Geographical variation in degree‐day requirements shows that mean thermal sums for insect egg development increase from tropical to temperate populations, reflecting local adaptation to cooler climates (Honĕk 1996). Eggs are laid singly on aphid-infested leaves, ensuring freshly emerged larvae immediate prey access and minimising egg crowding.

During the egg stage, S. scripta exhibits a clear inverse relationship between temperature and developmental duration (Table 1). At 10 °C, egg development requires approximately 12 days, whereas at 30 °C, this period is reduced to approximately 2.3 days (Nengel and Drescher 1991). Under moderate temperature conditions (approximately 20 °C), the egg stage typically lasts between 3 and 6 days (Agarwala et al. 1989; Krsteska 2008). When compared to other species (Table 1), Sphaerophoria rueppellii (Wiedemann, 1820) shows similar thermal responses, with egg durations ranging from 2.9 to 5.5 days when temperature decreased from 30 °C to 20 °C (Amoros-Jimenez et al. 2012). In contrast, Sphaerophoria cylindrica (Say, 1824) eggs require 6 to 12 days for development at approximately 20 °C (Curran 1920), and Allograpta (Sphaerophoria) javana (Wiedemann, 1824) demonstrates the shortest egg development time, completing this stage in just 1.96 ± 0.07 days at 27.9 °C (Patro and Behera 2002). Relative humidity appears to play an important role in the development of Sphaerophoria eggs as, at 25 °C, S. rueppellii eggs incubated at 90% relative humidity hatch in 2.93 days, compared to 4.72 days at 50% humidity (Amorós-Jiménez et al. 2012).

The larval stage is the longest and most ecologically significant period of syrphid development, as larvae serve as efficient predators of aphids and other soft-bodied insects (Dunn et al. 2020). Developmental duration during this stage is shaped by a complex interplay of temperature, humidity, and prey availability. Total larval development in Sphaerophoria ranges from approximately 6 to 27 days, depending on species and environmental conditions (Table 1).

At moderate temperatures (~20 °C), development of S. scripta typically spans 8 to 12 days when food is provided ad libitum (Bańkowska 1978; Polak 1980; Krsteska 2008). The larval stage comprises three instars with, at 27 °C, the first instar lasting approximately 3.2 days, the second 3.9 days, and the third 6.9 days, accounting for roughly 23%, 28%, and 50% of the total larval duration, respectively (Awadallah et al. 1980). Among related species, S. rueppellii completes larval development in 8.1 to 10.9 days under similar thermal and humidity conditions (Amoros-Jimenez et al. 2012), while Sphaerophoria sulphuripes (Thomson, 1869) requires 13.5 days at 19.3 °C (Hopper et al. 2011). Allograpta (Sphaerophoria) javana again demonstrates the fastest development, completing all three instars in just 6.3 days at 27.9 °C (Patro and Behera 2002).

Prey availability is a critical determinant of aphidophagous hoverfly larval development. At low prey densities, larval development is longer and pupation occurs at lower larval weights (Ruzicka and Cairo 1976; Cornelius and Barlow 1980). Polak (1980) demonstrated a clear inverse linear relationship between both aphid availability (Equation 1; R² = 0.87), consumption (Equation 2; R² = 0.64), and the developmental time of S. scripta larvae reared on A. pisum at a temperature of 20 °C (Fig. 1). Developmental time decreased markedly from approximately 15.5 to 9 days as the mean number of aphids per day increased from 5 to 60.

Dl=−0.076×Na+14.817 Equation 1

Dl=−0.237×Nc+15.361 Equation 2

where D_l is larva developmental time, N_a is the number of aphids available daily, and N_c is the number of aphids consumed daily.

Similarly, S. rueppellii larvae reared on M. persicae at 20 °C developed significantly faster under high food availability than under limited prey conditions (8.3 vs. 10.5 days) and pupation occurred at lower larval weights (11 vs. 9.3 mg) (Amorós-Jiménez et al. 2012) (Fig. 2). These findings are consistent with broader patterns observed across aphidophagous hoverflies. For example, Putra and Yasuda (2006) reported that increased aphid density significantly reduced larval development time in both Episyrphus balteatus and Eupeodes (Metasyrphus) corollae (Fabricius, 1794). Notably, the effect was prey-specific; E. balteatus developed more efficiently on A. pisum, whereas E. corollae showed faster development on Aphis craccivora (Koch, 1854). Collectively, these studies underscore the strong influence of prey availability on hoverfly developmental dynamics, particularly under thermally favourable conditions.

To date, no published studies have investigated larval longevity under starvation conditions in S. scripta. However, Rojo et al. (1996) examined the effects of aphid deprivation on larval survival in E. corollae and E. balteatus at various ages post-eclosion. In their study, larvae were initially provided with ad libitum access to aphids before being subjected to starvation. The results indicate that younger larvae exhibit greater sensitivity to starvation than older ones. Moreover, E. balteatus larvae demonstrated a higher tolerance to starvation compared to E. corollae, particularly in later instars (Fig. 3). Based on developmental time estimates, approximately 2 days for the first instar, 2 days for the second, and 3–4 days for the third in E. corollae (Li and Wu 2023), and 2–3 days, 3–3.5 days, and 4–6 days respectively for E. balteatus (Mushtaq et al. 2014), the mean survival times under starvation could be estimated as 1.0, 1.4, and 2.9 days for the first, second, and third instars of E. corollae, and 2.3, 3.5, and 5.8 days for E. balteatus. These findings are consistent with those of Ingels et al. (2015), who reported that third instar E. balteatus larvae survived an average of 4.6 days under starvation when earlier instars had been fed ad libitum, compared to only 2.9 days when earlier instars had been provided with limited aphid access.

Larvae of Sphaerophoria species are generalist predators, primarily consuming a variety of aphid species. Larvae of S. scripta have been found feeding on more than 30 genera of aphids. They have also been observed feeding on psyllids (jumping plant lice) and even lepidopteran larvae (e.g., Pieris brassicae), although aphids remain their primary prey (Rojo et al. 2003). Cannibalism has also been observed under high-density or food-limited conditions (Bańkowska 1964), suggesting behavioural plasticity in resource-scarce environments.

S. scripta larvae are aphid-feeding on herbaceous plants, including various crop plants, e.g. Avena, Brassica, Cichorium, Lactuca, Triticum, Vicia (Speight 2010). There is no indication of prey preference in S. scripta; instead, it tends to exploit local concentrations of aphids, showing opportunistic foraging. However, laboratory tests showed that in Sphaerophoria species, fitness-related parameters of adults may depend on the prey species consumed during their larval stage. For example, Amorós-Jiménez and Marcos-García (2020) showed that fecundity (number of eggs produced) and fertility (percentage of eggs hatched) in S. rueppellii females were higher when they were fed with Rhopalosiphum padi (Linnaeus, 1758) and showed the lowest values with Aphis nerii (Fonscolombe, 1841).

Studies indicate that S. scripta larvae need a daily minimum of five A. pisum aphids for complete development (Polak 1980). Under conditions close to natural and at a temperature of approximately 20 °C, S. scripta larvae demonstrated a wide range of aphid consumption, depending on aphid type. According to Krsteska (2008), larvae consumed in total between 300 and 365 individuals of M. persicae. In contrast, Bańkowska (1978) reported a mean consumption of 129 aphids of A. pisum, while Polak (1980) observed a slightly higher consumption of 167–192 aphids on the same aphid species. In comparison, the total aphid consumption by the smaller larvae of S. rueppellii was reported to be approximately 250 individuals of M. persicae (Amorós-Jiménez et al. 2012). Under laboratory conditions of 21 °C, S. scripta larvae consumed 190–306 A. fabae aphids, considerably less than the larger larvae of E. corollae and E. balteatus (400–500 aphids) (Wojciechowicz-Żytko 2000).

Aphid consumption by S. scripta larvae exhibits a pronounced ontogenetic increase, with minimal feeding activity observed during the initial 0–30% of the larval stage. This is followed by a rapid escalation in predation rates between 40 and 70–80% of development, culminating in peak consumption, which then decreases during the final 20–30% prior to pupation (Fig. 4B). These data indicate a strong positive correlation between larval maturity and predatory efficiency, suggesting that feeding behaviour is tightly regulated by developmental stage (Adams et al. 1987; Wojciechowicz-Żytko 2000). Furthermore, interspecific variation in daily consumption rates among Sphaerophoria species, as well as differences in aphid prey types, imply that both predator identity and prey characteristics influence feeding dynamics (Fig. 4A).

