The following summary comes from Madge (1962) for N. pronuba:

In an extensive study, Singh (1956) evaluated the time to hatch of eggs of N. pronuba, Agrostis segetum, and Xestia c-nigrum under different constant temperatures. Thresholds for development time were given as 7.5°C, 7.7°C, and 8.0°C, respectively. There were differences in the upper threshold between the species. N. pronuba failed to develop at 30°C, but both other species failed at 35°C. This indicates that similar developmental patterns are followed by these related species, but small differences in response thresholds occur.

Singh (1956) provides days-to-hatch values for temperatures ranging from 10°C to 35°C in 5-degree increments. Together with the data from Madge (1962), this information provides a solid basis for creating a TPC model for egg development in N. pronuba.

According to Singh (1956), the larval period consists of two distinct phases. The first phase, from egg emergence to the cessation of feeding, marks progressive development. The second phase, the pre-pupal stage, begins when feeding stops in preparation for pupation. The normal situation is that just before the pre-pupal stage, the larvae descend into the soil, where they construct earthen cells within 3–7 cm of the surface. Under favourable conditions, caterpillars transition directly to the pupal stage with a minimal pre-pupal period. However, under unfavourable conditions, such as temperature fluctuations, the pre-pupal phase is prolonged, and feeding ceases for an extended period, causing larvae to enter a state of torpor. In the USA, this species is often referred to as the snow or winter cutworm, as feeding can commence in warm conditions during winter (Difonzo and Russell 2010; Wagner 2010).

Larval development: Summarising Madge (1962) for larval development, who studied N. pronuba larvae at 10°C, 15°C, 20°C, 25°C, and 27.5°C:

Overall, the study presents a pattern of development increasing with temperature but with an optimum for survival at around 15–20°C. By 27.5°C, a thermal survival threshold is crossed, preventing survival.

Singh (1956) performed similar experiments at additional temperatures—10°C, 15°C, 18°C, 20°C, 23°C, 25°C, and 27°C for N. pronuba, and 10–35°C in 5-degree increments for A. segetum and X. c-nigrum. No development occurred at 35°C. For N. pronuba, development still occurred at 27°C, albeit slightly faster than at 25°C. Unfortunately, mortality rates were not reported, making direct comparison with the later study by Madge (1962) impossible. However, in Singh’s (1956) study, larvae exposed to temperatures of 8°C and below did not pupate, compared to 100% pupation at 21°C. Yet, larvae at 5–8°C survived in a dormant state for 170–190 days. In the same study, the effects of photoperiod and soil moisture were investigated; however, neither factor influenced hibernation or diapause in the larvae.

Larval growth was recorded as the length of each larval stage (stages 1–7), after moulting or emergence, reaching 48 mm before the pre-pupal stage. Head capsule widths were also provided. This information can be used to assess the proportion of development time associated with each stage. Both measures fit an exponential growth curve with similar slopes (length: y = 0.045e^0.4735x, R² = 0.9632, head width: y = 0.0618e^0.4064x, R² = 0.9965). However, when examining the proportion of length gained per stage, the pattern was almost linear (y = 0.0506x − 0.0595, R² = 0.9783) (Table 1). This calculation suggests that we can probably assume a linear progression between instars under constant temperatures.

Following development, the larvae enter a diapause state with arrested development until pupation.

Post-diapause development has been accurately modeled using TPCs in the pea moth Cydia nigricana (Lepidoptera, Tortricidae) (Riemer et al. 2021). In the same study, it was concluded that there was no response to photoperiod during post-diapause development. Singh (1956) provided pupal development rates for N. pronuba, A. segetum, and X. c-nigrum, which varied with temperature. As with egg and larval development, A. segetum was very similar to N. pronuba, with the multivoltine X. c-nigrum having faster development of larvae and pupae (Singh 1956). In N. pronuba, no pupae developed at 35°C, but the other two species completed development at this temperature. Although not investigated in detail, no effect of photoperiod was found in N. pronuba. The same study, however, did not provide data on temperature-related mortality.

Three parameterisations for eggs, larvae, and pupae were fitted to the data from Singh (1956) and Madge (1962) using the LRFTPC model in the R package rTPC (Padfield et al. 2024). The resulting estimates for the models, fitted to the data, are presented in Table 2.

