- Purpose -

- Approach -

- Model -

Eggs

Tortoise births in the model take place as a result of adult and elder egg-laying (elder tortoises are assumed to have a lower reproductive rate). Breeding activities in the wild take place during the spring, with peak breeding in March and June and eggs are laid in the model after a three month gestation, during the months of May thru July (Luckenbach, 1981; Woodbury & Hardy, 1948). Research and observation of tortoises under natural conditions indicates that females can produce either one or two clutches of eggs per year (Ernst & Barbour, 1972; Luckenbach, 1981), but other research indicates not all females lay a clutch every year (Hohman, Ohmart, & Schwartzmann, 1980). This model assumes that on average each adult female lays 1.84 clutches per season and, consequently, the model sub-divides the proportion of adult tortoises that reproduce as the following: 100% of the population lay eggs in May, 80% in June, and 4% in July. This assumption is based off of fieldwork that found the percentage of reproductive females observed laying one clutch was 100%, and 84% of females laid a second clutch during that same breeding season (Turner, Berry, Burge, Hayden, Nicholson, & Bickett, 1984).

Clutch size averages from four to five eggs, although num bers as low as two and as high as fourteen have been documented (Ernst & Barbour, 1972; Luckenbach, 1981). The model assumes a correlation between tortoise condition and habitat quality such that if the vegetative cover is sparse and water availability low, fewer eggs will be produced; whereas, good habitat conditions result in higher egg production levels--up to a maximum of fourteen eggs per clutch per reproductive female (Hohman, et al., 1980).

While the literature provides some description of egg survivorship rates, this information is not specific and assumptions have to be made about the interaction and importance of different factors affecting egg mortality. Research has found that "it is common for 50% of a clutch from desert tortoises in captivity to be infertile, and similar losses may occur in the wild" (Luckenbach, 1981), and that predation could account for approximately 23% of prenatal mortality in one desert tortoise population (Turner, et al., 1984).


Under natural conditions, incubation generally has been observed to vary between 90 and 120 days (Luckenbach, 1981). As mentioned above, the model assumes a 90 day incubation time. Immediately after eggs emerge from their shells, they move into the hatchling cohort of the model.

Hatchlings

From the desert tortoise literature, the actual annual mortality rate of hatchlings is not known (Turner, et al., 1984). So, like egg survivorship, assumptions were made to calculate hatchling survivorship. Hatchling survival depends on when the tortoises are hibernating or aestivating, predation, and natural causes including inadequate food or water supply. With the exception of eggs, all cohorts of tortoises hibernate and estivate (Medica, Bury, & Luckenbach, 1980). Hibernation generally occurs during the fall and winter in the months November through February (Luckenbach, 1981), and aestivation usually occurs in midsummer when temperatures approach 39.5 degrees Celsius, at which point tortoises would experience severe thermal stress and may die if they do not seek shade or cooler temperatures of burrows (Luckenbach, 1981). The summer months associated with aestivation are June and July (Nagy & Medica, 1986). Given the one month time-step, the model operates off of the average monthly temperature which doesn't reach 39.5 degrees C during the 20-year record, 1970-1990. Thus, estivation doesn't significantly influence tortoise behavior within the model.

When not hibernating, hatchling mortality is the sum of the proportion that die due to predation (we assume up to 32%) and natural causes, including inadequate food or water supply (constant of 10% in all cells). Based on the information that predation of young tortoises, and particularly hatchlings, tends to be higher than predation on adults (Luckenbach, 1981), we assume predation is a more important mortality factor. Under the best conditions, a total of 85% of the hatchlings survive, and under the worst conditions, a total of 58% survive. This gives some variation about the mean value of 79% used by Luke (Luke, 1987-1991), that we assume represents "average" to "good" conditions. This number differs greatly from previous estimates of 1-3% survival (Anonymous 1973 cited in Luke, 1987).


Tortoises remain in the hatchling cohort until their shells completely ossify, which usually occurs when the tortoise is five years old (Luckenbach, 1981). "Hatchling time" in the model is set accordingly. The reason for basing the age-class division, the "hatchling cohort," on the level of shell development is that a soft-shelled tortoise is much more vulnerable to predation than a tortoise with a hardened shell (Luckenbach, 1981). For example, raven predation on desert tortoises is primarily restricted to hatchlings whose shells are less than 110 mm maximum carapace length--in other words, small tortoises with soft shells . So, higher mortality rates distinguish hatchlings from the next cohort--juveniles.

Juveniles

Juvenile desert tortoises are those individuals who have ossified shells but who have not yet reached sexual maturity. This indicates that predation rates are lower in juveniles than hatchlings. Like the two preceeding cohorts, the literature available doesn't offer substantial empirical descriptions of survivorship within the juvenile population. Again, survivorship within the model is based on our best assumptions. When not hibernating, mortality is the sum of the proportion that die due to predation (we assume up to 22%), inadequate food (up to 4.4%), and inadequate water supply (up to 13.2%). We also have added a constant proportion of 1.7% of juveniles die each month (regardless of the season) due to diseases (frequency of disease has been assumed to be density-independent in another model--see Luke, 1990 p. 256). Under best conditions, a total of 87.1% of juveniles survive and under worst condition a total of 38.9% survive. This gives some variation about the mean value of 83% used by Luke (1990), which we assume represents "average" to "good" conditions. During hibernation, a constant 2.7% die--due to disease (1.7%) and other unknown factors (1%; undocumented).


Juveniles usually mature into adults sometime between the ages of fifteen and twenty, though it can take more or less time depending on habitat conditions (Woodbury & Hardy, 1948). The model assumes an average recruitment rate of 17.5 years. Juveniles enter the next cohort, adults, at 22.5 years of age.

Adults

Total adult mortality has been estimated to be between 1% and 2% per year (Luckenbach, 1981; Turner, et al., 1984), and as a result, is lower than the mortality of younger tortoises. Yet to complete the adult survivorship functions, we made assumptions about mortality based on predation, food and water supply, disease, and other natural causes. "Adult_Survive" is calculated the same way as the juvenile survivorship rates. The only differences between the adult and juvenile rates are that predation of juveniles is higher than adults. Tortoises remain adults until 62.5 years. All surviving adults older than 62.5 years move into the final cohort, elders.

Elders

This is the second adult cohort in the model, and the reason for dividing the adult population in this way is to distinguish between those mature individuals who can reproduce, and those who are reproducing but at a generally lower rate, the elder tortoises. In the model, elders can survive up to ten years. The maximum age that can be reached by a tortoise in our model is about 75 years, which is supported by the literature on desert tortoises (Turner, et al., 1984).