Figure 3 shows a scheme of the main features of the model being built for
H. rufipes. The life stages considered for each individual were (1) egg, (2) spiderling and (3) adult. Individuals entered the next life stage if they did not die first. Only female individuals were considered, because they are the ones that limit the size of next generation of individuals.
Figure 3 also shows the functions that apply to the individual in each life stage. These functions depend on variables including daily soil temperature (T—°C), because this is a spider that lives on the soil surface and topsoil (0–0.3 m), daily precipitation (P—mm), refuge (a categorical variable expressing the abundance of stones of each GIS polygon in the landscape), food availability (a categorical variable expressing the abundance of food of each GIS polygon in the landscape, and dependent only on farm management events) and farm management events.
3.1.1. Development
Development rates, r (day
−1), of the individuals at egg and spiderling life stages are dependent on T. We used the linear day-degree model, as referred to in [
7] to express these rates:
where T
d is the lower temperature threshold for development (°C) and K is the duration of the stage, a measure of the physiological time required for the completion of a developmental process, in day-degrees (dd) (
Table 1). The upper threshold for development was not considered because it was assumed that this spider is adapted to the climate of the study area, being able to regulate the heat to which its eggs are subjected by placing them under stones where they develop correctly [
8].
Spiderling development rate was dependent on the categorical variable food availability, assigned to each GIS polygon. The development rate was multiplied by a factor related to the food availability category (
Table 2). Food was considered as a non-limited item for the spider, because it is a generalist and does not depend only on prey biomass (which is a function of crop growth, represented by leaf area index and biomass metrics).
H. rufipes can eat food available in the soil, especially under stones, when there is less food available on the vegetation (e.g., prey, nectar, blackscale honeydew, etc.) because of farm management and/or climate occurrences. This way, we classify the food availability into two categories: excellent, corresponding to no farm management events, and high, corresponding to when tilling, pesticide and fertilizer application and harvest occur.
3.1.2. Mortality
Mortality is a stochastic function reflecting actions that arise from the landscape—abiotic conditions and farm management—and from interaction with other species or developmental problems—biotic conditions.
To these factors different probabilities of spider mortality were assigned, based on reasonable assumptions subjected to further tuning (
Table 3) which are implemented when each of them occurs.
Abiotic mortality is related to extreme events—insufficient soil water content and floods. Note that mortality associated with low and high temperatures was not considered because this spider is well adapted to the low temperatures that occur in the study area, and its behavior of living under stones allows it to cope with high temperatures.
Farm management mortality was related to farming operations such as tilling, application of pesticides and fertilizers, and consequences of harvest. In addition, a set of specific mortality probabilities for each of the actions occurring in the different types of crops, particularly different types of olive groves, is developed. Pesticide application was considered to influence the mortality of spiders to a lesser extent as compared to fertilizer application or consequences of harvest. This is because, hypothetically, the spider is protected under stones from toxicity by contact. However, there was the possibility of ingestion of prey that were killed by pesticides. This possibility will be further appraised.
Biotic mortality was related to failures during the molting process (for spiderlings), parasitism and predation.
Failures during the molting process can occur when spiderlings molt. As the molting process takes less than the time step of the model (1 day), it was not considered for modeling. However, the associated mortality probability was run at the end of the spiderling life stage (when development finishes).
Parasitism and predation were included in a mortality category called daily mortality. Daily mortality was different when the spiders are active and when they overwinter. Although adults are considered immobile during egg development, they have daily mortality as active spiders (opposite to overwintering) because they walk during the twilight and return to the same place.
3.1.3. Overwintering
H. rufipes overwinters during the period of the year when temperature and food supplies are low. During this period, all individuals are immobile and do not eat.
In the model, because the first day of the simulation was defined to be 1 January, the simulation initiates when the spiders are overwintering, so there is a small period of overwintering at the beginning of the simulation. The number of day-degrees was calculated for the shortest overwintering period and for the normal period corresponding to the simulation running for the subsequent year. For this, the mean temperature of soil was calculated for the periods 1 January–21 March and 21 December–21 March, with a result of 7.75 °C and 7.71 °C, respectively. The day-degrees for the two intervals were obtained by multiplying the mean temperature of soil by the number of days of each period (
Table 4).
This way, to start movement and ability to reproduce, the spider accumulates day-degrees from the beginning of the year and starts dispersal when the sum exceeds a threshold, 620 dd, or at day 80 counted from the beginning of the year. On day 355, adults start overwintering until the end of the simulation (if it goes only until 31 December). They start dispersal when the sum exceeds a threshold, 694 dd, or at day 445 counted from the beginning of the first year of simulation.
3.1.4. Movement
Movement is a stochastic function that runs between a lower T threshold (T
mi) and an upper T threshold (T
ms) (
Table 5).
Adults move more freely than spiderlings, except during the period of egg development. Each step corresponds to 1 m displacement. The tendency of a spider to occupy a particular polygon is determined by a categorical variable called refuge (
Table 6). If the spider is in a GIS polygon with a low refuge category (equal or less than 2), it will walk the allowed maximum number of spatial steps, so it can try to get out of that polygon. If the spider is in a GIS polygon with a high refuge category (equal to 3), it will walk less than the allowed maximum number of steps.
Table 7 shows the maximum number of steps that a spider can walk per day. An adult is considered immobile during the egg development period. This is because the movement during hunting ends always at the same place—the location of the eggs—and its duration (during twilight) is shorter to the time step of the model. In fact, Ref. [
4] observed adult females near eggsacs in the field. Therefore, it is expected that adult females will stay close to their eggsacs, even when they hunt during twilight.
3.1.5. Reproduction
Only the adults that are in polygons with category of refuge equal to 3 (
Table 6) in spring may initiate reproduction. This way, each adult infers what day of the year it is, and if it is in the proper place. This place is like a nest, where the eggs will be laid. The adult starts laying eggs as soon as it stops overwintering. Depending on the time of the year, it will have a certain probability of reproducing. The high summer temperatures diminish the movement of spiders and therefore there may be no encounters between males and females for mating. Therefore, in our model, we set that there will be no ability to lay eggs from 1 July, the 182nd day of the year, onwards. We also consider that it will only reproduce in its first year of life. The assumed reproduction probabilities according to time of the year are shown in
Table 8. Finally, during the period of development of the eggs, the probability of reproduction is 0.
It has been observed in the lab that from each eggsac, an average of 20 spiderlings hatch. As we are only considering females in this model, we established that half of this number corresponds to females. This way, each adult lays two sets of eggs, each containing 10 eggs. Therefore, each adult lays 20 eggs. A set of eggs represents an eggsac.
Currently, the code being built for the
H. rufipes model allows one to simulate the reproduction function in a generic landscape.
Figure 4 shows the eggs laid by adults in two different steps of the simulation of reproduction of
H. rufipes, using the ALMaSS framework in the generic landscape.