Adams et al. (1987) suggested that hoverfly larvae kill rates in the field populations are related to two main determinants of their range, i.e., larval size (expressed as body weight) and development rate (expressed as the percentage of development achieved). In controlled laboratory experiments, they examined the growth and predation dynamics of E. corollae larvae fed on S. avenae under two constant temperature regimes (10 °C and 15 °C). Their findings revealed that larval growth (Fig. 5A) and aphid kill (Fig. 5B) followed a similar exponential trajectory during the initial 75% of larval development, underscoring the importance of size as a determinant of predatory capacity. In addition, larval growth and aphid kill rates, expressed as mg per 1% of the larval stage achieved against developmental age, were closely comparable at both temperatures (Fig. 5). This suggests that temperature exerts a proportional influence on development, growth, and predation, allowing for the derivation of a standardised metric, relative kill rate (RKR), defined as the biomass of aphids killed per unit of larval biomass per 1% of the larval period. To further simplify this approach, mean RKR values can be calculated for each instar based on daily measurements. Adams et al. (1987) advocated for the application of this model in field settings, enabling the estimation of daily aphid mortality per syrphid larva using field-derived data on predator instar structure, mean weights of each larval instar predator, and ambient temperature, as formalised in their predictive equation (Equation 3):

kd=MRKR×Wl×D/Wa Equation 3

where k_d is an estimated number of aphids killed per larva per day, MRKR is a mean relative aphid kill rate for the instar, W₁ is the weight of the syrphid larva, W_a is a mean aphid weight, and D is the percentage of total larval development achieved in one day at the prevailing temperatures. For E. corollae, MRKR values were 0.29, 0.16, and 0.09 mg × mg^-1 × percent^-1 for first, second, and third instar, respectively.

Although empirical data on the relationship between larval biomass and aphid predation are not available for S. scripta, Hopper et al. (2011) investigated this relationship in four hoverfly species, including S. sulphuripes, under controlled conditions at 19.33 °C. In their study, larval growth was quantitatively described using a logistic growth model, which relates the day of development to larval fresh weight (Equation 4):

Ml=12.961+exp⁡(−0.68×(d−9.22)) Equation 4

where M_l is fresh larva weight and d is day of development.

They further investigated daily aphid biomass kill by larvae (B_a) in relation to larva fresh weight (M_l) and described it using the linear relationship (Equation 5):

Ba=0.48×Ml+6.06 Equation 5

Findings for S. sulphuripes of Hopper et al. (2011) can be presented in relation to percentage of the larval stage, instead of day of development, making them comparable with results of Adams et al. (1987) for E. corollae (Fig. 6).

Food utilisation in S. scripta is strongly dependent on aphid density. Experimental data from Khan (2016) reveal a Holling Type II functional response (Equation 6) in both second and third larval instars, characterised by a rapid increase in aphid consumption at low prey densities followed by a decelerating intake rate that asymptotically approaches a plateau as prey availability increases (Fig. 7). This saturation pattern reflects the constraints imposed by handling time. Notably, third instar larvae exhibit higher maximum consumption rates than second instars, indicating a greater predatory capacity at more advanced developmental stages. In contrast, Polak (1980) assessed food utilisation across the entire larval period without distinguishing between instars. Although prey availability was not stratified by developmental stage, the overall consumption pattern similarly conformed to a Holling Type II response (Fig. 7). These findings collectively support the conclusion that S. scripta larvae exhibit a saturating functional response to increasing aphid density, with developmental stage influencing the magnitude of consumption. The parameters of the fitted models are presented in Table 3.

f(R)=a×R1+a×h×R Equation 6

where f denotes the intake rate and R denotes food (or resource) density; a is the attack rate (i.e., the rate at which the hoverfly larva encounters food items per unit of food density), and h is handling time (i.e., the average time spent on processing a food item).

During the pupal stage, syrphid larvae undergo metamorphosis into adults. This transformation is also temperature-dependent. At 15 °C, pupation requires up to 16 days (Nengel and Drescher 1991), whereas at 30 °C, this stage is completed in approximately 6 days. According to Nengel and Drescher (1991) emergence does not occur at or below 10 °C. Under standard laboratory conditions (~20 °C), the pupal stage typically lasts between 6 and 10 days (Krsteska 2008; Bokina 2012), providing a relatively short final step before adult emergence. In comparison, S. rueppellii pupates in 4.80 to 9.14 days depending on temperature and humidity (Amoros-Jimenez et al. 2012), S. sulphuripes requires 9.77 days at 19.33 °C (Hopper et al. 2011), and A. javana completes pupation in 5.38 ± 0.04 days at 27.9 °C (Patro and Behera 2002). Humidity exerts a minor influence, with slightly longer durations observed at higher relative humidity levels. Food availability during the larval stage seems to have minimal impact on pupal duration in Sphaerophoria species, with only marginal differences observed (less than 0.1 day) in S. rueppellii (Amoros-Jimenez et al. 2012).

S. scripta is strictly diurnal, with adults active only in daylight hours (Gilbert 1985a; D’Amen et al. 2013). Like most syrphid pollinators, it visits flowers during sunny periods and different hoverfly species tend to forage in sequence over the course of a day (D’Amen et al. 2013). According to Gilbert (1985a), S. scripta spends 67.4% of the time feeding, 21.7% resting, and 8.7% flying, with female hoverflies spending more time feeding than males. Diurnal activity can be explained in terms of the temporal variation in floral resources and physiological limits of the species, which determine when during the day the flower-pollinator interactions occur. During the morning, more flowers open and pollen and nectar are more abundant, while the amount of nectar secreted per flower tends to decrease towards evening (Pleasants and Chaplin 1983). Nocturnal activity is absent except during long-distance migration (see Dispersal section). In practice, S. scripta is most often observed flying and feeding in mid‐morning to afternoon, when temperature and light levels favour flight. Its daytime activity leads to a succession of pollinator visits throughout the day (D’Amen et al. 2013), partitioning floral resources temporally.

There are no published studies measuring an intrinsic circadian clock in Sphaerophoria itself, but data from related hoverflies imply a robust endogenous rhythm. For example, Eristalis hoverflies remained continuously active throughout the 12-hour light phase of a 12L:12D cycle, and showed only minimal increases in night time activity when lights were briefly turned on; importantly, this did not shift their next-day activity peak (Thyselius and Nordström 2016). In that experiment, locomotor activity stayed consistent across the lifespan and was not altered by age or diet. These results indicate that hoverflies possess a self-sustained ~24‑h rhythm largely driven by an internal clock. By analogy, Sphaerophoria species are presumed to have similar circadian control over their daytime activity, with very little spontaneous nocturnal activity in constant conditions. Sphaerophoria do respond to photoperiodic changes over longer timescales. For example, in the hoverfly S. rueppellii, switching from a short day (12L:12D) to a long day (14L:10D) significantly altered development and reproductive output (Orengo-Green et al. 2022). These experiments showed that longer light periods (and higher temperatures) accelerated gonad maturation and oviposition in S. rueppellii. Although this study focused on reproduction rather than direct activity, it demonstrates that seasonal daylength cues affect Sphaerophoria biology (Orengo-Green et al. 2022).

Ambient temperature plays a critical role in modulating the diurnal activity patterns of hoverflies. Field observations of syrphid species indicate that activity is predominantly concentrated within a moderate thermal range of approximately 15–25 °C, with minimal activity recorded below 8–10 °C, suggesting a lower thermal threshold near 10 °C (Gilbert 1985). Conversely, peak activity levels are typically observed at higher temperatures of 20 °C and higher. In a field study conducted by Bańkowska (1961), diurnal activity patterns of Melanostoma mellinum (Linnaeus, 1758), S. scripta, and Chrysogaster viduata (Walker, 1852) were examined under sunny, windless conditions with maximum daily temperatures reaching 28 °C. All three species exhibited a bimodal activity pattern, characterised by an initial peak occurring prior to the daily thermal maximum and a secondary peak following the hottest part of the day (Fig. 13). Hoverflies remained inactive during early morning hours until ambient temperatures rose to approximately 16–17 °C, at which point activity gradually increased. However, when temperatures approached 27–28 °C, flight activity declined markedly, with individuals seeking shaded microhabitats to mitigate desiccation risk. For S. scripta, Bańkowska (1961) identified a thermal optimum in the range of 22–24 °C. These findings align with earlier studies on Eristalis tenax (Campan 1968, 1973), which also reported temperature-dependent shifts in diurnal activity rhythms. Specifically, S. scripta appears to transition from a unimodal to a bimodal activity pattern as ambient temperatures exceed approximately 25 °C, indicating a behavioural adaptation to thermal stress.

Flight activity in hoverflies is further influenced by weather conditions (Bańkowska 1964); rain and strong wind halt movement entirely, forcing flies to shelter under vegetation, and prolonged rain can result in significant mortality (Bańkowska 1961).

We will incorporate weather effects on hoverfly activity through an hourly weather assessment. Gilbert (1985a) provides the lowest temperatures at which different hoverfly species were seen, and temperatures at which more than 50% of flies seen were active. Sphaerophoria scripta was omitted, but data for a similar species, E. balteatus, indicates that 50% of the population becomes active when the hourly daytime temperature reaches 12 °C. Furthermore, if we assume that the minimum temperature at which E. balteatus was seen active, being 10 °C (Gilbert 1985a), is the minimum temperature for activity for S. scripta, and the temperature optimum is around 22–24 °C (after Bańkowska 1961), we can model the fraction of the S. scripta population being active (F_activ) at specific hourly temperatures (T_h) during the day with linear functions (Equation 16).

