2.2.3 Death proportion

A proportion of individuals from each compartment die each day. In an initial pass, the death proportion for each day is taken directly from the experimental data. In this case, we compare each replicate separately and use the proportion of individuals that die each day from that specific replicate. We use the daily death proportions by replicate to fit the development time. After we fit the daily maximum development proportion (k_m, k_f, see section 2.4.1), we combine data on mortality from all replicates and fit a single constant for the death proportion.

We then consider a density-dependent death function for females. In the experiments, we observed that females had greater survival in low density compared to high density (Fig 1C). While males showed a similar trend as females, the difference observed between low and high density treatments was not statistically significant. Thus, we do not consider density-dependent mortality for males. To incorporate density dependence into our death function for females, we use a Hill function, given by

where n = 3 is the Hill exponent, h and f are constants such that h < f and μfhf3 is the minimum proportion of individuals that die and μ_f is the maximum proportion. The inclusion of the h in the numerator, a departure from a traditional Hill function, allows the lower bound of the function to be greater than zero. If h equals zero, this returns the traditional Hill function. We fix h = 100, so that the lower bound is 100μff3. See section 3.4.4 for more discussion and a sensitivity analysis of f.