limits of the interquartile range (IQR); whiskers indicate 2*IQR; and red plus signs represent outliers. (C) The proportion of mosquitoes which survive by density treatment and sex for each replicate of the low (left) and high (middle) density treatments. The mean and median survival proportion for all experiments by density (right). In (C), blue triangles represent females and red triangles males. The experiments are sorted by female survival proportion, where we assume 50% males and 50% females initially. As individual replicates may differ in their initial sex percentages, some calculated survival proportions are greater than one. (D) Female mosquito emergence by body mass group: < 1.5 mg (small) in blue, 1.5–2.5 mg (medium) in green and > 2.5 mg (large) in red. The top row is the low density treatment and the bottom row is high density.
Table 1.
Mosquito emergence by body mass in low and high density conditions.
The number (percentage) of mosquitoes in each body mass group: <1.5 mg (small), 1.5–2.5 mg (medium), and >2.5 mg (large) divided by environmental conditions: low density and high density. A histogram of masses by density treatment is found in Fig 1D.
Fig 2.
Model formulation and variations.
(A) Schematic of our mathematical model describing stage and mass. As an individual moves horizontally (age axis), it advances to a later biological stage from larval stages 1 to 4 to pupae to adult. As an individual moves vertically (mass axis), it grows larger in mass. (B) Flow chart of each variation considered. The first variation (top row) is in regards to the number of compartments. We include 5, 6, or 7 total compartments, in C1, C2, and C3 respectively. The second variation is in mortality: single constant death (D1), two constant deaths for each of male and female (D2), and a density-dependent death for females and constant death for males (D3). The third variation is the inclusion of a growth function, E. The darker boxes are the version of each variation chosen as best based on the AIC. See section 2.4 for description of the fitting.
Table 2.
For each parameter, we include its representative symbol, a description, the standard value used, and the range of values considered. For parameters with a value given, we used that value during the fitting process, but performed univariate sensitivity. For parameters marked fitted, the range listed under variation is the constraint when fitting using MatLab function fmincon.
Fig 3.
Fitting results for compartment versions, C1-C3.
(A) Data and model output in the high density (top row) and low density (bottom row) treatments. The results are split by sex: males (left column) and females (right column). Each panel shows the number of adults that emerged on a given day. The gray lines each represent an individual experimental replicate. For the model, the only difference between low and high density treatments is that the initial values are different. The best fit for: C1, the base model with only one compartment per biological stage (dashed dotted green line); C2, including a second compartment for pupae (dashed maroon line); and C3, including second compartments for both pupae and L4 (solid blue line). (B) Model output in version C3, where both L4 and pupae have two compartments, in high density (top row) or low density (bottom row) treatments. From left to right, the panels show: combined L1 and L2 stages; L3 stage; L4 stage; pupae; emerging males; and emerging females. Each gray line is an experimental replicate.
Fig 4.
Total survival proportion by sex and density treatment for experimental data and model versions D1-D3.
Survival proportion of males (red) and females (blue). The model (D1-D3) under low density (left) and high density (right) treatments. On the far right of each panel, the values for median and mean of all 13 high and 20 low density replicates, with dashed lines indicating one quartile above and below the median and one standard deviation around the mean.
Fig 5.
Fitting results for inclusion of the growth function, variation E.
(A) The proportion of emerged females in a particular mass group is represented on the x-axis, and the mass group of these females on the y-axis. The green diamond is the best fit model. The median of the data is represented with a purple triangle with a dashed line for one quartile above and below. The blue triangle represents the mean of the data, and the dashed line is one standard deviation around the mean. The left panel is low density and right is high density. (B) Proportion of females that emerge from each mass group through time: small (left), medium (middle), large (right). The top row is high density and the bottom is low density. The model output is in solid blue. Individual replicates of the data are in gray.
Fig 6.
Proportion of females that emerge as resource usage rate, q, varies.
(A) Simulated available resources throughout the time of the experiment for different values of q. (B) The proportion of emerging females in each mass group as q varies. Blue, red, and gold represent small, medium, and large mass groups, respectively. The black dashed lines indicate the divisions at which different mass groups were expected based on means of proportions of the mass groups from the data. In particular, the lower dashed line separates small and medium mosquitoes, and the upper dashed line separates medium and large mosquitoes. For close fits to the data, the blue bar would be below the lower dashed line, the red bar would be entirely between the two dashed lines, and the gold bar would be above the higher dashed line. (C) The proportion of females emerging over time by mass group: small (left), medium (middle), and large (right). The top row is the high density treatment, and the bottom row is the low density treatment. The solid color lines are model output with different q values. The black dashed line represents the mean of the data.
Table 3.
AICc values for density-dependent functions with different parameters.
The original parameter choice was a = 0.0043 and b = 1.61. We then consider a = 0.001 and a = 0.01, each with b = 1.61, as well as b = 1 and b = 2, each with a = 0.0043.