Factiv (Th)={10×Th−100, if Th∈[10,20)−10×Th+350, if Th∈(25,35]100, if Th∈[20,25]0, if Th<10 or Th>35 Equation 16

With Equation 16, the temperature at which 50% of S. scripta population becomes active is 15 °C, thus higher than the one provided by E. balteatus by Gilbert (1985a). However, it corresponds well with observations of Bańkowska (1961), in which S. scripta started to be active in the morning when temperatures exceeded 16 °C.

This activity is further restricted to daylight hours only (Fig. 14), and to specific rainfall and wind conditions (maximum acceptable rainfall R_max and wind speed W_max, which will be calibrated). Individuals that become active at a given temperature are selected randomly from the population, reflecting the influence of varying local microclimatic conditions. In addition, after Nangel and Drescher (1991), we will assume that the maximum temperature for activity is 35 °C (as the temperature in their greenhouse experiment varied between 15 and 35 °C).

Knowing when a given hoverfly starts and ceases to be active during the day (based on temperature, rainfall and wind profiles during the day), we can calculate the total number of activity hours per day (h_tot). The total activity hours per day will then be divided into time spent on feeding (h_f), resting (h_r), and flying (h_m) based on proportions provided by Gilbert (1985a). These proportions were derived from instantaneous behavioural observations recorded at the moment of first sighting, with the aggregated data interpreted as representative of the species’ energy budget. For the purposes of this study, we assume that ‘feeding’ time includes all local movements within the flower patch, whereas ‘flying’ time covers movements between flower patches. This would imply that there is a local movement distance threshold d_l (to be calibrated) above which a movement bout is considered to be long enough to allow a hoverfly reaching flight speed to find a new flower patch (see ‘Dispersal’ for details). We further assume, following Thyselius’s (2022) study on E. tenax, that activity pattern of S. scripta does not change with hoverfly age.

Gilbert (1985b) analysed dietary preferences (estimated feeding-time-budgets) of hoverflies based on field observations and categorised hoverflies according to the proportion of time spent feeding on nectar versus pollen. In this study, S. scripta was categorised as a mixed-feeder, feeding similarly frequently on pollen and nectar. Nectar serves as a main energy source, needed for flying, mate searching, and thermoregulation. Pollen, on the other hand, is required for oogenesis in females.

To date, detailed information on the energetics of S. scripta and other hoverfly species remains scarce. The most comprehensive analyses of foraging energetics are available for E. tenax (Sotavalta and Laulajainen 1961; Gilbert 1983). Gilbert (1983) quantified the net energy gain of E. tenax during continuous foraging on Aster flowers as rather low (0.01 W), while Sotavalta and Laulajainen (1961) reported an average flight energy consumption rate (C_f) of approximately 8.6 × 10^–4 mg of sugar per second (after App et al. 2025). When converted using an energy density of 17 J/mg for sugar, this corresponds to an energy consumption rate of approximately 0.015 W during flight. Sotavalta and Laulajainen (1961) (after App et al. 2025) also described E. tenax energy consumption rate while resting (C_r) with the following equation (Equation 17):

Cr=kr×M0.73 Equation 17

where k_r is the scaling parameter [J/(s × mg)] and M is the hoverfly mass [mg].

App et al. (2025) proposed to estimate C_r [W] based on the maximum possible daily energy gain E_max [J] (which provides an estimate of the upper energetic ceiling available to an organism for allocation to flight, maintenance, and reproduction within a 24-hour period) and the maximum starvation time t_{starvationmax} [s] (the time an individual is able to survive without feeding) using the following equation (Equation 18):

Cr=Emax×1tstarvationmax Equation 18

where

Emax=Cf×tflightmax +Fat%×M×Efatdensity Equation 19

where t_flightmax is maximum possible time of flight without feeding, Fat% is percentage of fat deposit related to mass, and E_fatdensity is the energy density of fat (assumed to be 37 J/mg).

Given the lack of direct measurements for S. scripta, we can estimate its flight and resting energy consumption using an allometric scaling approach. This method applies a mass-dependent scaling law with an exponent b < 1, consistent with empirical findings in insect flight energetics. The scaling relationship is expressed as (Equation 20):

MRS. scripta =MRE. tenax ×(MS. scripta ME. tenax )b Equation 20

where MR is metabolic rate, and M is body mass.

As data on the body mass of adult S. scripta are scarce (with only one study of Belyaev and Farisenkov (2019) mentioning the body mass of males to be 15.4 mg), we decided to estimate the body mass employing a general allometric scaling approach (Equation 21):

M=a×Lb Equation 21

where L is body length (mm), and a and b are scaling constants. Using E. balteatus as a reference species, with a reported mean body mass of 22.3 mg (App et al. 2025) and S. scripta body length range of 9–12 mm, we assumed an allometric exponent b = 3, a commonly accepted value for insects. The scaling constant a was derived from the average length and mass of E. balteatus, and subsequently applied to the length range of S. scripta (7–12 mm) to estimate its body mass. This yielded an estimated weight range of approximately 6.6 mg to 33.3 mg for S. scripta, with an average of 16.5 mg. This estimate aligns well with the body mass of S. scripta males reported by Belyaev and Farisenkov (2019).

Assuming an allometric scaling exponent of approximately 0.85 (which is typical for flying insects) in Equation 19, and using a mean body mass of 149 mg for E. tenax females (based on field-collected specimens, Nicholas et al. 2018), the predicted flight energy consumption rate C_f for S. scripta, with an estimated body mass range of 6.6–33.3 mg (with mean of 16.5 mg), falls between approximately 0.00106 W and 0.00419 W (with a mean of 0.00231 W).

To estimate the maximum possible daily energy gain (Emax) and, consequently, the resting energy consumption rate (C_r), the maximum starvation time (t_{starvationmax}) and the maximum possible time of flight without feeding (t_flightmax) need to be assessed for S. scripta. Arringtion et al. (2007) reported t_{starvationmax} of 7 days for E. balteatus, while Sotavalta and Laulajainen (1961) reported t_flightmax of 7 hours for E. tenax. Energy reserves generally scale roughly linearly with body mass, assuming similar relative lipid and glycogen storage. Thus, to calculate the total time until reserves are depleted, we can apply a metabolic scaling relationship with an exponent of b = 0.75 (Equation 22):

tscaled =treference ×(Mscripta Mreference )0.75 Equation 22

If we further assume that t_{starvationmax} for E. balteatus is valid for a hoverfly of mean body mass of 22.3 mg (App et al. 2025), and t_flightmax for E. tenax is valid for a hoverfly of mean body mass of 148 mg (Nicholas et al. 2018), then maximum starvation and flight times rescaled for S. scripta can be calculated as (assuming mean body mass for S. scripta of 16.5 mg):

If we assume that body mass of S. scripta can vary between 6.6 and 33.3 mg (see above), we can estimate the maximum possible daily energy gain E_max of S. scripta as varying from 14.8 J to 96.1 J depending on body mass (with a mean of 43.3 J for a mean body mass of 16.5 mg), assuming fat deposit of 5% (the same as in E. balteatus, Hondelmann and Poehling 2007). Thus, the energy consumption rate of S. scripta during resting C_r can be estimated to vary between 6.1 × 10^-5 and 11.8 × 10^‑5 W (with a mean of 8.6 × 10^-5 W for a mean body mass of 16.5 mg).

On the other hand, maximum nectar intake per foraging bout is constrained by the crop capacity. Gilbert (1983) provides average and maximum gut volumes for E. tenax of 5.8 and 17.2 µl, respectively. We can predict gut volume for S. scripta using an allometric re-scaling approach, applying a metabolic scaling relationship with an exponent of b = 0.75, based on the average gut volume (11.08 µl) and body mass (148 mg) reported for E. tenax. To simplify practical application, we then fitted a linear regression to the scaled values (Equation 23):

Gv(M)=0.094×M+0.537 Equation 23

This equation gives us gut volumes for S. scripta between 1.08 and 3.62 µl across a body mass range of 6.6−33.3 mg (with a mean value of 2.14 µl for a hoverfly with a body mass of 16.5 mg).

The maximum gut fill can be translated into the maximum energy per gut fill E_max(Gv) (reflecting the instantaneous energy intake capacity per feeding event), based on nectar sugar concentration (Equation 24):

Emax(Gv)=Gv×ρsolution ×Csugar ×esugar ×ηassim Equation 24

where ρ_solution is the density of the sugar solution (depends on concentration, ~1.0–1.4 mg/ µl), C_sugar is the sugar mass fraction (e.g., sugar concentration of 30% = 0.30 g sugar per g solution), e_sugar is energy content of sugar (assumed to be 17 J/mg), and η_assim is the assimilation efficiency (if all of the energy ingested is absorbed, then η_assim = 1).

Assuming a mean gut volume of 2.14 µl (for S. scripta with a mean body mass of 16.5 mg), the maximum energy per gut fill E_max(Gv), calculated for a 50% sugar concentration (ρ_solution = ~ 1.23 mg/µl) and an assimilation efficiency of 1, is estimated at 22.4 J.

