We used life tables to model rates of population growth when egg cannibalism by specific life stages increases developmental rate and/or fecundity, using aphidophagous coccinellids as a model system. The uploaded files contain the raw data used to delimit parameters of the model, data obtained from previously published observations on Hippodamia convergens (RawData). The oviposition period and daily fecundity followed Weibull and negative binomial distributions (see uploaded CSV files), respectively. The uploaded files do not contain the data generated by life table model simulations, as these can be obtained by anyone choosing to run the simulations.

The probability that a female survives and oviposits on a given day was defined as a Weibull function:

P(t)= exp(- t/b)^c                                                                                                                    Eq. 1

where t is female age at oviposition, p denotes probability, b and c are parameters, and exp is the base of natural logarithms. b and c were estimated to be 24.9 and 1.77, respectively (F_1,53 = 50.50, p < 0.001, R² = 0953, Suppl. Figure 1).

To fit a suitable function to fecundity data, the age-dependence of per capita daily fecundity data was characterized by regressing the number of eggs laid over female age. A very poor, but significant, linear relationship was observed (F_1,460 = 5.25, p = 0.0223, R² = 0.0113) and, for the sake of simplicity, was ignored in the simulation. The observed frequency distribution of female daily fecundities was then fitted to a negative binomial function, which was used to predict the probability of observing x number of eggs (x = 0, 1, 2, …) (Suppl. Figure 1B). First, the sample mean ( and variance (S²) of the daily per capita fecundities was obtained, and then parameters K and C of the negative binomial function were obtained from Eqs. 2 and 3:

• Equation 2: K = \frac{\bar{X}^2}{S^2 - \bar{X}}
• Equation 3: C = K/\bar{X}

The probability of observing X eggs was then obtained using Eq. 4 (Southwood & Henderson, 2009):

p^k{1, kq, [k(k+1)/2!]q², [k(k+1)(k+2)/3!]q³...}

where p = c/(c+1), and q = 1-p. For the first observation, P(0) = p^k was calculated, and subsequent probabilities were obtained using Eq. 5:

P(x) = p(x-1)(k+x-1)q/(x!)

Cumulative probabilities were then obtained by summing simple probabilities over ages to achieve unity and, for simulation purposes, random probabilities were assigned for each female from a cohort as large as 100, with the number of eggs randomly assigned. For example, the cumulative probabilities of observing 15 and 16 eggs were 0.21871, and 0.24798, respectively; therefore, a random intermediate value suggests an individual will lay 15 eggs.

In order to construct a cohort-life table, stage-specific immature survival rates and developmental times were similarly assigned by random probabilities and a normal function for developmental time was assigned a value of 20 ± 0.7 d (mean ± SD). Immature development was split into 3.0 ± 0.2, 3.2 ± 0.2, 2.2 ± 0.2, 2.2 ± 0.2 and 4.4 ± 0.2 and 5.0 ± 0.25 d for eggs, L1, L2, L3, L4, and pupa, respectively, approximating median values observed for H. convergens fed S. graminum at 24 °C (Stowe et al., 2021). A 3.8 ± 0.2 d pre-oviposition period was added which corresponds to the mean time required for egg maturation when females have immediate access to aphid prey post-emergence (Vargas et al., 2012). Stage-specific survival rates, p_x were considered to be 93.2, 86.0, and 98.5% for survivorship of eggs, larvae and pupae, respectively (typical values observed under laboratory conditions), and were multiplied sequentially to obtain l_x (per-radix-survival).