[Journal of Agricultural, Biological and Environmental Statistics, 16 November 2023]

The management of forest pests relies on an accurate understanding of the species’ phenology. Thermal performance curves (TPCs) have traditionally been used to model insect phenology. Many such models have been proposed and fitted to data from both wild and laboratory-reared populations. Using Hamiltonian Monte Carlo for estimation, we implement and fit an individual-level, Bayesian hierarchical model of insect development to the observed larval stage durations of a population reared in a laboratory at constant temperatures. This hierarchical model handles interval censoring and temperature transfers between two constant temperatures during rearing. It also incorporates individual variation, quadratic variation in development rates across insects’ larval stages, and “flexibility” parameters that allow for deviations from a parametric TPC. Using a Bayesian method ensures a proper propagation of parameter uncertainty into predictions and provides insights into the model at hand. The model is applied to a population of eastern spruce budworm (Choristoneura fumiferana) reared at 7 constant temperatures. Resulting posterior distributions can be incorporated into a workflow that provides prediction intervals for the timing of life stages under different temperature regimes. We provide a basic example for the spruce budworm using a year of hourly temperature data from Timmins, Ontario, Canada. Supplementary materials accompanying this paper appear on-line.

[Bulletin of Mathematical Biology, 29 September 2023]

Mountain pine beetle (MPB) in Canada have spread well beyond their historical range. Accurate modelling of the long-term dynamics of MPB is critical for assessing the risk of further expansion and informing management strategies, particularly in the context of climate change and variable forest resilience. Most previous models have focused on capturing a single outbreak without tree replacement. While these models are useful for understanding MPB biology and outbreak dynamics, they cannot accurately model long-term forest dynamics. Past models that incorporate forest growth tend to simplify beetle dynamics. We present a new model that couples forest growth to MPB population dynamics and accurately captures key aspects of MPB biology, including a threshold for the number of beetles needed to overcome tree defenses and beetle aggregation that facilitates mass attacks. These mechanisms lead to a demographic Allee effect, which is known to be important in beetle population dynamics. We show that as forest resilience decreases, a fold bifurcation emerges and there is a stable fixed point with a non-zero MPB population. We derive conditions for the existence of this equilibrium. We then simulate biologically relevant scenarios and show that the beetle population approaches this equilibrium with transient boom and bust cycles with period related to the time of forest recovery. As forest resilience decreases, the Allee threshold also decreases. Thus, if host resilience decreases under climate change, for example under increased stress from drought, then the lower Allee threshold makes transient outbreaks more likely to occur in the future.

[Ecological Modelling, 31 July 2023]

Populations of wild insect pollinators such as bumble bees are threatened worldwide, which compromises pollinator-dependent crop yields. Intentionally planting wildflower patches in agricultural landscapes can support these populations and increase the pollination of nearby crops via the “spillover effect” (i.e., the exporter hypothesis), but may also distract bees from the crops and reduce their pollination via the “Circe principle” (i.e., the aggregation hypothesis). Considering the potentially high costs of these management strategies and the necessity to support wild insect pollinators in the Anthropocene, there is a pressing need to provide simulation tools that can inform best practices for wildflower plantings in agro-ecosystems. We developed a spatially implicit ordinary differential equations (ODEs) model specifically designed to determine the optimal wildflower-to-crop ratio as a function of wildflower patch (i) attractiveness, (ii) nutritional benefits, and (iii) blooming period relative to the crop. The model represents the population dynamics of a bumble bee colony and floral resources (crop and wildflower) in the landscape and nest during one harvesting season. We conduct a full factorial simulation experiment to identify the optimal characteristics of the wildflower patch (i.e., blooming period, attractiveness, relative abundance) that maximise crop yield via the enhancement of the number of bees pollinating crop flowers in a fictional blueberry farm. Our results suggest that providing highly attractive and nutritive wildflower resources before and not during the crop blooming season is the most beneficial strategy. When both flower types are in competition, pollination services can decrease, either when wildflowers are too attractive, or if they provide less benefits to the bees than the crop due to a trade-off between resources quality versus quantity.