The stakes are considerable. Arthropod abundance has fallen dramatically worldwide, especially in farmed landscapes, and pollinators such as butterflies and bees have declined rapidly. The suspected drivers include agrochemical use, agricultural intensification, habitat degradation, parasites and pathogens, invasive species, poor nutrition and climate change. Because these factors co-vary and interact, the authors argue that only a broader system-based perspective can untangle the complexity and determine the relative importance of each stressor. Coupling a detailed spatiotemporal landscape model with agent-based population modelling has already proved useful for understanding populations under multiple stressors at large spatial and temporal scales.

Previous agent-based models of solitary bees have addressed parts of this problem but not all of it. The SOLBEE model simulates pollen-collecting solitary bees with different life history traits in a one-square-kilometre agricultural landscape, tracking pollination services within a single foraging day at one-second time steps, but it does not address population dynamics at larger scales. An earlier individual-based model of O. bicornis investigated long-term population development in response to fluctuating environmental conditions, yet simplified habitat quality and resource availability into cell construction time without considering the environmental factors affecting them. The new ALMaSS model, by contrast, will be the first fully spatially explicit one to model population-level responses to multiple factors at landscape scales of up to hundreds of square kilometres over periods of decades.

The technical foundation is an agent-based approach in which each bee is represented as a separate object with properties such as age and size, characteristics that influence foraging, dispersal, reproduction and provisioning, and therefore total reproductive potential, progeny sex ratio and cocoon mass. The model assumes that O. bicornis females balance offspring size and number following optimal allocation theory, with local environmental factors modifying the actual parental investment decisions. The ALMaSS environment provides a highly detailed dynamic landscape simulation with a one-square-metre raster land-cover map, accurate field maps grouped into farm units, individually tailored crop management plans including pesticide treatments, pluri-annual crop rotations, weather conditions and vegetation growth models, all updated daily.

The red mason bee is a univoltine species with one generation per year, common in central and northern Europe. Its flying season starts in spring and continues into early summer, with males appearing roughly a week earlier than females and living shorter lives; laboratory data show adult males developed in natural conditions may live up to 38 days and females up to 90 days. Development passes through six main life stages: egg, larva, prepupa, pupa, cocooned adult and adult. The first five occur inside the nest, and only the cocooned adult overwinters, emerging the following spring. The model will include all six life stages of female individuals, assume all adult females are fertilised, and omit males except for their role in the mother’s nesting and provisioning activities.

In-nest development will be temperature-driven. Transitions between the egg, larval and pupal stages will occur when the sum of effective temperatures, or accumulated degree days, reaches a threshold, with different lower developmental thresholds for each life stage. The prepupal stage, which lasts roughly one to three months depending on geography, will be related to temperature using a quadratic function with an optimum at 22 degrees Celsius, where maximal developmental speed of 24.3 days is reached, plus individual variation of about ten percent around that maximum. The duration of prepupal diapause is considered the main mechanism through which Osmia populations from different geographical areas synchronise adult eclosion with local temperature declines in autumn.

Overwintering will be divided into pre-wintering, diapause and post-diapause quiescence. The initiation of pre-wintering requires no temperature or photoperiod signal; it is a fixed component of the bee’s ontogenic programme. The transition to winter diapause, however, is triggered by low temperatures, and the model will detect a sharp and stable temperature drop after 1 September using rules based on temperatures currently experienced by the bees, so no prediction of future weather is required. Temperature conditions during pre-wintering will influence overwintering mortality, while conditions during diapause will determine the timing of spring emergence. Emergence will be related to accumulated degree days during wintering, following a linear relationship showing that the warmer the winter, the earlier bees start to emerge, with sigmoid-shaped cumulative emergence distributions implemented from laboratory data.

Body mass will be central to the model’s reproduction logic. The fresh mass of adult females after emergence varies from 25 to 150 milligrams and depends on the provision mass in the brood cell. The model will assume larvae consume all provided pollen, since under natural conditions incompletely used provisions rarely occur, and will calculate cocooned adult mass from provision mass using linear relationships, then adult mass from cocooned mass. Two size classifications of adult females will drive key decisions: a coarse four-class score determining the number of eggs in the first nest, and a finer score used for foraging and dispersal distances, planned sex ratio and the mass of provision needed for each egg. Reproductive potential, expressed as the total number of eggs a female can lay in her lifetime, will depend on her mass, and the sex ratio per nest will combine dependence on both maternal mass and reproductive age through a family of logistic curves.

Provisioning will follow a plan that can be deviated from. Each bee will carry a plan to build a set number of cells with a given sex ratio and target cocoon mass per cell, but landscape resource availability, weather and other factors mean execution is not guaranteed. Under optimal conditions a bee can fulfil her plan in the minimum effective cell construction time of five to six daylight hours, but if floral resources are suboptimal she will continue provisioning the same cell, raising the risk of parasitism, until either the maximum acceptable construction time of about 22.7 hours is reached or the planned provision is achieved. If a stopping rule triggers before the plan is achieved, a female egg will still be laid only if the provision exceeds a threshold; otherwise the bee switches to male eggs, which are cheaper, and abandons the nest location if the provision is too small even for a male.

Mortality and parasitism complete the picture. The model will apply constant daily mortality rates for the egg-to-cocoon and prepupa-to-pupa stages, overwintering mortality related to pre-wintering degree day accumulation, and a daily background mortality of 0.02 for adult females outside the nest. Parasitism will be simplified to open-cell parasitism, with probability increasing linearly with the time the brood cell remains open, following field observations that the longer a cell is open, the higher the risk from cleptoparasites such as the drosophilid fly Cacoxenus indagator and parasitoids such as the bombylid fly Anthrax anthrax. Nesting resources, identified as a limiting factor for local populations, will be evaluated as nest density per square metre of each landscape element based on cavity nesting suitability, while pollen resources for offspring will be sampled daily from the ALMaSS landscape model using a radial-spoke search algorithm in eight directions from the nest. With the European Food Safety Authority having suggested O. bicornis as a model organism for non-Apis solitary bees in pesticide risk assessment, the authors hope this model will be a first step toward building future landscape-scale risk assessments for solitary bees, with pesticide response modules planned for the next version.

Subject of Research: A formal agent-based model of the solitary bee Osmia bicornis for landscape-scale pollinator risk assessment

Article Title: The Formal Model for the solitary bee Osmia bicornis L. agent‑based model

Article References: Ziółkowska, E., Bednarska, A., Laskowski, R., & Topping, C. (2023). The Formal Model for the solitary bee Osmia bicornis L. agent‑based model. Food and Ecological Systems Modelling Journal, 4, Article e102102. https://doi.org/10.3897/fmj.4.102102

Image Credits: AI Generated

DOI: 10.3897/fmj.4.102102

Keywords: Osmia bicornis, red mason bee, agent-based model, ALMaSS, solitary bees, pollinator decline, pesticide risk assessment, EFSA, agricultural landscapes, overwintering, parasitism, landscape modelling