The observed difference between the maximum possible daily energy gain E_max and the maximum energy per gut fill E_max(Gv) is expected because E_max integrates longer-term energy reserves (fat), whereas E_max(Gv) reflects only short-term carbohydrate intake. For energy-budget modelling, this distinction is crucial: E_max(Gv) constrains the instantaneous rate of energy acquisition and thus short-term activity patterns, while E_max defines the maximum daily energy allocation potential, including contributions from stored reserves. Comparing these two metrics allows estimation of gut-filling frequency necessary to sustain activity (E_max / E_max(Gv) ≈ 2 gut fills/day in case of S. scripta of 16.5 mg body mass feeding on nectar with 50% sugar concentration) and provides a framework for modelling trade-offs between feeding, flight, and reproductive investment under varying ecological conditions.

Female Sphaerophoria require pollen to mature their ovaries. As in other syrphids, newly emerged females are not sexually mature until they have fed on pollen (Amorós-Jiménez et al. 2014; Orengo-Green et al. 2022). In S. scripta, for example, laboratory studies found that females given sugar plus pollen mated and laid hundreds of eggs, whereas females on sugar alone laid no eggs (Nengel and Drescher 1991). Pollen nutrition also greatly extended adult longevity (e.g. mean female lifespan ~31 days with pollen vs ~9.5 days without, Nengel and Drescher 1991). Male Sphaerophoria mature their reproductive organs more rapidly. In S. rueppellii, one-day-old males at 25 °C were able to mate (though initial matings were infertile) by day 2, and produced fertile matings by day 3, while at 20 °C, full maturation took ~5–6 days (Orengo-Green et al. 2022). These results imply that males rely mainly on carbohydrate (nectar) reserves to fuel rapid maturation and mating activity.

To our knowledge, detailed information on the nectar preferences of S. scripta, particularly regarding sugar concentration preferences, is lacking. Gilbert (1981) investigated the sucking and ingestion rates of sugar solutions ranging from 10% to 67% in various hoverfly species, including two aphidophagous ones, Syrphus ribesii (Linnaeus, 1758) and Scaeva pyrastri (Linnaeus, 1758). For both species, sucking rates are at the level of around 0.3–0.4 µl per second for sucrose concentrations between 10 and 50%, and then drops with further increase of sucrose concentration (Fig. 15). Sugar ingestion in S. ribesii, on the other hand, indicate an optimal energy intake rate at approximately 50% sugar concentration (Fig. 15).

Adults are flower-visiting generalists (Madureira et al. 2024). They forage on a wide variety of blossoms (especially open, bowl-shaped flowers), feeding on both nectar and pollen (Klecka et al. 2018; Villa et al. 2021) (Table 7). In agricultural and urban habitats they are attracted to flowering plants (e.g. Asteraceae, Apiaceae) and even ornamental gardens (Wojciechowicz-Żytko and Dobińska-Graczyk 2025). For example, surveys in olive groves found S. scripta present wherever groundcover plants like daisies and plantains were in bloom (Madureira et al. 2024). In green spaces and orchards, adults locate flowering shrubs and herb layers and use these as sources of carbohydrates and protein. This floral visitation also makes S. scripta an important pollinator of various plants (Klecka et al. 2018).

Experiments with floral resources have shown that hoverfly flower choice is influenced by flower colour, shape, and abundance. A study on S. rueppellii by Gasol et al. (2019) demonstrated that while mating status affected overall foraging activity, with mated females moving less than virgins, it did not alter floral preferences. Both virgin and mated adults consistently favoured flat, circular, white or yellow flowers, indicating that visual floral traits are key determinants of foraging behaviour regardless of reproductive condition. In addition, adults of Sphaerophoria and other aphidophagous hoverflies possess a relatively short, sponging proboscis that is structurally adapted for nectar and pollen uptake from open flowers with accessible rewards, rather than from flowers with long corolla tubes (Gilbert 1981). This morphological trait underlies their preference for shallow-flowered taxa such as Asteraceae and Apiaceae, further constraining the set of floral resources effectively used by these species.

Since foraging movements are intertwined with reproduction and dispersal, we treat them under the heading ‘Dispersal’ below.

The amount of pollen, nectar, and sucrose concentration available to S. scripta from each habitat patch in the landscape per day will be modelled in ALMaSS using the floral resource models. The floral resource models have been developed within the B-GOOD Horizon 2020 project (Ziółkowska et al., unpublished). The framework integrates data on the amount of pollen, nectar, and sugars produced by a single flower/inflorescence of a given plant species with information on flower/inflorescence abundance (i.e. density of flowers/inflorescences per unit area), flowering phenology, plant composition of the habitat, and habitat composition and configuration within the landscape. This approach enables prediction of the spatio-temporal availability of floral resources across different habitat types and landscapes.

The amount of pollen and nectar available to S. scripta in the landscape will be limited to those plants visited only by S. scripta. Such a list of plants will be available based on analysis of plant-pollinator interactions. Table 7 presents a preliminary list of plants visited by S. scripta, which could be further revised by additional literature searches and expert knowledge.

When foraging, a hoverfly will perceive the landscape as consisting of patches of different landscape elements. All vegetated patches are attributed daily with the amount of floral resources provided by different plants composing those patches. The local perception range for resources is assumed as 150–200 m, similar to the perception range for E. balteatus provided by Arrignon et al. (2007) based on field observations. Thus, a hoverfly in a given location will only sense resources within this perception range. As individual flower positions are not modelled, floral resource availability in a given location will be assessed at the patch level, scaled by the area within the perceptual range.

In addition, the daily pollen attractiveness P_h of a given habitat patch h will be calculated by multiplying the amount of pollen resources P available to S. scripta from each plant p in the patch on day d by the plant’s pollen preference score p_s (Equation 25). The amount of pollen resources produced by plant p on day d in habitat patch h results from the daily pollen production of the plant, the proportion of the plant in the habitat patch and the area of the habitat patch. The pollen preference score p_s of a plant is a pollinator-specific measure defined on a semi-quantitative scale from 0 to 3. It is being developed within the Better-B Horizon Europe project and is intended to be linked to the floral resource models of the ALMaSS modelling framework. The pollen preference score was originally developed for bees and is based on documented plant-pollinator interactions, along with the nutritional and chemical properties of pollen, including the protein-to-lipid (P:L) and potassium-to-sodium (K:Na) ratios. While pollen nutritional traits are known to influence pollen selection in bees, no empirical studies are currently available that directly link pollen nutritional composition to pollen preference in hoverflies. Consequently, for S. scripta, the pollen preference score is presently derived solely from documented plant-hoverfly interaction data, reflecting whether a given plant species is known to be used as a pollen source. The integration of additional modifiers relevant to hoverflies (e.g. flower colour, floral morphology, or pollen accessibility) is under development and will be incorporated into future model versions once sufficient empirical evidence becomes available.

Ph=∑pPp,d×ps Equation 25

The daily pollen attractiveness P_h of a given habitat patch h in a landscape will be further scaled by the nectar attractiveness N_h to obtain the daily food attractiveness F_h of the patch (Equation 26). Scalars c_p and c_n, for the pollen and nectar attractiveness components, will be calibrated parameters.

Fh=(cp×Ph)×(cn×Nh) Equation 26

The daily nectar attractiveness of a given habitat patch N_h will combine the total amount of nectar produced by each plant species with the relative preference for sucrose concentration, modelled with constrained Gaussian model on observed ingestion rates of S. ribesii, a closely related aphidophagous species in terms of preferred habitats (meadows, grasslands, crop fields) and egg-laying preferences (herbaceous plants, crops), across a gradient of sucrose concentrations (Equation 27):

Nh=∑i=1nNi×w(Si) Equation 27

where N_i is the total nectar amount (mg/day) produced by plant species i in a patch, S_i is sucrose concentration (%) of nectar from species i, and w(S_i) is weight assigned to sucrose concentration, modelled by the constrained Gaussian ingestion function I(S_i) (Equation 28):

w(Si)=I(Si)−I(Si)minI(Si)max−I(Si)min Equation 28

I(Si)=a×[exp⁡(−(Si−b)22×c2)−exp⁡(−(0−b)22×c2)] Equation 29

Parameters a = 179.73, b = 48.84 and c = 21.98 for Equation 29 were derived from the best-fit ingestion model (R² = 0.93) to data on S. ribesii from Gilbert (1981) (Fig. 15).

The daily food attractiveness F_h of a patch will be used to drive the long-distance movement between floral patches (see section ‘Dispersal’ for details).

