Aphids are the classic case. These tiny insects can reach population sizes in the billions across a landscape, and for many species the detailed individual behaviour information needed to build an agent-based model does not exist. Running billions of agents alongside the detailed predator models that depend on them, such as ladybirds hunting aphids across fields, would be either computationally ruinous or outright unfeasible. Yet aphids matter enormously, both as crop pests and as the prey base that drives predator population dynamics. A new study published in the Food and Ecological Systems Modelling Journal introduces a general subpopulation model framework that solves this problem, allowing ALMaSS to represent entire landscapes of aphids efficiently while keeping the detailed landscape simulation intact.

The key insight is that the minimal unit of simulation does not have to be the individual. Instead, the new framework divides the entire simulated landscape into a non-overlapping grid, with a default cell size of 10 metres by 10 metres. Within each grid cell, the population is managed as a stage-structured subpopulation, tracking the number of individuals at each life stage and at each age within that stage. A standard 10 kilometre by 10 kilometre landscape therefore contains one million subpopulation objects, each one a compact numerical model rather than a swarm of agents. The approach draws on the Lefkovitch stage-structured population model, which classifies individuals by characteristics such as developmental stage or reproductive status rather than chronological age alone, and associates each stage with its own transition probabilities.

What makes the framework unique, according to its developers, is the integration of three modelling traditions that are usually kept apart: stage-structured population models, spatially structured population models, and highly detailed landscape simulation. Previous aphid models have typically relied on just one of these approaches, from lattice models of carabid-aphid systems to multi-patch differential equation models of aphid and ladybird dynamics. The ALMaSS subpopulation model links its numerical population engine directly to the ALMaSS landscape simulation, which resolves the underlying topographical map at one square metre and simulates daily farm management, field operations, and plant growth. Every subpopulation therefore receives dynamic, landscape-specific information as the simulation progresses, from crop rotations to seasonal vegetation change.

The implementation is organised around two C++ classes. The Subpopulation class represents a single stage-structured subpopulation within one grid cell, while the Subpopulation_Population_Manager class administers the entire population across the landscape, initialising every cell, assigning suitability values based on habitat and crop type, and stepping the whole system forward in daily time increments. Suitability is determined by the habitat or crop type at the grid centre: if it matches a host list stored in an external text file, the suitability is set to one, otherwise zero. Arable fields are handled separately through a crop list, because their vegetation is dynamically determined by the farming simulation. When suitability drops to zero, for instance after a non-host crop is planted, the mortality function removes the entire subpopulation from that cell.

Development is driven by degree days, the accumulated physiological age that insects gain as temperatures rise above a stage-specific base temperature. Because the whole landscape shares the same weather, the manager class calculates degree days once per day for every life stage, rather than recalculating them in each of the million subpopulations. A two-dimensional array tracks accumulated degree days for each life stage and each calendar day of birth or transition, with oldest and newest indices marking where the extant population sits and where newborn individuals should be added. When a cohort accumulates enough degree days to exceed the maximum for its stage, it is flagged as ready to transition, and the subpopulation moves those individuals into the next life stage, whether that is egg to larva, larva to pupa, or pupa to adult.

Dispersal operates at two spatial scales. Short-distance movement shifts a proportion of the subpopulation to one of the eight adjacent cells, chosen randomly, but only if the destination is suitable and less crowded than the departure cell. Long-distance dispersal belongs to the winged adult stage and is modelled as partly passive flight influenced by wind. The framework pre-calculates two-dimensional landing masks for four wind directions and discrete wind speed ranges, generated from a polynomial landing curve along the wind direction. Most dispersers land near a peak distance, with a long tail out to a longest distance that scales upward as wind speed increases. Above a maximum wind speed of 12 metres per second, the model species does not attempt to fly at all. The masks are skewed using the cosine of the angle between the dispersal path and the wind direction, so more individuals land downwind and none land directly upwind, and they are normalised so their sum equals one.

Performance is the other half of the story. The three daily loops over all subpopulation objects, calling BeginStep, Step, and EndStep in sequence, are parallelised at the thread level using OpenMP. In a five-year simulation on a 10 kilometre by 10 kilometre Danish landscape, running on a single thread took 1472 seconds, while five threads cut that to 748 seconds and twenty threads brought it down to 615 seconds, a relative speed of 0.417. The gains diminish with additional threads, but the parallel design is what allows the model to handle up to one million grid cells efficiently. The developers demonstrated the framework with a hypothetical generic species parameterised purely for illustration, with five life stages spanning egg, larva, pupa, winged adult, and wingless adult, and showed that it captures annual population cycles while responding to landscape dynamics such as weather and crop variation.

The real test came with four aphid species implemented within ALMaSS: the black bean aphid Aphis fabae, the pea aphid Acyrthosiphon pisum, the peach potato aphid Myzus persicae, and the English grain aphid Sitobion avenae. Combined with an agent-based ladybird model simulating predator behaviour, the subpopulation framework handled billions of modelled aphids of four species in a single 30-year simulation running simultaneously with the ladybird agents. Visualisations of the simulation show aphids concentrated in natural habitat areas at first, then migrating into crop areas through long-distance dispersal as crops grow, with ladybirds tracking the aphid abundance and reproducing in response. The heatmap time series reveals the spatial and temporal complexity that emerges when a numerical prey base interacts with individual predators across a dynamic landscape.

The framework is provided as a set of C++ classes that can be integrated directly into the ALMaSS software environment or adapted to other simulation systems capable of supplying the necessary landscape data. Its conceptual structure is straightforward, but its implementation requires a solid understanding of the ALMaSS programming environment, a trade-off between complexity and flexibility that the developers argue is worth making. Because the stage-structured table and vital rate parameters can be tuned to represent a wide range of species, from aphids that give birth to live nymphs to species with entirely different life cycles, the model offers a versatile foundation for future ecological modelling. For researchers studying pest outbreaks, predator-prey dynamics, or the knock-on effects of insecticide treatments, the ability to simulate billions of individuals within a realistic landscape, without sacrificing the detail that makes agent-based modelling valuable, opens a door that has been closed for years.

Subject of Research: A general subpopulation model for the Animal Landscape and Man Simulation System ( ALMaSS )

Article Title: A general subpopulation model for the Animal Landscape and Man Simulation System ( ALMaSS )

Article References: Duan, X., & Topping, C. J. (2024). A general subpopulation model for the Animal Landscape and Man Simulation System (ALMaSS). Food and Ecological Systems Modelling Journal, 5, Article e122467. https://doi.org/10.3897/fmj.5.122467

Image Credits: AI Generated

DOI: 10.3897/fmj.5.122467

Keywords: general, subpopulation, model, Animal, Landscape, Simulation, System, ALMaSS, scientific research