For the larvae, the earlier study data from Singh (1956) were used to fit the model, except for the zero development at 27.5°C. The resulting parameter estimates for development are given in Table 3.

Unfortunately, this model does not allow us to identify the point at which each instar matures. To include this, we need an estimate of the proportion of development required for each maturation point. Since a linear response in body size measures with larval stage was observed, we will make the simplifying assumption that stage progression occurs at each 1/7 of the total development time. This estimate can be adjusted if more detailed information becomes available.

For pupae, fitting the LRF model to the data provided by Singh (1956) resulted in a good fit (Table 4).

The data points used, along with the fitted lines for all three life stages, are shown in Figure 1. In all cases, the fits to the parameters were highly significant, except for T_min, for which the estimate is highly uncertain. In the case of eggs and larvae, using a linear model, the thermal minimum was calculated to be 7.5°C and 7.0°C, respectively. In cold tolerance experiments, no development of eggs or larvae was observed below 6°C. To match observations and due to the poor fit to T_min, we propose that the curve be truncated at 6.0°C, below which there is no development. For pupae, similar results were obtained in the same study, with a threshold temperature of 7–8°C. In this case, we propose truncating the curve at 7°C.

Larval hibernation and the onset of diapause seem to be linked to temperature. We will assume that growth stops below the developmental threshold of 6.0°C. Above this threshold, development will occur until pupation.

An investigation of the behavior of N. pronuba larvae in relation to light and temperature (Madge 1964b, 1964a) identified different activity patterns. First-instar larvae were active during the day (diurnal), while instars III to VII were primarily active at night (nocturnal). Instar II larvae showed intermediate behavior, being somewhat active during both day and night. Thus, the entry of instar I larvae into the soil is associated with a decrease in light and a drop in temperature. For instars III to VII, activity was mostly unaffected by temperature changes but was closely related to the absence of light, indicating that these later instars prefer to be active in complete darkness, even avoiding moonlight. This may have consequences for pesticide exposure, since overspray is less likely during dark hours. Singh (1956) noted that larval instars I–VII were active on the surface of the ground, but that larval stage VII burrowed into the top layers of the soil, which may confirm Madge’s observation that this stage strongly avoids light.

Heinrich (1975) reviewed the literature on insect energetics, providing information particularly relevant to Sphingidae. He calculated that a sphinx moth of 2.0 g requires 30 cal to warm up from 15°C, equivalent to the energy expended during approximately 3.7 min of flight, and that sphinx moths have a metabolic rate during flight that is near 60 mL O₂ (g hr)⁻¹. Jones (2014) measured the weight of N. pronuba after feeding as 0.48 g and after flying the maximum distance in a flight mill as 0.38 g. Casey and Joos (1983) showed that, despite differences attributed to physiological characteristics, these energy equations are generally transferable between moth types. Using this information, we can estimate a flight expenditure of 60 × 0.48 / 2.0 = 14.4 mL O₂ (g hr)⁻¹, assuming that sphinx moth energetics can be directly translated and scaled to weight. Heinrich (1975) calculated that a 3 g moth would expend 11 cal per minute of flight. Scaling for size suggests that N. pronuba should use approximately 1.76 cal per minute of flight.

There is a suggestion (Heinrich 1975) that foraging moths use trapline foraging, that is, repeated sequential visits to a series of feeding locations, similar to bumblebees (Buatois and Lihoreau 2016). However, this strategy is typically associated with central-place foragers. Given the high mobility of this species, central-place foraging appears unlikely, although data from mark-release-recapture experiments (Merckx et al. 2009; Slade et al. 2013) indicate that N. pronuba and other noctuid moths have home ranges and revisit patches that are hundreds of meters apart. However, currently there is no firm evidence to determine the foraging strategy employed by N. pronuba.

We assume the mean day length required to trigger the start of reproduction is approximately 15 hours, but that each individual moth has its own value, drawn from a Gaussian distribution ranging from 14.5 to 15.5 hours. Once reproduction begins, the minimum lifespan is set to 30 days, but the actual lifespan is variable such that, under UK weather conditions for 1961, the model would result in a peak of adult activity during August and September and would end before November (Table 5; cf. Madge 1962). Given that we assumed weather-dependent activity, the effective lifespan is measured in active days and is therefore shorter than lifespans measured in the field. As a consequence, poor weather for activity would shift the phenology curve to the right. Final values for both Gaussian distributions will be calibrated when the model is fully operational using the currently available phenology and location data.

