Modeling the Effects of Developmental Variation on Insect Phenology

Abstract

Phenology, the timing of developmental events such as oviposition or pupation, is highly dependent on temperature; since insects are ectotherms, the time it takes them to complete a life stage (development time) depends on the temperatures they experience. This dependence varies within and between populations due to variation among individuals that is fixed within a life stage (giving rise to what we call persistent variation) and variation from random effects within a life stage (giving rise to what we call random variation). It is important to understand how both types of variation affect phenology if we are to predict the effects of climate change on insect populations.We present three nested phenology models incorporating increasing levels of variation. First, we derive an advection equation to describe the temperature-dependent development of a population with no variation in development time. This model is extended to incorporate persistent variation by introducing a developmental phenotype that varies within a population, yielding a phenotype-dependent advection equation. This is further extended by including a diffusion term describing random variation in a phenotype-dependent Fokker-Planck development equation. These models are also novel because they are formulated in terms of development time rather than developmental rate; development time can be measured directly in the laboratory, whereas developmental rate is calculated by transforming laboratory data. We fit the phenology models to development time data for mountain pine beetles (MPB) (Dendroctonus ponderosae Hopkins [Coleoptera: Scolytidae]) held at constant temperatures in laboratory experiments. The nested models are parameterized using a maximum likelihood approach. The results of the parameterization show that the phenotype-dependent advection model provides the best fit to laboratory data, suggesting that MPB phenology may be adequately described in terms of persistent variation alone. MPB phenology is simulated using phloem temperatures and attack time distributions measured in central Idaho. The resulting emergence time distributions compare favorably to field observations.

Development and validation of a phenological model for the univoltine European corn borer

“…The variability in development has also been represented using different approaches (Gilbert et al. ; Yurk and Powell ). The distributed delay approach (Manetsch ; Plant and Wilson ) was previously implemented in our modelling environment with satisfaction (Graf et al.…”

“…A linear relationship has the advantage of simplicity and validity in most cases (Matteson and Decker 1965;Kelker et al 1990). The variability in development has also been represented using different approaches (Gilbert et al 2004;Yurk and Powell 2010). The distributed delay approach (Manetsch 1976;Plant and Wilson 1986) was previously implemented in our modelling environment with satisfaction (Graf et al 1996;Schaub et al 2005;Samietz et al 2007).…”

Quantitative and qualitative dynamics of exotic and native blowflies (Diptera: Calliphoridae) with migrations among municipalities

“…Ecological modeling has been used to show population oscillations or persistence patterns of insects in both the laboratory and the field (Desharnais 2005). Population models extract information from laboratory experiments in order to investigate specific ecological aspects that are important for conservation and pest control (Yurk and Powell 2010). Field studies are important to supply models with data describing more realistic situations, in order to confirm patterns obtained in the laboratory or to compare results by using analytical tools (Petrovskii et al 2012).…”

“…Dynamic behavior of insects has been assessed by using models that explore the association between stability and magnitude of demographic parameter values, resulting in complex patterns in response to population growth (Desharnais 2005). Particularly, population dynamics has been strongly linked to laboratory ecology by the use of models, which have been particularly useful for understanding development, persistence, life history, foraging, demography, nonlinear dynamics, evolutionary dy-namics and parasitism (Burd and Howard 2005, Desharnais 2005, Yurk and Powell 2010. Modeling focused on field studies has more recently been emphasizing swarm systems, foraging environment, epidemics and insect outbreaks (Fuller et al 2012, Granovskiy et al 2012, Hamann and Schmickl 2012.…”

Economic Effect of Insect Pest Management Strategies on Small-scale Tomato Production in Mississippi

“…Thus, plant phenology may influence pest populations because of factors such as maturation date, which vary according to plant cultivar. In addition, pest population development is favored by high temperatures and plant cultivars that vary in their development time may experience differing levels of pest pressure (Yurk and Powell, 2010). Under field conditions, temperature and relative humidity have been shown to affect populations of tomato pests such as aphids (Aphidoidea) and whiteflies (Aleyrodidae) (Waluniba and Alemla Ao, 2014).…”