Furthermore, multiple feeding bouts (i.e., discrete foraging events during which the hoverfly fills its gut to its maximum capacity G_v, after which it leaves the flower patch or reduces intake until the gut is sufficiently emptied to resume feeding) need to be considered during the day. In reality, hoverflies will combine foraging and reproduction and integrate these activities together. From the modelling perspective, this integration is not easy, so we suggest viewing this as maximum of N_f feeding bouts where the maximum intake of nectar is limited by the gut volume (Equation 23). During a foraging bout, the hoverfly will attempt to fill its gut to maximum capacity. Each feeding bout can be then translated to the maximum energy per gut fill E_max(Gv), depending on sugar concentration in nectar (Equation 24). The actual energy gain during a feeding bout will be, however, a difference between potential energy gain per bout and the energy loss per bout associated with local foraging movements and flower handling (see ‘Dispersal’ section for energy budget details).

Number of feeding bouts actually performed during a day (N_real) will be restricted by a time spent on each foraging bout t_s^bout (which includes time spent in local foraging flights within the patch and total flower handling time in the bout) and time available for foraging per day (being a fraction of time available for all activities daily; see ‘Diurnal activity’ section for details). The time spent within a patch will be estimated based on the mean foraging speed (see ‘Dispersal’ section), the mean distance between floral units of plant species accepted by S. scripta within the patch, and the number of floral units required to obtain the assumed nectar intake (i.e., to fill the gut). The nectar reward per floral unit will be represented by the mean nectar amount per flower unit across all plant species accepted by S. scripta in the patch. This generalisation is necessary because the model does not operate at the level of individual plants; thus, the specific sequence of floral units visited by an individual cannot be determined.

The daily activity of S. scripta will be simulated as a state-dependent sequence of foraging, dispersal, reproduction, and resting, constrained by both time budgets and energetic state (see ‘Dispersal’ section for details. Foraging will be initiated whenever the current short-term energy level E_current falls below a predefined threshold E_{forage_threshold}, which will be calibrated as a model parameter.

Following Honĕk (1993), we assume that the S. scripta potential fecundity (potential total number of eggs to be laid) depends linearly on female mass and thus is set at the female’s emergence. As data on individual mass and fecundity were not available for S. scripta, we based the linear relationship on the minimum and maximum values reported/estimated in the literature, assuming that the minimum reported mass corresponds to the minimum reported fecundity, and the maximum reported mass corresponds to the maximum reported fecundity (Equation 30). Regarding fecundity, we take the data from Nangel and Drescher (1991). Regarding body mass, we assume a range between 6.6 and 33.3 mg (see explanation provided in section ‘Foraging’).

FT=12.097×Mf+148.16 Equation 30

where F_T is the potential fecundity of a female, and M_f is the mass of a female.

The actual lifetime egg number laid will depend on environmental conditions (weather experienced), amount of food (pollen) consumed, as pollen is necessary for the maturation of eggs, and availability of oviposition sites (i.e., plants infested with aphids). We will further assume that S. scripta females experience enough mating events during their lifetime to fertilise all the possible eggs to be laid, i.e., the potential fecundity is not decreased because of missed mating. We assume a constant pre-oviposition time of 5 days based on Nengel and Drescher (1991).

S. scripta will employ a highly adaptive oviposition strategy; females will prefer to lay eggs in immediate proximity to high-density, young aphid colonies on infested leaves, using both prey-derived semiochemicals and plant volatiles to locate optimal sites. During local movements, females will prioritise oviposition sites with higher aphid densities, as these provide better resources for larval development. Females will only lay eggs when the aphid density at a specific location (in a 10 × 10 m grid cell at which aphid densities are provided) exceeds a predetermined threshold. This behaviour may be influenced by the habitat type, but due to the lack of species-specific data and the generalist feeding behaviour of S. scripta larvae, we assume a constant threshold, expressed as a minimum aphid biomass A_th required for oviposition. Based on Polak (1980), five A. pisum aphids (≈1.3 mg each) ensure larval survival, giving a baseline threshold of 6.5 mg of aphids. This value will be scaled by a mobility factor m_l to account for the limited foraging range of first-instar larvae. To replicate natural field variability, stochastic variation around this threshold will be included.

The probability of oviposition site selection will be modelled using a logistic function, which is appropriate for this coarse spatial resolution as it captures a biologically plausible threshold-like response: low-density patches are rarely selected, probability increases steeply after exceeding the minimum biomass, and saturates at high densities. This reflects the adaptive oviposition strategy of syrphids while avoiding unrealistic fine-scale selectivity. The function is expressed as (Equation 31):

P(A,C)={11+exp⁡[−k×(A−A50)],A≥Ath0,A<Ath Equation 31

where A is aphid biomass (mg per 10 × 10 m cell), A_th is the daily biomass threshold (6.5 mg × m_l / f per cell with stochastic variation), A₅₀ is the biomass giving 50% oviposition probability, and k is the steepness parameter.

S. scripta lay eggs individually; however more than one egg can be laid per plant if aphid densities are high (Fig. 16B). Furthermore, there may be more than one suitable plant for oviposition present in a 10 × 10 m grid cell, for which the aphid density/biomass is assessed. Thus, in the model, we assume a maximum number of eggs laid per 10 × 10 m grid cell, which will be scaled by aphid density/biomass. In addition, a female will avoid laying eggs in cells already occupied by eggs or larvae.

The expected daily egg production of a female hoverfly will be modelled as a product of baseline oviposition rate and environmental scaling factors reflecting temperature and photoperiod. Formally, the daily oviposition rate E_d(t, A, T, P), where t denotes the female’s reproductive age in days, A is the aphid biomass available at the oviposition site, T is the ambient temperature, and P is the photoperiod length in hours, is given by Equation 32:

Ed(t,A,T,P)=[fA(A)×fage (t)]×fT(T)×fP(P) Equation 32

where the first bracketed term represents the baseline daily oviposition under optimal temperature and photoperiod conditions, and f_T(T) and f_P(P) are scaling factors for temperature and photoperiod, respectively.

The baseline oviposition rate will be composed of a prey-dependent term, f_A(A), and an age-dependent shape function, f_age(t) (Fig. 17). The prey-dependent term is a logarithmic function of the aphid biomass A, limited to a maximum value A_max to avoid unrealistic values, and is expressed as (Equation 33):

f(A)=a×ln⁡(min(A,Amax))+b Equation 33

where the parameters a = 10.270 and b = 20.841 represent averaged coefficients derived from Wnuk and Starmach (1977) for three hoverfly species: E. corollae, S. vitripennis, and E. balteatus (Table 8). As hoverflies in the experiment of Wnuk and Starmach (1977) were provided with plants infested with A. fabae, aphid biomass was calculated assuming an average individual aphid weight of 0.82 mg (see Table 5). An additional scaling factor may be required, as A. fabae appears to be a suboptimal prey species for S. scripta larvae. Larvae reared on A. fabae exhibit significantly higher aphid biomass requirements to complete development compared to those fed on alternative aphid species (see Fig. 11).

The age-dependent oviposition function, f_age(t), describing the temporal pattern of egg-laying over the oviposition period will be modelled using a Gaussian (normal) distribution normalized over the oviposition period, T_ovip, to ensure that total eggs sum to the maximum potential egg number (set to 550 eggs after Nangel and Drescher 1991). This is expressed as (Equation 34):

fage (t)=1Z×exp⁡(−(t−μ)22×σ2) Equation 34

with Z is defined as (Equation 35):

Z=∑1Toviexp⁡(−(t−μ)22×σ2) Equation 35

where the parameters μ = 8.33 and σ = 5 define the peak and spread of the oviposition curve. The peak was set at one-third of the oviposition period, consistent with the pattern observed for S. rueppellii at 25 °C under longer photoperiod (Orengo-Green et al. 2022). The oviposition period was set to 25 days, accounting for the mean female lifespan of 31 days with pre- and post-oviposition periods of 5 and 1 day, respectively (Nangel and Dreschel 1991).

The baseline oviposition rate is valid for the optimal temperature and photoperiod conditions, and thus will be further multiplied by a scaling factor depending on these variables (Fig. 18). Temperature will influence oviposition through the scaling factor f_T(T), modelled by a normalised Weibull probability density function (PDF). This function was fitted to limited experimental data from Orengo-Green et al. (2022), scaled between 20 °C and 25 °C, where the mean total egg numbers showed a scaling factor of 0.34 to 1. In addition, the Weibull PDF was parameterised with a minimum temperature threshold T_min = 11 °C and assumed an optimum between 25 and 30 °C. The minimum temperature threshold was established based on the Coccinella septempunctata (Linnaeus, 1758) study by Xia et al. (1999), and that of Bellefeville et al. (2019) in which at a temperature of 12 °C, some oviposition of L. glyphinivora and E. americanus was observed. The temperature scaling function is given by Equation 36:

fT(T)=WeibullPDF(T)WeibullPDF(T') Equation 36

where

WeibullPDF(T)=kλ×(T−Tminλ)k−1×exp⁡(−(T−Tminλ)k) Equation 37

with shape and scale parameters k = 4.321 and λ = 16.991 estimated from the fitting procedure and T' is the temperature that results in the maximum WeibullPDF, i.e., the optimum temperature.