We have no information concerning what drives the number of eggs produced by a female. However, a review of the ecology of Heliothis species suggested that fecundity is influenced by temperature, humidity, and larval and adult nutrition and is positively, though weakly, linked to body size (Fitt 1989). Assuming the temperature is high enough for activity, there does not appear to be a clear predictor of egg numbers in N. pronuba. Therefore, we will assume that each moth is allotted a total number of eggs it can produce, drawn from a skewed beta distribution with a mean of 1,323 (the average of the three results) and a maximum and minimum of 1,680 and 75, respectively (Figure 3). The value of k = 20 is arbitrary but constrains 97% of the values to fall between 1,000 and 1,600, which seems reasonable based on the observations in the literature.

To determine the number of eggs and egg batches, we will use the broken-stick model with the following modifications: the maximum and minimum number of eggs per segment must be 850 and 75, respectively, and the number of segments (egg batches) must be 3–5, or 1 if the total egg number is below 225. This method reflects the observations but provides no mechanistic explanation, which would require additional information.

Regarding oviposition location, we can assume that the moth selects suitable herbaceous vegetation within its normal dispersal range and oviposits there. Suitable vegetation can be defined as any herbaceous vegetation except that found in arable and rotational grassland fields. The probability of selection should be linearly related to the polygon area, assuming a maximum area of A (e.g., 1 ha), corresponding to maximum attractiveness. Hence, oviposition site selection should be based on stochastic probability among all polygons with suitable vegetation, scaled to size, for those below A.

If more detailed information becomes available or it is determined that cropped areas of fields can be utilised, they can be added based on vegetation type. In this way, flexibility is maintained to model other species with different host-selection behaviours.

Given the evidence of relatively large-scale adult moth movement within the 10 × 10 km range of typical ALMaSS landscapes, we may assume that dispersal, when weather is suitable, is not a limitation for finding food or reproductive locations. Thus, we will assume that dispersal distances are up to 11 km; hence, with wrap-around boundaries normal in ALMaSS, dispersal distance will not hinder movement toward food or reproductive sites, but it will limit movement between days. If we assume that the daily dispersal distance is drawn from a Gaussian distribution varying from Dmin to Dmax, where Dmax is 11 km and Dmin is 100 m, then this will simulate the situation for N. pronuba. This also allows Dmax and Dmin to be changed to simulate other species.

Whether dispersal—and therefore foraging and reproduction—can occur will depend on weather conditions. We assume that a minimum temperature is required for activity. Temperature effects on moth activity are well documented (e.g., Williams 1940; Williams 1961). While activity is often influenced by the preceding temperature rather than absolute values (Williams and Buxton 1951), low temperatures reduce activity. The influence of precipitation or high wind velocities is less clear, and there may be substantial moth activity even during rainfall and strong winds, and effects may interact with temperature (Esbjerg 1987; Neff et al. 2025). Williams (1940) emphasises the importance of season for moth activity; rainfall can substantially lower moth activity in summer but has negligible effects in winter. Temperature changes, on the other hand, have strong effects in winter but can be neglected in summer.

Summarising Singh (1956), the main sources of biotic mortality for N. pronuba include bacterial and viral infections; parasitism by various Ichneumonidae, Braconidae, Tachinidae, and Bombyliidae species; predation by carabid beetles such as Pterostichus madidus; and vertebrate predators, including birds, bats, and rodents (Tinbergen 1981; Mikula and Cmokova 2012; Lindstedt et al. 2019). Cannibalism among larvae is also a significant mortality factor, particularly under crowded conditions. It should be noted that many of these observations derive from captive populations and may not be directly transferable to wild population dynamics.

