Lethal and sublethal effects of toxicants on bumble bee populations: a modelling approach.

Pollinator decline worldwide is well-documented; globally, chemical pesticides (especially the class of pesticides known as neonicotinoids) have been implicated in hymenopteran decline, but the mechanics and drivers of population trends and dynamics of wild bees is poorly understood. Declines and shifts in community composition of bumble bees (Bombus spp.) have been documented in North America and Europe, with a suite of lethal and sub-lethal effects of pesticides on bumble bee populations documented. We employ a mathematical model parameterized with values taken from the literature that uses differential equations to track bumble bee populations through time in order to attain a better understanding of toxicant effects on a developing colony of bumble bees. We use a delay differential equation (DDE) model, which requires fewer parameter estimations than agent-based models while affording us the ability to explicitly describe the effect of larval incubation and colony history on population outcomes. We explore how both lethal and sublethal effects such as reduced foraging ability may combine to affect population outcomes, and discuss the implications for the protection and conservation of ecosystem services.

Optimal design for dynamical modeling of pest populations.

We apply SE-optimal design methodology to investigate optimal data collection procedures as a first step in investigating information content in ecoinformatics data sets. To illustrate ideas we use a simple phenomenological citrus red mite population model for pest dynamics. First the optimal sampling distributions for a varying number of data points are determined. We then analyze these optimal distributions by comparing the standard errors of parameter estimates corresponding to each distribution. This allows us to investigate how many data are required to have confidence in model parameter estimates in order to employ dynamical modeling to infer population dynamics. Our results suggest that a field researcher should collect at least 12 data points at the optimal times. Data collected according to this procedure along with dynamical modeling will allow us to estimate population dynamics from presence/absence-based data sets through the development of a scaling relationship. These Likert-type data sets are commonly collected by agricultural pest management consultants and are increasingly being used in ecoinformatics studies. By applying mathematical modeling with the relationship scale from the new data, we can then explore important integrated pest management questions using past and future presence/absence data sets.

From theory to experimental design-Quantifying a trait-based theory of predator-prey dynamics.

Successfully applying theoretical models to natural communities and predicting ecosystem behavior under changing conditions is the backbone of predictive ecology. However, the experiments required to test these models are dictated by practical constraints, and models are often opportunistically validated against data for which they were never intended. Alternatively, we can inform and improve experimental design by an in-depth pre-experimental analysis of the model, generating experiments better targeted at testing the validity of a theory. Here, we describe this process for a specific experiment. Starting from food web ecological theory, we formulate a model and design an experiment to optimally test the validity of the theory, supplementing traditional design considerations with model analysis. The experiment itself will be run and described in a separate paper. The theory we test is that trophic population dynamics are dictated by species traits, and we study this in a community of terrestrial arthropods. We depart from the Allometric Trophic Network (ATN) model and hypothesize that including habitat use, in addition to body mass, is necessary to better model trophic interactions. We therefore formulate new terms which account for micro-habitat use as well as intra- and interspecific interference in the ATN model. We design an experiment and an effective sampling regime to test this model and the underlying assumptions about the traits dominating trophic interactions. We arrive at a detailed sampling protocol to maximize information content in the empirical data obtained from the experiment and, relying on theoretical analysis of the proposed model, explore potential shortcomings of our design. Consequently, since this is a "pre-experimental" exercise aimed at improving the links between hypothesis formulation, model construction, experimental design and data collection, we hasten to publish our findings before analyzing data from the actual experiment, thus setting the stage for strong inference.

Modelling populations of Lygus hesperus on cotton fields in the San Joaquin Valley of California: the importance of statistical and mathematical model choice.

Understanding the population dynamics of herbivorous insects is critical to developing and implementing effective pest control protocols. In the context of inverse problems, we explore the dynamic effects of pesticide treatments on Lygus hesperus, a common pest of cotton in the western United States. Fitting models to field data, we explore the topic of model selection for an appropriate mathematical model and corresponding statistical models, and use techniques including ANOVA-based model comparison tests and residual plot analysis to make the best selections. In addition we explore the topic of data information content: in this example, we are testing the question of whether data, as it is currently collected, can support time-dependent parameter estimation. Furthermore, we investigate the statistical assumptions often haphazardly made in the process of parameter estimation and consider the implications of unfounded assumptions.

Model Comparison Tests to Determine Data Information Content.

In the context of inverse or parameter estimation problems we demonstrate the use of statistically based model comparison tests in several examples of practical interest. In these examples we are interested in questions related to information content of a particular given data set and whether the data will support a more complicated model to describe it. In the first example we compare fits for several different models to describe simple decay in a size histogram for aggregates in amyloid fibril formation. In a second example we investigate whether the information content in data sets for the pest Lygus hesperus in cotton fields as it is currently collected is sufficient to support a model in which one distinguishes between nymphs and adults. Finally in a third example with data for patients having undergone an organ transplant, we question whether the data content is sufficient to estimate more than 5 of the fundamental parameters in a particular dynamic model.

Using semifield studies to examine the effects of pesticides on mobile terrestrial invertebrates.

Many farmers rely on regular pesticide applications to avoid losses from arthropod pests and the diseases they vector. However, widespread and injudicious use of pesticides is detrimental to the environment, poses a health risk, and undermines biocontrol services. Researchers are increasingly required to develop techniques to quantify the trade-offs and risks associated with pesticides. Laboratory studies, though useful for assessing short-term impacts (e.g., mortality), cannot detect longer-term or indirect effects that can potentially be assessed using semifield studies. Here we review the range and scope of studies that have used semifield methods for regulatory testing and risk assessment of pesticides and for understanding the community-level effects of pesticide use in agricultural landscapes. We include studies on target and nontarget species, with an emphasis on quantifying effects when the target species is highly mobile. We suggest improvements in the design and analysis of semifield studies to more effectively assess effects on highly mobile species.

Population dynamics models in plant-insect herbivore-pesticide interactions.

We consider several population dynamics models in investigating data from controlled experiments with aphids in broccoli patches surrounded by different margin types (bare or weedy ground) and three levels of insecticide spray (no, light, or heavy spray). We carry out parameter estimation computations along with statistical analysis to compare autonomous versus non-autonomous model dynamics. We conclude with a brief discussion of some not-so-subtle pitfalls that can arise when using quantitative measures of model fit-to-data to make biological inferences as well as offer a positive example of how one might combine a priori biological hypothesis and intuition with rather sophisticated (from a field biology viewpoint) mathematical methodologies to suggest synergisms.