Photoperiod effects on oviposition will be incorporated through the scaling factor f_P(P), which linearly scales oviposition between a minimum photoperiod threshold P_min​ = 11 hours and a maximum threshold P_max​ = 14 hours as (Equation 38):

fP(P)=min(1,max[fmin,P−PminPmax−Pmin]) Equation 38

and is clipped between f_min and 1 to represent biological constraints on egg laying, where f_min is nonnegative and the minimum scaling factor based on photoperiod.

Several studies suggest that syrphid flies respond most strongly to landscape composition at spatial scales between 500 and 1,500 m (Kleijn and Van Langevelde 2006; Meyer et al. 2009; Madureira et al. 2023), although species-specific differences exist. For example, Sphaerophoria spp. appear unaffected by the proportion of arable land at any scale (Haenke et al. 2009). Dispersal patterns in syrphids vary, with capture-recapture studies indicating that non-migrant syrphids typically move up to 100 m, occasionally reaching 400 m (Conn 1976; Wratten et al. 2003); however, gut content analyses over seven-day periods provide only net displacement, limiting understanding of their daily movement. Foraging behaviour can be context-dependent: Sphaerophoria spp. demonstrate cautious, darting flight in response to camouflaged predators like Thomisus labefactus (Karsch, 1881) (Araneae, Thomisidae), but not when predators are overtly visible (Yokoi and Fujisaki 2009).

Perception range in E. balteatus estimated from field observations is 200 m (Arrignon et al. 2007).

The timing of migration is a complex phenomenon influenced by a range of factors, including endogenous mechanisms such as the circadian clock (Denlinger et al. 2017) and abiotic factors such as weather conditions (Hlaváček et al. 2022). Recent work by Hlaváček et al. (2022) demonstrated that the peak migration of S. scripta typically occurs in September and October, with notable interannual variability in both timing and sex-specific patterns. In one observed year, females initiated migration earlier than males, although males remained consistently abundant throughout the period. In the following year, both sexes exhibited synchronous migration. Despite these variations, a female-biased sex ratio was consistently observed, with females comprising 64% and 77% of migrants across the two years. This pattern may be partially explained by the greater fat reserves in females, which can sustain longer flights and enhance survival in the harsher climates of higher latitudes (Guo et al. 2019). These energy reserves, which would otherwise be allocated to ovarian development, may also contribute to enhanced flight capabilities in females.

We will treat S. scripta as a partially migratory species. Specifically, we assume that the proportion of females from the last autumn generation will exhibit migratory behavior, departing from the local landscape before oviposition. Those which stay will lay eggs which hatch into larvae which, in the last stage, will start the overwintering. A given female from the autumn generation will initiate migration movement with a defined probability p_m.

There are two movement types planned for implementation: short-range movement and long-range movement. Short-range movement simulates intensive search behavior when the adult hoverfly scans the local surroundings in search of food (nectar and pollen) and oviposition sites (aphid prey for larvae). Based on foraging speeds reported for honey bees and bumble bees (Osborne et al. 2013; Wright 2013, cited in Becher et al. 2016), and the assumed 1 m/s foraging speed estimated for E. balteatus by App et al. (2025), we assume that S. scripta forages at approximately 0.8–1.2 m/s, depending on individual body mass. This range reflects both its smaller size relative to bees and its likely non-linear, cruising search behavior during resource exploration. Long-range movement simulates the extensive search for a different type of landscape element or vegetation. This movement could be part of dispersal behavior as a response to insufficient resources at the current location. To estimate the maximum flight speed and potential flight range of S. scripta across its body mass range, we applied allometric scaling principles derived from Ellington’s (1984) analysis of insect hovering flight. Ellington (1984) found that wing loading (q) scales with body mass (q α M^0.23), while flight speed (V) varies with the square root of wing loading (V α q^0.5). Collett and Land (1978) measured E. tenax flight behavior and velocities in the field as being at least 10 m/s but for short periods of time only. Using E. tenax’s mean body mass of 148 mg and allometric scaling principles from Ellington (1984), we can estimate S. scripta’s maximum speed when flying to range from approximately 6.6 m/s at 6.6 mg to 8.1 m/s at 33.3 mg (with 7.8 m/s for an mean body mass of 16.5 mg).

To determine whether remaining in a current location for foraging is energetically profitable for S. scripta, the balance (Equation 39) between potential energy gain per bout (gut-limited) (Equation 40) and the energy loss per bout (Equation 41) associated with local foraging movements (assuming foraging flight speed of 1 m) and flower handling will be evaluated:

Egain bout >Eloss bout Equation 39

where:

Egain bout =min[Emax(Gv),ϵf×Npatch ×πrp2×tsbout hf] Equation 40

where E_max(Gv) is maximum energy that can be stored in the crop per bout (Equation 24), ϵ_f is hoverfly foraging efficiency (fraction of available resources acquired based on visitation and handling, calibrated parameter), r_p is perception range, N_patch is patch-level nectar production (in mg/m²/day) by plants accessible by S. scripta, t_s^bout is time spent in a patch (where t_s = time spent in local foraging flights within the patch t_{local_fligh} + total flower handling time in the bout t_handle) and h_f is time within a day spend on foraging (calculated based on weather conditions and photoperiod, see section ‘Diurnal activity’).

Eloss bout =Cf×tlocal_flight +Crest ×thandle Equation 41

where C_f is flight energy consumption rate and C_rest is energy consumption when resting/handling on flowers (see ‘Foraging’ section).

A patch will be deemed profitable if the daily energy that can be obtained from accessible nectar sources exceeds the energy required for local search flights within the perceptual range (assuming, for simplicity, that energy gain comes only from nectar). This approach ensures that S. scripta preferentially remains in patches where resource availability is sufficient to offset the energetic cost of local search, and otherwise engages in long-range movements to locate more rewarding habitat. The long-range foraging movement will be restricted by a maximum daily dispersal ability and can be carried out in N_f movement bouts. This movement is driven by the availability and distance to foraging resources. The maximum daily dispersal ability D_tmax (for movements between floral patches) will be calculated from the available daily flight time (h_m) and the flight speed v. The maximum distance achieved during one bout will be restricted by available usable energy calculated based on percentage of stomach filling (Table 9).

When dispersing for oviposition sites, a hoverfly will be driven by aphid density / aphid biomass updated in a landscape daily with a resolution of 10 × 10 m. Within the perception range a hoverfly (the same as for foraging) will be capable of performing local search movements for cells providing a minimum aphid density / aphid biomass needed for larvae to survive (see section ‘Reproduction and oviposition’). During this local search, energy will be spent in a similar way as described above for foraging. If not enough aphids are available locally, then hoverfy switches to long-range movement, occurring with similar rules as long-range movement for foraging patches.

Dispersal activity will be tracked individually for each hoverfly, both in terms of time and energy spent and distance travelled, and once daily limits are reached a hoverfly will suspend its activity for that day. Importantly, daily time available for flying (h_m) includes long-range movements for both foraging and oviposition sites.

In the model, a hoverfly will switch between four behavioral states – foraging, flying/dispersing, reproduction, and resting – according to a state-dependent energy budget. Energy reserves will be represented at the individual level and divided into:

The model will simulate daytime activities under time and energetic constraints, with behavioral decisions depending on internal energy state, resource distribution, and movement costs.

The daily activity budget will be divided based on observations of Gilbert (1985a); 67.4% of daylight will be allocated to foraging and within-patch flower visits, 8.7% to inter-patch flights, and 21.7% to resting, used only when other activities are complete. Time budgets will set upper limits for each activity type; actual durations will vary daily based on resource availability and behavioral decisions.

Each activity (flying, foraging, reproduction, and resting) will consume energy at a rate dependent on body mass. Cost of flying activities will be calculated as (Equation 42):

Efly=Cf×hm Equation 42

where h_m is time spend on flying.

During a foraging bout, the hoverfly will attempt to fill its gut to maximum capacity with the potential energy gain per bout depending on nectar sugar concentration (Equation 40). The total daily nectar intake will be constrained by gut-emptying time (t_empty), determining the maximum number of bouts per day (N_max).

Egg maturation requires pollen ingestion, modelled as a daily pollen intake threshold (P_threshold) before oviposition can begin. Once mature eggs are available and E_current exceeds an oviposition energy threshold (E_ovip), the hoverfly switches to searching for oviposition sites.

The energy cost of oviposition will be calculated as (Equation 43):

Eovip =Neggs,laid ×Eegg Equation 43

where N_eggs,laid is number of eggs laid per day, an E_egg is energy needed for laying an egg (~0.05–0.2 J/egg, based on lipid- protein content of syrphid eggs; estimation from aphidophagous species). Maximum daily egg-laying rate is imposed as an additional stopping rule.

Resting will occur when all other activities are completed or constrained by time budgets. The resting metabolic cost will be calculated as (Equation 44):

Erest =Cr×hr Equation 44

where h_r is time spend on resting.