In addition to what is known about N. pronuba, data for other moths indicate additional parasitoid species and genera that could be important, such as Pales pavida and Ramonda spathulata (Tachinidae) (Ford and Shaw 1991), and Trichogrammatidae, such as Trichogramma cordubensis (Roriz et al. 2006). Microplitis mediator (Hymenoptera, Braconidae) is a major cause of mortality for the cabbage moth (Belz et al. 2014), and Braconidae such as Cotesia marginiventris exhibit Type II functional responses to Spodoptera larvae (Riggin et al. 1994). Beauveria bassiana is a mortality factor for multiple noctuid pests (e.g., Hicks et al. 2001; Mantzoukas et al. 2013; Apirajkamol et al. 2023), and microsporidia and viruses also contribute to mortality pressure (e.g., Hamm and Lynch 1982).

Taken together, these multiple mortality sources—with their potential for rapid buildup—suggest that, in all these species, density-dependent mortality may occur at high densities due to parasitoids, diseases, and cannibalism. However, it is difficult to determine the rates or density thresholds due to the variability in mortality levels among species and locations.

The literature does not provide a clear picture or sufficient data to support the development of a specific mortality model. We therefore propose adopting a spatially explicit model representation at two levels. For high densities, an area-based modifier to mortality chance per day will simulate increased direct density-dependent mortality by transmissible diseases and cannibalism. In addition, a parasitoid model of the type suggested for Pieris napi, using an agent-based representation, would provide a time-delayed spatial density-dependent function. Since these will be implemented in a general manner, calibration against time series of real data will be necessary during the calibration phase.

In the P. napi model (Topping and Duan 2025), the parasitoid population is simulated using a spatially explicit agent-based model tracking individual life histories. The core reproductive behavior follows a functional response combining search efficiency and handling-time constraints:

Elaid =min(Eremaining ,DTh+1H⋅Se⋅Ts) Equation 2

where E_remaining is the remaining egg complement, D is daylength, T_h is handling time per host, H is host density, S_e is search efficiency, and T_s is searching time. Individual agents disperse spatially to locate hosts, with development, emergence, and overwinter survival governed by temperature and photoperiod thresholds as described in the model documentation. Superparasitism by different individuals was permitted.

We assume the non-parasitoid density-dependent mortality will follow Equation 3:

m (d) = m₀ + αd^β Equation 3

Where m (d) is the daily mortality rate at density d, m₀ is the baseline mortality rate (density-independent), α is a scaling coefficient, β is the density exponent (typically β > 0 for density-dependent mortality), and d is the local density (e.g., individuals per hectare). Mortality rates, thresholds, and areas over which density dependence operates will all need to be calibrated.

As with Pieris napi, we follow the basic approach used in the development of the ApisRAM honey bee colony model (Duan et al. 2022). Pesticide exposure can occur through the consumption of contaminated nectar, contact, and overspray. By considering these three exposure pathways, we represent how model moths may encounter pesticides in contaminated environments. P_B (t) is used to represent the accumulated pesticide burden for the individual until day t. P_B (t) is updated by all three exposure paths and is used to calculate the stress caused by pesticide exposure. The new pesticide exposure on day t is represented by P_N (t), which is calculated by Equation 4.

P_N (t) = P_I (t) + P_C (t) + P_O (t) Equation 4

where P_I (t) is the new contamination from intake, P_C (t) is from the contact exposure, and P_O (t) is from the overspray exposure.

This pathway accounts for pesticides that larval and adult moths ingest. Foraging moths may be exposed by collecting nectar from contaminated flowers, while larvae may eat contaminated leaves. The pesticide amount in the consumed resource is represented by P_I (t) and is assumed to move directly into the moth’s body (P_N (t)).

The overspray exposure pathways are relevant only to any moth life stage present at the moment of pesticide spraying. Contact exposure can occur when a mobile stage moves through a contaminated area. In both cases, a simple one-time absorption model is used, meaning we assume that the pesticide is absorbed into the moth’s body only once, controlled by separate parameters for contact and overspray.

Contact exposure specifically pertains to foraging adults and larvae and occurs when a moth touches a contaminated surface during its foraging activities. The amount of pesticide transferred to the body through contact is controlled by two user-defined parameters, as shown in Equation 5.

P_C = s_cSP_s Equation 5

where P_s is the pesticide amount per square meter on the plant surface, S is a constant representing the area of the moth in contact with the surface (for adults, this may include the feet, abdomen, and wings), and s_c is the absorption rate that determines how much of P_s is transferred to the body. This implementation does not account for foraging time, but both parameters can be adjusted to make the approach more or less conservative.

