Folsomia candida is a euedaphic collembolan species that inhabits the upper soil layers, typically within the top 5 cm of the soil profile. Its life cycle comprises three stages: egg, juvenile, and adult. Under suitable temperature and soil moisture conditions, eggs hatch at age day 0, and the age of each individual increases by one day thereafter. Both hatching success and hatching time are influenced by temperature and soil moisture. After hatching, juveniles begin feeding immediately. As they consume sufficient food, they undergo successive moults, each marking the transition to the next instar. Following six moults, juveniles reach sexual maturity and become adults. Adults continue moulting throughout life but without further morphological change.

Temperature, soil moisture, and food conditions determine growth and development in animals. However, the interactions among these factors remain poorly understood. It is therefore assumed that the total development rate (r_{dev, total}) at each life stage is limited by the most restrictive of the temperature-dependent and soil-moisture-dependent development rates. This reflects the principle that favourable moisture cannot compensate for temperatures that already impose strong physiological constraints. The plausibility of this assumption was evaluated by visualising development rates across all combinations of temperature and soil moisture (Suppl. material 1: figs S2–S4). The limiting development rate is subsequently scaled by the food score, as expressed in Equation 6.

rdev , total = food score ×min(rdev,temperature ,rdev,soil moisture ) (6)

Folsomia candida reproduces via parthenogenesis, with males rarely present in laboratory culture or the field. Once juveniles reach sexual maturity, typically at the sixth instar, females begin laying eggs in batches. Batch size depends on the animal’s age, food availability, and environmental conditions (Booth and Anderson 1979; Roeben et al. 2023; Snider and Butcher 1973; van Amelsvoort and Usher 1989). Age-specific variation in batch size, although documented, is not incorporated in the present model due to limited data across environmental gradients.

In this model, the total reproduction rate (r_rep,total) is determined by temperature, soil moisture, and food conditions. These components are modelled independently, and the minimum of the temperature-driven and moisture-driven reproduction rates is taken as the total reproductive rate rate (Equation 14). The plausibility of this assumption was evaluated (see Suppl. material 1: fig. S5).

rrep,total = Food score × min( rate rep,temperature , rate rep,soil moisture ) (14)

Mortality in the model arises from three components: temperature stress, soil-moisture stress, and predation. The total daily mortality rate is assumed to be the sum of these independent components (additive mortality). Mortality is recalculated as the death rate per day for each life stage. Mortality is expressed as a daily death-rate increment; individuals die when their accumulated death value reaches one.

Euedaphic species, especially parthenogenetic species, have poor dispersal capacity. Becoming parthenogenetic instead of dispersing might be the strategy for them to tackle the changing environment (Ponge 2020). Therefore, dispersal is modelled simply. Juvenile F. candida is largely sedentary, and the foraging range of adults scales with body size, with a 2 mm adult typically moving up to 20 cm (Johnson and Wellington 1983). For simplicity, only adults disperse in the model. Dispersal occurs by random movement into the eight surrounding grid cells. Dispersal of adults only occurs when population density is over 10⁵ per square metre (Petersen 1994; Petersen and Luxton 1982) or the food score is less than 0.008 (assuming plant litter is the only food source and food availability is lowest, which is 0.04).

Studies of temperature effects on Folsomia candida often only mentioned that the experiment carried under controlled humidity (i.e., air humidity). In soil-based experiments, moisture is frequently reported as gravimetric or volumetric water content rather than soil water potential. In other cases, F. candida is reared on moist plaster, where the moisture condition is reported as "water is added regularly to maintain saturation". When water-potential data are missing, assumptions must be made. We assumed that animals experienced optimal soil water potential (approximately 1.8 -kPa) in cases mentioned above. This approach ensures consistency across datasets used for model parameterisation.

Temperature and soil moisture jointly shape physiological performance in soil invertebrates. In this model, the combined effects of temperature and moisture are represented using a limiting-factor approach in which the realised rate is the minimum of the temperature-driven and moisture-driven rates. This reflects the idea that extreme drought cannot be compensated for by optimal temperature, and vice versa. The true interaction between temperature and soil moisture in F. candida remains poorly quantified. Potential synergistic, antagonistic, or additive effects are not well resolved in the literature. In the absence of mechanistic data, the minimum-rate approach provides a conservative approximation while avoiding structurally unjustified interaction terms.

The model predicts complete mortality when soil temperature exceeds approximately 32 °C, whereas soil moisture exerts a comparatively minor influence within most of its range. However, natural soils exhibit substantial microclimatic heterogeneity, and individual springtails may occupy cooler or moister microsites within soil aggregates or pore spaces. Microhabitats may buffer exposure to temperature extremes, allowing survival even when surface or bulk soil temperatures exceed lethal thresholds.

Explicit representation of microclimatic could improve biological realism but would require spatial resolutions far finer than the 1 m² grid used in ALMaSS. While desirable for future mechanistic studies of soil arthropod thermal ecology, such fine-scale resolution is beyond the scope of landscape-scale modelling.