At the end of each day, remaining energy will be computed as (Equation 45):

Eend =Ecurrent +Egut +Eunused_eggs −Erest_night Equation 45

where E_gut is energy remaining in the gut (if feeding ended late), E_{unused_eggs} = (Eggs_mature – Eggs_laid) × E_egg, assuming non-laid eggs are reabsorbed and converted to fat (similar assumption as in App et al. 2025). E_{rest_night} is overnight resting metabolic cost.

Then, the daily fat balance will be updated as (Equation 46):

Fat reserve (t+1)= Fat reserve (t)+(Eend −Ethreshold ) Equation 46

where Fat_reserve(t) is the reserve level at the start of day t, and Fat_reserve(t+1) is the updated level for the following day. When the daily energy balance E_end exceeds the threshold E_threshold, the surplus is stored as fat, increasing Fat_reserve. Conversly, when E_end is below the threshold, fat reserves are mobilized to cover the deficit, decreasing Fat_reserve. This formulation ensures that fat reserves function as a dynamic energy buffer, capable of both recovery and depletion depending on the daily energy balance.

The energy available at the start of the next day will be calculated as (Equation 47):

Ecurrent next =min(Emax ,Ebaseline +αmobil ×Fatreserve (t+1)) Equation 47

where α_mobil is the fraction of fat that can be mobilized overnight, and E_baseline is the minimum short-term energy level (sugar pool) that a hoverfly naturally maintains overnight or at rest, even without recent feeding (it will be a calibrated parameter).

This structure allows day-to-day feedback, with reproductive output and survival probability depending on the previous day’s energetic balance.

In the model, a hoverfly will switch between the foraging and oviposition behavior once enough energy is gained from nectar consumption and enough pollen is consumed for egg maturation. Thus, two thresholds will be introduced, one for percentage of filling of the stomach needed for oviposition expressed in energetic terms (E_{ovip_threshold}, calibrated parameter), and a second related to pollen consumption (P_threshold). Here we assume that there is a certain amount of pollen needed for maturation of a single egg (P_egg, calibrated parameter). Thus if, for a given day, we know a daily egg production rate, we know how much pollen needs to be consumed to allow the eggs to mature. Only if this is achieved, and if enough energy has been obtained, can a female switch to reproductive behavior. We assume that pollen can be consumed at the same time as nectar. As pollen intake rate is unknown, this will be a calibrated parameter in the model, allowing to scale the amount of pollen consumed with the time a hoverfly spends in a given location, assuming a certain amount of pollen is available within the perception range of a hoverfly.

Four types of dispersal actions will be considered:

We plan to represent the movement using the following rules:

This behavior requires the specification of two functions, one for oviposition site acceptance and one for foraging site acceptance. The first is given by Equation 31, and the latter is related to assessment of patch profitability (Equation 39). At each step, the current level of energy E_current is evaluated, i.e., flying energy cost is subtracted after each flight (inter-patch or to oviposition sites), and reproduction cost is subtracted after each egg laying. Thus, if E_current falls below forage threshold during oviposition or dispersal, a hoverfly will switch back to foraging.

The above logic does not include hibernation and migration behaviors. Individuals from the last autumn generation will be assigned to one of two seasonal strategies, depending on a migration probability (p_m): (i) migration mode or (ii) overwintering/hibernation mode, producing a larval overwintering generation. In migration mode, reproduction is halted; unlaid eggs are reabsorbed, and their energy is converted into fat. Foraging is directed exclusively toward sugar intake to build long-term energy reserves until a fat threshold is reached. Once this threshold and appropriate environmental conditions (e.g., a photoperiod threshold) are met, the hoverfly migrates (and is removed from the landscape). In overwintering/hibernation mode, individuals continue to follow the standard logic, ovipositing until the daily maximum egg-laying potential is reached or until energy constraints prevent further reproduction.

In autumn, adult hoverflies preferentially exploit landscape elements with dense and structurally complex vegetation—such as field margins, hedgerows, woodland edges, meadows, extensively managed grasslands, and agricultural fields infested with aphids late in the season—which provide late-season floral resources and aphid-infested host plants, while also incidentally offering suitable microhabitats for overwintering of late-instar larvae or pupae.

Start and end of overwintering will be primarily driven by photoperiod, with temperature factor acting as an additional trigger which may fasten the onset and offset of hibernation. Thus, a threshold date H_Sdate after which the start of hibernation is mandatory will be applied. This threshold will be set as day in the year at which the photoperiod falls below a certain number of hours (Ph_start). However, if S. scripta larva experience cold temperatures earlier, the start of overwintering will come earlier. Thus a certain number of days (H_days) with minimum night temperatures below a threshold (Th_start) will be required to initiate hibernation of S. scripta. H_days, Th_start will be initially set to 5 days and 12° C, respectively, and H_date will be set as date corresponding to photoperiod of 11 h (assumed after E. balteatus).

Offset of hibernation will also be related to photoperiod and temperature. A certain number of days (E_days) with maximum day temperatures above a threshold (Th_end) will be required; however, emergence will also be restricted by date, not being earlier than a given day (E_date) corresponding with photoperiod of Ph_end. E_days and Th_end. It will be initially set to 5 days and 10° C, respectively, and E_date will be set as date corresponding to photoperiod of 11 h.

As no data on distribution of individual larvae entering and leaving the hibernation sites is available, we will assume this process to follow a non-linear saturation function, with fast initial increase and gradual slowdown (Equation 48):

CA(t)=100×(1−e−kt) Equation 48

where C_A(t) is cumulative percentage of individuals entering and leaving habitat site, and k (rate constant) and t (time in days) are parameters which will be fitted in the calibration process.

The mortality of aphidophagous hoverflies during its immature stages is generally high, although exact rates depend on species, and vary depending on habitat conditions, prey availability, and natural enemies. Like other aphidophagous syrphids (e.g. E. balteatus, E. corollae), S. scripta experiences its greatest losses during the egg and early larval stages. Survival rates documented by Nengel and Drescher (1991) were 33.1 ± 8.1% from oviposition to third instar, 53.5 ± 9.7% from third instar to pupation, and 80.6 ± 9.7% from pupation to adult emergence. These losses are primarily due to predation by ants, lacewings, ladybirds, spiders, and other generalist predators, as well as intraguild predation by other aphid predators, including syrphid larvae (Rojo et al. 2003). Additional mortality arises from egg desiccation, failure to hatch, and parasitism.

Although no specific studies on S. scripta are available, the study of Amorós‑Jiménez et al. (2012) on S. rueppellii shows that mortality in Sphaerophoria species is primarily driven by temperature and humidity. Relative humidity is a particularly critical determinant of mortality of egg and larval stages; at 50% relative humidity, larval mortality reached 100% across all tested temperatures (20 °C, 25 °C, 30 °C), and egg mortality was significantly higher than at 90% RH, exceeding 80% at some temperature-humidity combinations. In contrast, pupal mortality was largely unaffected by humidity, suggesting that the pupal stage is more tolerant of desiccation. Temperature also had an impact; higher temperatures (30 °C) led to a notable increase in pupal mortality, regardless of humidity conditions. Impact of mortality in egg and larva stages was less pronounced, especially at high relative humidity of 90%.

Aphid type and density seems to be important factor determining mortality at larval stages of aphidophagous hoverflies. Increasing mortality of larvae with decreasing aphid density was reported for E. balteatus (Putra and Yasuda 2006). Interestingly, when comparing high and low prey availability, Amorós‑Jiménez et al. (2012) reported no significant effect on larval or pupal mortality; larvae experienced 25% mortality under both regimes, and pupal mortality ranged from 5–15%. In addition, Amorós‑Jiménez and Marcos‑García (2020) found that larvae reared on R. padi and M. persicae attained higher survival rates (70% and 74%, respectively), whereas those fed on A. nerii survived at only ~40%.

Another important source of mortality in aphidophagous hoverflies is parasitism. Under certain conditions, field data suggest that the impact of parasitoids on hoverfly populations can be substantial and, in some cases, potentially severe, particularly in intensively managed agricultural landscapes (Sommaggio et al. 2014). Despite this, a comprehensive understanding of the dynamics between aphidophagous hoverflies and their parasitoids remains limited, especially with respect to species-specific effects and population-level consequences.

Parasitoids of aphidophagous hoverflies such as S. scripta primarily attack the preimaginal stages, including larvae and pupae. Many parasitoid taxa exploit Syrphinae hosts as koinobiont endoparasitoids, laying eggs in or on early larval instars and allowing the host to continue developing for some time before the parasitoid larva consumes it from within (Schneider 1969; Rotheray 1981, 1984). Consistent with this mode of parasitism, studies by Wnuk (1974) and Wnuk and Wojciechowicz (1993) indicate that parasitization does not measurably reduce the feeding capacity of syrphid larvae during their development. Instead, parasitoids primarily affect hoverfly populations by preventing successful adult emergence, thereby exerting a delayed but negative effect on future syrphid population sizes. The host ultimately dies prior to adult emergence, and the adult parasitoid emerges from the host puparium. This mode of action is characteristic of several Ichneumonidae, such as Diplazon laetatorius (Fabricius, 1781), widely regarded as one of the most frequent and ecologically important syrphid parasitoids (e.g., Schneider 1969; Rotheray 1984; Jankowska 2004; Sommagio et al. 2014). Other parasitoid families associated with aphidophagous syrphids include Pteromalidae (e.g., Pachyneuron Walker, 1833 species), which often attack later instar larvae or pupae as pupal parasitoids, and Encyrtidae (e.g., Syrphophagus aeruginosus Dalman, 1820), which also emerge from the puparium (e.g., Schneider 1969; Rotheray 1984; Jankowska 2004; Sommagio et al. 2014). In contrast to koinobionts, some parasitoids manipulate host development differently, but in all cases the outcome for the host is mortality before adulthood.