Overspray occurs only when moths are active or resting (adults or larvae) in a field where pesticide spraying is taking place and/or where drift is occurring in an adjacent area containing the moths. Two parameters—starting time and ending time—determine whether overspray can occur. Overspray can occur only if a moth is in the exact location and not protected from the spray (e.g., not in the soil). When overspray occurs, the contaminated pesticide amount (P_O) entering the moth’s body is calculated using Equation 6.

P_O = s_oSa Equation 6

where S represent a proportion of the body surface, a is the pesticide spraying application rate, s_o is the absorption rate for overspray.

To determine the effect of pesticide body burden, the initial model considers only acute mortality. This approach requires three parameters: first, a threshold for effect (P_t) above which mortality occurs; second, a daily probability of mortality (P_m) when the threshold is exceeded; and third, a daily decay rate (D) of the pesticide in the moth’s body. This provides a first-stage model for evaluating pesticide effects and assumes that an ALMaSS or equivalent landscape model is available to generate pesticide concentrations in nectar, vegetation, and overspray.

These are mortalities not specifically modelled above and include random predation events, mortalities as a result of management (e.g., ploughing (Badenes-Pérez 2022)), and “catch-alls,” which simply prevent exceedingly long lifespans, which could result from applying probabilities. Here we consider mortality related to soil moisture, temperature, and management events.

Temperature-related mortality: assumes that life-stage survival at temperature T is the result of exposure to a constant daily jeopardy that is a function of temperature. Under variable conditions, this can be represented by Equation 7:

St=∏tγ(Tt,C)Δt Equation 7

Equation 7 describes the overall survival probability of an insect’s life stage under variable temperature conditions. It states that the survival probability St over a given time period is the product of daily survival probabilities ɣ(T_t, C) raised to the power of the time step (Δt). This means that the survival probability for each day (or fraction of a day) is calculated based on the temperature for that day, and these daily probabilities are multiplied together to get the total survival probability over the entire period. C is a vector of parameters, for example, representing a polynomial function.

Implementing Equation 7 will have the advantage of including temperature-induced variation in background mortalities associated with functions not specifically addressed in the model. This is typically represented as a fixed daily mortality, but here, we propose that the daily mortality should be adjusted using Equation 7 and replaced by S_tBs, where Bs represents the stage-specific daily survival chance as a constant, calculated daily from the daily mean temperature (T). Régnière et al. (2012) used a second-degree polynomial in a logistic model to represent Choristoneura fumiferana larvae survival with temperature as ɣ(T_t, C), and this seems a reasonable choice given we have no equivalent data set for a suitable noctuid species, Equation 8:

ɣ = 1/(1 + exp (a + bT + cT²)) Equation 8

Singh (1956) provides information for larval survival at different temperatures, which can be used to parameterise the curve. Although not comprehensive, the data suggested optimal survival at 15–20°C and no development below 5°C, with no increase in mortality observed either. At 10°C, mortality was 90%. At 25°C, 7% of the larvae survived, and almost 100% died at 27.5°C. We must assume that either the 5°C or 10°C values are correct. Given that no larvae survived at 5°C, we will assume the value at 10°C is correct. However, at optimal development, 50% of the larvae also died; thus, to fit the curve, which must range from 0 to 1.0, it was fitted with 20, 14, and 0% survival at 10, 25, and 28°C. The values from the study are confounded by the length of development, which means that the actual survival chance per day needs to be calculated based on the developmental time predicted by Equation 1. This was done by raising the survivorship by the power of the development time for that day and then fitting the curve.

Equation 8 provides a survivorship probability of the form shown in Fig. 5, with C (a = –22.33, b = –4.0, and c = 0.119). The final values for C and βs will be determined during the calibration stage of the final model.