Differences in available data between temperature and soil moisture effects result in distinct approaches for modelling the daily death rate for juveniles and adults. The juvenile daily death rate derives from full life-cycle experiments. Under excessively high temperatures, juveniles never reach adulthood, and the daily death rate is defined as the inverse of lifespan. Under optimal temperatures, all juveniles mature, and the daily death rate is zero. Intermediate temperatures yield partial mortality, calculated as deaths divided by time to first oviposition among survivors. The soil-moisture-dependent daily death rate for juveniles is based on sparse data; complete survival is observed between –0.00262 and –0.0147 MPa (Xie 2023). Mortality is therefore assumed to be zero within this range and follows the egg-stage function under drier conditions – which is a conservative assumption, as juveniles are typically more drought-tolerant than eggs.

Adult temperature-dependent mortality is derived from full life-cycle studies (Roeben et al. 2023; Snider and Butcher 1973; Wehrli et al. 2024), where the daily death rate is calculated as the inverse of the interval between first oviposition and death. Soil-moisture-dependent mortality is inferred from chronic exposure experiments on adults (Wang et al. 2022; Wang et al. 2023), where mortality is measured only at the end of exposure. The daily death rate is therefore mortality divided by exposure duration.

Together, these adaptations reflect the limitations of available empirical data and the need for pragmatic modelling assumptions.

This model is designed to simulate population dynamics of Folsomia candida at spatial scales ranging from 100 to 1000 m², using daily time steps for simulations of up to five years. It explicitly represents eggs, juveniles, and adults and requires inputs for initial population density, daily soil temperature (top 7 cm), soil moisture (top 7 cm), and dimensionless food scores.

The model assumes linear effects of soil moisture on development from egg to juvenile and from juvenile to adult. Although non-linear effects may occur, current empirical data do not support more complex functions. The model also assumes no long-distance dispersal, and predation is implemented as a fixed consumption rate for all life stages. The predation rate is assumed to be constant, which might not be the case in reality. Additionally, food quality and availability are simplified as a score rather than mechanistic diet dynamics. It does not include explicit predator dynamics or long-term evolution (e.g., drought or heat tolerance). The model is explicitly tailored for F. candida, a parthenogenetic, opportunistic species with rapid reproduction under favourable conditions. It may be less representative of specialist or sexually reproducing springtails. However, with sufficient life-history data, the modelling framework could be adapted to other species.

The model does not incorporate physiological acclimation, i.e., the reversible adjustment of physiology to prevailing temperature or soil moisture regimes, although acclimation can enhance stress tolerance in Collembola (Wehrli et al. 2024). All parameterisations use data from experiments in which specimens were not pre-acclimated to stress or sub-stress conditions.

Processes such as evolutionary adaptation and genetic variation are not included due to a lack of empirical data and the desire to avoid structural overcomplexity.

The model considers temperature and soil moisture intensively but only considers a rather simple food modelling. Although vegetation decomposition strongly influences available food resources, decomposition is not mechanistically linked to food score in the present version.

The model is built on a population-matrix framework with explicit spatial structure. Spatially explicit matrix models are uncommon and represent an innovation within development in modelling spatially distributed subpopulations (Duan and Topping 2024). The philosophical boundaries of the model arise from three main sources: the intrinsic limitations of matrix models, the assumptions embedded in the model design, and the constraints imposed by the ALMaSS framework with which it is integrated.

Because matrix models aggregate individuals into classes, this approach cannot capture individual variability arising from genetic or environmental heterogeneity, nor can it represent emergent behaviours that result from interactions among individuals. Furthermore, the use of thermal performance curves assumes that development is fundamentally predictable under given environmental conditions, potentially overlooking stochastic elements that contribute to population resilience, such as the interplay between individual health and developmental processes. Finally, the ALMaSS spatial framework further constrains environmental heterogeneity by assuming uniform conditions across each grid cell, thereby treating space as discrete rather than continuous.

Many exclusions in this formal model are not just a form of simplification but rather a balance between biological realism and data availability. The model is intended for exploring population-level consequences of multiple stressors in agricultural landscapes. Outputs include population growth rates, spatial distribution, equilibrium population size, or recovery of the population. These outputs should be interpreted as indicators of relative risk rather than absolute estimates of abundance. The model is thus primarily designed for comparing the relative impacts of different scenarios.

The EFSA Good Modelling Practice guidelines (2014) caution against modelling F. candida for use in the regulatory environmental risk assessment of plant protection products, as it does not represent natural soil communities well. However, this species remains highly relevant within ecotoxicological testing frameworks. F. candida is widely used in standardised laboratory and higher-tier tests (i.e., micro- or mesocosm experiments), including those conducted under environmentally realistic conditions, where it serves as a sensitive and well-characterised test organism. In this context, the model can be used to improve the interpretation and prediction of results of ecotoxicological experiments. This species is also found in agricultural and disturbed habitats (Fountain and Hopkin 2005) and has been used as an indicator of soil quality (Nelson et al. 2011). With adaptation, the model could be extended to additional species with comparable ecology and available datasets.

Despite its integration within ALMaSS, the model can be implemented in any landscape modelling framework capable of supplying temperature, soil moisture, and soil classification data. The model structure is flexible and could be extended to incorporate elements such as explicit competition, predation, or pollutant exposure.