- Tortoise Dispersal Submodel -

Purpose

The purpose of this sub model was to simulate movements of tortoises between adjacent cells as well as calculate changes in juvenile, adult, and elder tortoise densities due to dispersal. Values generated in this submodel are utilized by the tortoise submodel to adjust tortoise densities within each cell.

Approach

The general approach was to simulate juvenile, adult, and elder tortoise dispersal movements by designing a set of rules that dictate when and where tortoises move. Net change in the number of tortoises within a cell due to dispersal is the difference between the number of tortoises that emigrated and the number of tortoises that immigrated. Dispersal movements are restricted by three primary factors: hibernation, tortoise density, and cell conditions -vegetative cover and availability of green vegetation. Conditions of adjacent cells do not entice animals to emigrate from an acceptable cell. But, the condition of each adjacent cell, relative to the other three adjacent cells, determines the proportion of emigrants that immigrate into that cell. The total number of tortoises immigrating into a cell is the sum of immigrants from each of four directions, and represents the number of animals that emigrate from adjacent cells into the cell of interest. Due to limitations in the available software, tortoises can only move the distance of one cell per time-step, 1 km/month, and the direction of movement is restricted to the four cardinal directions (i.e., no diagonal movement).

Model

To date, no published study has investigated the long range dispersal movements of desert tortoises. Given the importance of movement between populations or sub-populations to population genetics and long-term viability, more detailed studies are needed for threatened and endangered species such as the desert tortoise. Gibbons (1986) borrowed generalizations about dispersal in other turtles to infer causes of long-distance movements in desert tortoises. The following four behavioral and habitat conditions, documented in other turtles, each may contribute to dispersal in desert tortoises (Gibbons, 1986): 1) nest site selection, 2) seasonal migration, 3) departure from unfavorable habitat conditions, and 4) movement by males in search of females. The relative importance of each condition is unknown for many turtle species; clearly, such information should be collected in order to manage threatened and endangered species more effectively.

As mentioned earlier, the desert tortoise model assumes that male and female tortoises are similar with regard to growth, reproduction, and survivorship; therefore, only females are modeled explicitly, and a 1:1 sex ratio is used (see "tortoise submodel" section above). Given this modeling structure, it was not possible to incorporate dispersal patterns due to movement by males in search of females. Also, the spatial resolution of 1 square kilometer limits the model's ability to describe potential nest site locations in detail. Burrows are often located in the walls of washes, but with a 1 square km resolution, washes are too small a detail to detect. Thus it is assumed that each cell can have multiple burrow sites, thus burrow sites do not specifically determine where tortoises migrate. Of the four conditions described above, two were incorporated into the model as incentives for dispersal, and it was assumed that both forces affected males and females equally: seasonal migration and departure from unfavorable habitat conditions.

Desert tortoises hibernate and aestivate in order to reduce physiological stresses associated with temperature extremes. However, as mentioned earlier, the one month time step precludes incorporating aestivation behavior, given that average monthly temperature data doesn't reveal the daily fluctuations of temperature extremes during the summer. For this reason, of those two behaviors, only hibernation significantly influences tortoise movement.

Tortoises emigrate from cells that have relatively low amounts of vegetative cover, low amounts of available green forage, and high tortoise densities. The first two factors are included the habitat suitability of a cell. This is an index (from 0-1) that determines the degree of "push" that forces a tortoise to leave a cell. The index is a function of the vegetation cover and the available food within the cell.

Tortoise density also affects the tortoise's desire to remain within a cell. Tortoises are not territorial, their home ranges do overlap, but they are social animals. Exactly how the social relations within the population work is not well known, and there isn't any published literature on the topic. Given that juveniles are younger and not reproducing, it was assumed that they were more mobile and less valued within the social structure. Thus, juveniles were more sensitive to densities.

The two general push forces, habitat suitability and density were then combined and augmented with the parameters of elevation and seasonality. If the elevation is above 3500 feet it's highly unlikely that one would find a tortoise in that environment, although there are anomalies. Physiological constraints may prevent tortoises from utilizing high elevation areas, regardless of the availability of food and shelter. Additionally, if the tortoise is hibernating then migration is assumed to not occur.