For the eggs, the following summary comes from Madge (1962) for N. pronuba:

Unfortunately, more detailed data on egg survivorship were not presented; however, the data provided suggest that the pattern is quite similar to that of the larvae (see above). Therefore, the same type of curve was fitted with the constraints that mortality should reach 100% at 5°C and 100% at 29°C, with “high” mortality at 27°C. Non-zero values were needed to allow fitting, so the curve was fitted with 5% survivorship at 6 and 28°C. The resulting parameters for Equation 8, assuming the development times of eggs predicted by Equation 1, were a = 15.48, b = −4.0, and c = 0.1157, respectively.

Finally, we assume that the mortality of non-diapause stages will occur with the onset of winter (here we assume December 1^st) or with negative temperatures lower than a minimum temperature threshold (Min_T), initially assumed to be −10°C, and that mortalities will also be associated with management events for juvenile stages.

From Singh (1956), we know that larvae and pupae resting in the soil require a certain soil moisture content for survival (6–8% for larvae and 4–6% for pupae), given a soil water maximum capacity of 27%. Above and below these levels, survival is reduced, with zero survival at 2% and 10% soil moisture (as a percentage of dry weight). Unfortunately, Singh did not report on egg survival, but unless other information comes to light, we can assume it is the same as for larvae.

The model assumes fixed behavioural and physiological parameters, excluding potential evolutionary adaptations to pesticide exposure or changing agricultural practices. Real populations may develop resistance, alter behavioural patterns, or shift phenology in response to selection pressures, i.e., processes that could significantly influence long-term risk assessments but operate on timescales beyond typical regulatory evaluations.

While N. pronuba likely uses visual and chemical cues to locate resources and mates, the model treats each individual as making independent decisions. We do not include pheromone communication, aggregation behaviours, or information transfer between individuals that could influence exposure patterns. For instance, if moths avoid or are drawn to areas where conspecifics have died from pesticide exposure, actual population-level impacts might differ from model predictions.

The model operates at a 1 m² spatial resolution, and polygons are, for the most part, assumed to be uniform. However, larvae make behavioural decisions at much finer scales. We do not capture how individuals might select specific positions on plants, exploit microclimatic refugia, or preferentially use field margins versus crop centres. These fine-scale behaviours could create spatial heterogeneity in exposure that buffers populations from pesticide impacts. They will result in variation in the effect of environmental factors, which cannot be explicitly included at this scale.

We do not consider diel variability in nectar production in ALMaSS. However, this is known to be a feature of some plants (Kendall and Nicholson 2025). This would alter the nectar availability as seen by nocturnal species such as N. pronuba. While the model includes nectar availability, it treats all suitable vegetation equally for larval development. In reality, N. pronuba shows preferences in its polyphagous diet, and larval performance varies with host plant species, nutritional quality, defensive compounds, and the microclimates in which plants are growing. This simplification may overlook important dynamics in which pesticide applications interact with host plant availability, thereby creating population bottlenecks.

The current toxicology module primarily focuses on acute mortality; however, growing evidence suggests that sublethal pesticide exposure can impair navigation, reduce fecundity, alter development rates, and even affect offspring fitness through epigenetic mechanisms. These cascading effects could accumulate over generations in ways our single-generation mortality approach cannot capture.

N. pronuba exists within a complex ecological network, competing with other herbivores, serving as prey for various predators beyond the modeled parasitoids, and potentially benefiting from or being hindered by the activities of other species. The single-species focus misses important indirect effects. For example, pesticides might reduce N. pronuba populations more by eliminating their preferred larval hosts than through direct toxicity or by impacting parasitoid populations, thereby reducing mortality.

While the model incorporates temperature and moisture effects on development and survival, it assumes these follow predictable daily patterns. Extreme weather events, such as heat waves, flooding, and late frosts, can cause catastrophic mortality or trigger unusual behavioral responses not captured by smooth functions fitted to laboratory data (Oliver et al. 2015). However, there is great variability in lepidopteran responses to extreme climate events (Palmer et al. 2017). Climate change may also alter the synchrony between moth phenology and resource availability in ways the current framework cannot anticipate or alter voltinism.

The multi-faceted mortality framework, incorporating density-dependent factors (parasitism, disease, and cannibalism), temperature-related survival, and management impacts, provides a realistic representation of population regulation. The high diversity of mortality sources identified, from viral and bacterial infections to multiple parasitoid families, suggests that N. pronuba populations are subject to strong but variable natural control. Thus, dynamics not considered may occur in reality.