Heterogeneity in hidden developmental processes: interference and analysis for stage-structured populations in fluctuating environments

In this work, I present a new matrix-based model for biological stage-structured populations (SSPs) that greatly improves the characterisation of variation in development times by tracking individual histories within each stage. Neglecting such heterogeneity has historically limited the realism and predictive performance of most SSP modelling approaches. The key idea of the new model is to augment a classic Lefkovitch matrix with stage-specific integral projection models (IPMs) that track within-stage dynamics. This new “integral projection Lefkovitch matrix” (IPLM) model drastically reduces stage-duration errors; is robust to stage distribution instabilities arising from perturbations; permits parsimonious parameterisation with random variables or time-varying covariates; and can be fitted, even when within-stage development is unmeasurable, using developmental cohort data. By using maturation-time (and not size) data, our methods greatly improve the precision of stage-structured IPMs whenever size is a poor, or unavailable, predictor of stage duration. This scenario is ubiquitous in ecology: egg (e.g. fish, bird, insects) and exoskeleton (e.g. Ecdysozoa) dimensions often remain relatively constant, and more appropriate developmental metrics can be too expensive or difficult to collect routinely. Furthermore, by incorporating a combination of laboratory and field data, Bayesian methods permit the estimation of cryptic parameters in natura, such as the strength of regulatory density-dependent mechanisms or environmental stochasticity in vital rates. Thus, by assimilating time series data – even of incomplete life-cycles – IPLMs permit upscaling from the laboratory to the field. Initially, the identifiability of IPLM parameters is studied with simulated data from marked cohort studies where individual qualities correlate maturation-times. Results demonstrate that accurate sojourn-time distributions are reproduced even from small samples. Next, a temperature-dependent model is fitted to Culicoides (biting midge) unmarked laboratory cohort data to assess the relative role of transient and asymptotic dynamics in constant and seasonal climates. Results demonstrate that the traditional negligence of individual developmental heterogeneity affects asymptotic dynamic metrics in various ways and greatly underestimates the importance (both amplitude and duration) of transient dynamics. Three applications/extensions of the Culicoides IPLM are studied. First, the fitted model is used to assess the validity and robustness of linearity assumptions of classic degree-day insect development models. Results show that linearity only provides a robust developmental model over extremely narrow temperature intervals. Secondly, projections of adult densities are used to assess transient and asymptotic dynamics in the basic reproduction ratio (R 0) of bluetongue following the initialisation of a hypothetical adulticide-based vector control program. Results show that R 0 drops suddenly following a reduction in adult survival. But this is only a transitory effect when the vector population growth rate is not brought below one. Whether or not, and for how long, a given adulticide can maintain R 0 < 1 is temperature dependent, a result that has implications for integrated vector management. Finally, the Culicoides IPLM is used to construct a state-space model (SSM) for analysing typical multi- annual time series data from vector abundance studies. With simulated time-series of weekly adult flight-trap data, the SSM is used to explore the identifiability of key cryptic parameters in natura, including the level of environmental stochasticity in mortality; the strength of density dependent mortality among larvae; the initial population density; and the expected efficiency of flight-traps. Results show that when flight-trap efficiency is known, the parameters are identifiable to a high level of precision using simulated weekly trap counts over three years. However, when trying to estimate flight-trap efficiency, a very strong correlation with the density- dependence parameter is detected, suggesting that additional data sources are required to calibrate the model for epidemiological purposes. Applications for many state-structured populations - particularly those where cryptic developmental status has to date prevented study with IPMs - are foreseen in fields including ecological forecasting, mechanistic niche modelling, demographic compensation studies or eco-evolutionary analysis. Diverse applications are expected for conservation, agricultural, epidemiological or theoretical purposes. (Resume d'auteur)