Parasitoids locate syrphid hosts using chemical cues associated with aphid colonies and the host itself. Volatile aphid-derived odours guide parasitoids to infested plants, while contact cues on the larval cuticle trigger ovipositor insertion. Final host acceptance and oviposition appear to depend on internal cues, likely from larval haemolymph (Rotheray 1981, 1984). Field surveys of parasitoid impact on syrphid larvae and pupae report highly variable parasitism rates, reflecting both temporal variation and ecological context (e.g. country, crop type, and landscape complexity). In a three-year study of parasitoids of aphidophagous hoverflies on cabbage vegetables in Poland, Jankowska (2004) documented substantial interannual variation, with overall parasitism rates ranging from 14.4% to 46.4%. D. laetatorius was the most frequent parasitoid, reaching parasitism levels of up to 21.7%. Similarly, Wnuk and Wojciechowicz (1993), also working in Polish cabbage systems infested by B. brassicae, reported that 27–40% of syrphid larvae were parasitised. Very high parasitism pressure has been recorded in cereal systems; in maize crops in Poland, Krawczyk et al. (2011) found that total parasitism ranged from 32.8% to 84.4%, with Pachyneuron grande (Thomson, 1878) as the dominant parasitoid. Comparable patterns were observed in a three-year study in northeastern Italy by Sommaggio et al. (2014), where Pachyneuron species dominated intensively managed maize fields, while Diplazon species were more prevalent in wheat and extensive habitats. In that study, parasitism rates varied from 32% in extensive habitats to 48% in wheat and up to 78% in maize, highlighting the strong influence of crop type and landscape simplification on parasitism pressure. High parasitism levels have also been documented outside Europe. On lettuce farms in Iran, Mohammadi-Khoramabadi et al. (2016) found that Enizemum ornatum (Gravenhorst, 1829), D. laetatorius, and Pachyneuron formosum (Walker, 1833) parasitized 45.0%, 14.0%, and 1.83% of syrphid larvae, respectively. In a two-year survey of lettuce and broccoli crops in Argentina, Díaz Lucas et al. (2020) reported parasitism rates ranging from 8% to 100%. D. laetatorius was recorded in both crops, whereas Pachyneuron species were found exclusively in broccoli, further supporting crop-specific differences in parasitoid assemblages and host exploitation.

Unfortunately, none of the published studies focus exclusively on Sphaerophoria species. Typically, field surveys collect all aphidophagous hoverflies present in a study system, rear them under laboratory conditions, and record the parasitoids that emerge. In many cases, parasitism rates are reported per parasitoid species rather than per host species. When host-specific data are available, the number of Sphaerophoria individuals examined is often very small compared to other hoverfly species, particularly E. balteatus. Consequently, parasitism rates reported for aphidophagous hoverflies are difficult to extrapolate directly to S. scripta. Nevertheless, parasitoid species repeatedly recorded from Sphaerophoria hosts across different studies provide valuable qualitative information on host-parasitoid associations. An overview of parasitoids reported for Sphaerophoria species, together with their mode of action and the developmental stages attacked, is therefore presented in Table 10.

Background mortality will be defined separately for the egg-to-pupa stages. This mortality is a daily probability applied at the start of each daily time step. For all the immature stages of S. scripta, this background mortality probability will depend on both temperature and humidity and will be calculated based on the polynomial regression models fitted to the mortality data on immature stages of S. rueppellii (Amorós‑Jiménez et al. 2012) (Fig. 19, Equation 49).

M(T,RH)=a1×T2+a2×T+a3×RH2+a4×RH+a5×T×RH+a6 Equation 49

The effects of aphid species and prey density on larval mortality will not be included in the model directly. The influence of aphid species has only been investigated for a limited number of taxa (R. padi, M. persicae, and A. nerii), and remains uncharacterised for other aphid species. Furthermore, unlike findings reported for other aphidophagous syrphids such as E. balteatus, the effect of aphid prey density on larval mortality in Sphaerophoria species has not been confirmed. In the only study conducted on S. rueppellii, no significant relationship was observed. We will, however, include a density-dependent mortality factor refelecting the competition among larvae and possible cannibalism. Density dependence will be introduced by limiting the number of S. scripta that could be present in a surrounding of any larva, to a fixed number of larvae. Additional larvae will be removed from the simulation (died because of food limitation, or eaten). The size of the surrounding will be defined separately for each larval instar, reflecting their increasing mobility with age.

In addition to the background and density-dependent mortality, parasitism-induced mortality will be incorporated as a distinct process acting on immature stages of S. scripta. Aphidophagous hoverfly parasitoids typically oviposit into late larval instars, but host mortality is delayed, with parasitised larvae continuing to feed, grow, and pupate normally before dying at or shortly before adult emergence. To reflect this biology, parasitism will not be implemented as an immediate stage-specific mortality factor.

Parasitism will be modelled as a two-step process. Individuals reaching susceptible larval stages (late second and third instars) are assigned a baseline daily parasitism probability (p_para0), derived from cumulative parasitism rates (P_para) observed over n days of larval susceptibility (Equation 50):

ppara 0=1−(1−Ppara )1/n Equation 50

Because species-specific parasitism rates for S. scripta are largely unavailable, the cumulative parasitism rate used in the model will be based on values reported for D. laetatorius, one of the most common and consistently reported parasitoids of Sphaerophoria species (Table 10). In the three-year field study by Jankowska (2004), a substantial fraction of the aphidophagous hoverfly larvae collected belonged to the Sphaerophoria species (11% in 1993, 48% in 1994, and 35% in 1995), making this dataset one of the strongest empirical datasets for this genus. Across the study period, D. laetatorius exhibited a mean parasitism rate of 21.7%, which will therefore be used as the reference cumulative parasitism rate (P_para) for parameterising parasitism pressure in the model. This parameter will subsequently be refined during the model calibration phase to ensure consistency with observed population dynamics under field conditions.

The effective daily parasitism probability (p_paraL) will be then adjusted for landscape-dependent variation (Equation 51):

pparaL =ppara 0×L Equation 51

where (L) is a dimensionless modifier reflecting habitat complexity (L > 1) in simplified landscapes, (L < 1) in complex landscapes. Parasitised larvae develop normally, with no reduction in aphid consumption, and all parasitised individuals experience mortality at the pupal-adult transition, representing successful parasitoid development and emergence from the host puparium.

This formulation allows parasitism-induced mortality to be incorporated as a delayed-lethal process, mechanistically distinct from background mortality defined in Equation 49, while enabling modulation of parasitism risk by landscape structure.

Foraging hoverflies may be exposed by collecting pollen and nectar from contaminated flowers. The pesticide amount in the consumed resource is represented by P_I(t) and is assumed to move directly to the hoverfly’s body (P_N(t)).

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

Contact exposure specifically pertains to foraging adults and occurs when a hoverfly touches a contaminated plant surface during foraging. The amount of pesticide transferred to the body through contact is controlled by two user-defined parameters as shown in Equation 53.

Pc=sc×S×Ps Equation 53

where P_S is the pesticide amount per square meter on the plant surface, S is a constant representing the area of the hoverfly that is in contact with the surface. Here, we might imagine that foot, abdomen, and wing contact could occur. S_C is the absorption rate that determines the amount of pesticide P_S that will be transferred to the body. This implementation does not consider foraging time, but both parameters can be adjusted to make this approach more or less conservative.

Overspray exclusively occurs when hoverflies (adults or larvae) are active in a field where simultaneous pesticide spraying occurs and/or where drift occurs in the adjacent area. Two parameters, starting time and ending time, for a pesticide spray event are used to control whether overspray can happen. Overspray can only occur if a hoverfly is in the exact location when the pesticide is being sprayed. When the overspray happens, the contaminated pesticide amount (P_O) going to the hoverfly’s body is calculated using Equation 54.

Po=so×Sa Equation 54

where S represent a proportion of the body surface, as for Equation 28, α is the pesticide spraying application rate, S_o is the absorption rate for overspray.

To determine the effect of the pesticide body burden, the initial model only considers acute mortality. To do this requires three parameters. The first is a threshold for effect, P_t, above which there is a daily probability of mortality P_m. The third threshold D is the daily decay rate of the pesticide in the hoverfly’s body. This approach will implement a first model for implementing pesticide effects and assumes that an ALMaSS or equivalent landscape model is available to generate the pesticide concentration in the nectar and vegetation, as well as overspray.