The economic stakes are enormous. Aphids damage crops in three distinct ways. They feed directly on phloem sap, diverting nutrients and stunting plant growth when numbers per plant climb high enough. They transmit plant viruses, spreading 275 of the more than 700 insect-vectored plant viruses known to science; in Australia, feeding and virus injuries on grain crops have been estimated to cost 241 and 482 million dollars annually respectively, while medium and severe outbreaks in Britain were once estimated at 70 to 120 million pounds per year for wheat alone. Finally, the sticky honeydew they excrete impairs photosynthesis and promotes fungal growth on leaves.

Modelling aphids at the level of individual agents is simply not feasible. The enormous numbers involved, combined with limited knowledge of individual behaviour, rule out both standard agent-based approaches and even super-individual shortcuts. The team therefore designed a hybrid between stage-structured population models and dynamic spatial models. The landscape, typically a 10 by 10 kilometre area, is split into 10 by 10 metre grid squares, and each square carries a subpopulation tracked day by day. Conditions in each cell—host plant availability, weather, vegetation—determine how the aphids there develop, reproduce and die, while dispersal by local movement and long-distance flight links the cells together.

Within each grid square, aphids are organised into age cohorts grouped by life stage. Each day, individuals accumulate degree days, a measure of physiological development driven by temperature, and when a cohort reaches the maximum degree days for its stage it moves on to the next stage or dies. New individuals enter only as eggs or newly produced nymphs. This structure allows the model to cope with many billions of aphids while still capturing the essential physiology of development, reproduction and mortality, and it permits explicit interactions with other organisms such as parasitoid wasps and predators.

A central feature of the model is its treatment of aphid life cycles, which display remarkable phenotypic plasticity. Genetically identical aphids can produce winged or wingless forms, and in autumn a sexual generation appears in response to shortening days and falling temperatures. In the model, winged offspring production is triggered by crowding and declining host quality, using a function adapted from earlier work on the grain aphid. Sexual morphs are determined by day length: males appear when daylight drops below 13.5 hours and sexual females below 13 hours, with a seasonal timer suppressing sexual production in spring so that populations can exploit favourable conditions through asexual reproduction.

Development in the model is governed by accumulated degree days, with lower development thresholds and thermal constants drawn from published laboratory studies for each species and morph. Because egg development data for the four target species were unavailable, the researchers calibrated egg thermal requirements using related species as starting points. Adult longevity is likewise modelled with a degree-day approach, converting published survival curves into daily mortality probabilities at 25-degree-day intervals. The authors acknowledge that laboratory parameters obtained at constant temperatures may not perfectly reflect development under fluctuating field conditions, a known complication since insect development is non-linear and asymmetrical near temperature extremes.

Mortality in the model combines several sources. Eggs face a constant daily death chance derived from an overall 70 percent overwintering mortality. Nymphs and adults experience density-independent background mortality simulating generalist predators, set at 2.5 percent for pea and grain aphids and 2 percent for the other two species, plus delayed density-dependent mortality driven by aphid density four days earlier, capturing the effects of disease, host quality decline and specialist predators. A sub-model for the parasitoid Aphidius smithi adds another layer, with parasitoid eggs developing in aphid hosts, killing adult aphids at the mummification stage, and adults laying eggs according to the ratio of parasitoids to aphids in each cell.

Reproduction depends on both age and temperature, with fecundity functions fitted to laboratory data for each species on its typical host plant. Winged morphs are less fecund than wingless ones, reflecting the evolutionary trade-off between dispersal and reproduction. Movement occurs locally, when crowded cells send up to 2.5 percent of their population to neighbours, or over long distances, when winged adults take flight. Because aphids are weak fliers unable to fly against winds above roughly half a metre per second, the model uses wind speed and direction to generate two-dimensional landing masks that distribute flying aphids across the landscape, skewing landing probabilities downwind of the departure point.

The model is not without acknowledged limitations. Aphid populations show considerable ecological specialisation, performing better on the host plants they were collected from, sometimes with fecundity more than twice as high on their home plant. Tracking such specialisation would be too resource-intensive, so every simulated population performs equally on every host, which may cause populations to spread faster and grow larger than they naturally would. Host plants are also assigned at the level of general vegetation types, producing a more homogeneous distribution than reality. Intraspecific variation in overwintering strategies and responses to photoperiod is likewise simplified. The authors stress that these compromises are the price of achieving landscape-scale simulation at all.

Even so, the researchers argue that no model of comparable detail linked to a realistic dynamic landscape simulation exists for aphids. Previous models typically focused on a single host in a single field, or used simpler spatial formulations. The new framework is designed to couple with aphid predators such as ladybirds within the same system, enabling regional-scale evaluation of integrated pest management, including the consequences of insecticide use that can inadvertently destroy natural enemies and worsen outbreaks. The formal model now published marks the starting point for implementation and calibration, with field and laboratory datasets for each species lined up to test whether the simulated populations hatch, peak, migrate and reproduce at the right times and places. If calibration succeeds, the model could become a powerful tool for understanding and managing one of agriculture’s most persistent pests.

Subject of Research: A spatial subpopulation model for simulating four aphid pest species in dynamic agricultural landscapes

Article Title: Formal model for Acyrthosiphon pisum , Aphis fabae , Myzus persicae and Sitobion avenae using the ALMaSS subpopulation approach

Article References: Formal model for Acyrthosiphon pisum , Aphis fabae , Myzus persicae and Sitobion avenae using the ALMaSS subpopulation approach. (n.d.). https://doi.org/10.3897/fmj.5.123747

Image Credits: AI Generated

DOI: 10.3897/fmj.5.123747

Keywords: aphids, ALMaSS, subpopulation model, pest management, agricultural modelling, Acyrthosiphon pisum, Aphis fabae, Myzus persicae, Sitobion avenae, landscape ecology, integrated pest management, degree days