A new modelling approach to insect reproduction with same-shape reproduction distribution and rate summation: with particular reference to Russian wheat aphid.

Same-shape distribution model and rate summation approach are widely used to describe the insect developmental process. In this approach, by integrating a nonlinear deterministic developmental rate model and a probabilistic same-shape distribution model, the proportion of the cohort completing development is quantified as a function of accumulating developmental rates, which themselves are temperature dependent. This method is considered to be more accurate in modelling insect phenology because it can address a well-known biological fact, individual variability, that insect individual developmental rates respond to temperature differently, and because rate-summation essentially simulates developmental rates under variable temperatures instead of constant temperatures. By comparing insect development and reproduction with respect to their responses to temperatures, we argue for the extension of the same-shape and rate-summation approaches to modelling insect reproduction process under variable temperatures. We justify our arguments by the fact that individual variation universally exists in almost all biological characteristics, and the phenomenon that insect development and reproduction respond to temperature very similarly, which is supported by some endocrinological evidences reported in literature. In addition, the approach for testing the applicability of the original same-shape developmental modelling, experimentally verifying the sameness of the same-shape curves or that the shape of the curves is invariant with respect to the temperature regimes, equally applies to our extended version for reproduction modelling. We successfully tested the extension and its applicability with our experimental data of 1800 Russian wheat aphids' (RWA) (Diuraphis noxia (Mordvilko)) reproduction under various temperature and plant growth stage regimes. We also extended Taylor's (1981) nonlinear model for insect development to describe RWA mean (median) nymphal production under different temperatures and barley plant growth stages. Three same-shape distribution models, Weibull distribution, Stinner's model and logistic model, are used to construct the same-shape reproduction distribution models for RWA. The extensions performed in this paper contribute a new modelling approach for predicting insect reproduction under field variable temperatures and plant growth stages. The prediction model can be parameterized with data from typical laboratory demography experiments and further integrated into simulation models for insect population dynamics. Finally, we discussed why the sameness test of the same-shape distribution curves is sufficient in validating the approach and proposed a strategy for dealing with exceptional cases where the sameness test fails.