Requirements for Long-term Persistence of the Texas Horned Lizard
by E. J. Allen, Department of Mathematics at Texas Tech University
Presented at the First Annual Conference on Horned Lizards on May 27,1993
Reprinted from Phrynosomatics, August-September 1993
This paper examines what requirements are needed for the long-term persistence of the Texas Horned Lizard. Mathematical models for persistence-time are used to obtain estimations. Here are some facts to keep in mind.
Population size and persistence through time are random processes; and populations, whether they be animal or plant, experience random fluctuations. These are due to fluctuations in birth and death rates and to environmental variations. In addition, populations are limited by resources, habitat size, and loss of individuals by emigration.
These persistence-over-time models used by mathematicians take into account the inherently random behavior of the birth-death process. They also incorporate environmental variations and emigration losses. And they've been tested against persistence data for mountain animals in the southwestern U. S. [E. J. Allen et al., J.Theor. Biol. (1992)].
Here's an example of a mathematically simulated population: with a birth rate of 0.5 (or 50%), and death rate of 0.5, and a maximum population size of 200, the mean [average] persistence time T of that population would be 338 years. Then that population would be gone.
The basic results of persistence-time models are very useful. For example, persistence-time is proportional to maximum population size, and therefore to habitat area. Persistence-time decreases rapidly as the ratio of death rate to birth rate increases. Hypothetically, if a population of 10,000 horned lizards has a birth rate of 0.35 and a death rate of 0.385, they could only persist for 210 years.
There are several benefits and limitations of persistence- time modeling. Models help us understand how changes in population parameters can affect persistence-time. They can also assist in assessing management strategies for long-term persistence.
However, due to a lack of actual field data on persistence, accurate estimates of persistence-time are difficult to make for a particular species. One must also assume that there are no irreversible or systematic changes in the environment, such as a climatic shift or the introduction of a new species.
The effectiveness of management strategies can be evaluated in terms of persistence-time.
Take, for example, the simple management strategy of removing individuals from the population when the population exceeds a maximum level (to prevent deterioration of the habitat). Or a researcher might simply notice the habitat is improved because the population has fallen below a critical level (that is, the death rate is greater than the birth rate). If the population level is less than 10,000 individuals, and the birth rate is 0.28, with a death rate of 0.42, then the persistence of the population over time would theoretically be 62.1 years. If management techniques decreased the death rate to 0.335, the persistence-time would be 14,300 years. Think about it - a difference in the death rate by only 55 lizards per 1000 has dramatic effects.
The long-term persistence of the Texas Horned Lizard is influenced by many factors.
Here are some requirements for the long-term persistence of the Texas Horned Lizard:
1. A viable harvester ant population, which is about 66% of the Texas horned lizard diet according to E. R. Pianka and W. S. Parker [Copeia (1975)];
2. A large land area [persistence time is proportional to the maximum population size, which in turn is proportional to habitat area ]
3. No changes in the environment that may increase the ratio of death rate to birth rate.
Unfortunately, irreversible changes in the environment may occur that could decrease the persistence time of the Texas Horned Lizard.
For example, increased agricultural expansion in semi-arid regions can reduce horned lizard habitat. There are new or improved drought-resistant plants that may affect land usage in West Texas. Also, invading species, such as fire ants, can negatively affect harvester ant and horned lizard populations. And research shows that fire ants appear to be adapting to the drier climate of West Texas [Sherman Phillips, Texas Tech University (1993)].
However, an appropriate management strategy can significantly increase persistence time. Recall that persistence-time can increase dramatically – if the management strategy successfully decreases the ratio of death rate to birth rate. (In the earlier example, persistence time increased from 62 years to 14,300 years.)
This model shows that there are some simple strategies that deserve examination.
1. Relocation of individuals from a population, if the population exceeds a maximum level, to prevent deterioration of the habitat. The flip side of this action is noticing that when the population falls below a critical level, that the habitat is improved, which theoretically decreases the ratio of death rate to birth rate.
2. Rearing of young horned lizards: The death rate for juvenile horned lizards is about 70%, but it is only about 35% for adult horned lizards [E. R. Pianka and W. S. Parker, in Copeia (1975)]. By improving survivorship of young to adulthood could have a dramatic impact.
3. Improve the habitat for harvester ants – perhaps by providing desirable colony sites.
In conclusion, continuing environmental and agricultural changes can significantly reduce the persistence time of the Texas Horned Lizard in Texas.
But management strategies may be used to increase the persistence time. For example, one might improve harvester ant habitat. Or promote harvester ants as beneficial to rangeland. Harvester ants improve the tilth, fertility, and aeration of the soil and also are useful as scavengers and predators of insects [G. C. Wheeler and J. N. Wheeler, The Ants of Nevada (1986)]. Or one might raise or protect young horned lizards to reduce the population death rate. Unfortunately, the rearing of young horned lizards is extremely difficult in captivity.
by E. J. Allen, Department of Mathematics at Texas Tech University
Presented at the First Annual Conference on Horned Lizards on May 27,1993
Reprinted from Phrynosomatics, August-September 1993
This paper examines what requirements are needed for the long-term persistence of the Texas Horned Lizard. Mathematical models for persistence-time are used to obtain estimations. Here are some facts to keep in mind.
Population size and persistence through time are random processes; and populations, whether they be animal or plant, experience random fluctuations. These are due to fluctuations in birth and death rates and to environmental variations. In addition, populations are limited by resources, habitat size, and loss of individuals by emigration.
These persistence-over-time models used by mathematicians take into account the inherently random behavior of the birth-death process. They also incorporate environmental variations and emigration losses. And they've been tested against persistence data for mountain animals in the southwestern U. S. [E. J. Allen et al., J.Theor. Biol. (1992)].
Here's an example of a mathematically simulated population: with a birth rate of 0.5 (or 50%), and death rate of 0.5, and a maximum population size of 200, the mean [average] persistence time T of that population would be 338 years. Then that population would be gone.
The basic results of persistence-time models are very useful. For example, persistence-time is proportional to maximum population size, and therefore to habitat area. Persistence-time decreases rapidly as the ratio of death rate to birth rate increases. Hypothetically, if a population of 10,000 horned lizards has a birth rate of 0.35 and a death rate of 0.385, they could only persist for 210 years.
There are several benefits and limitations of persistence- time modeling. Models help us understand how changes in population parameters can affect persistence-time. They can also assist in assessing management strategies for long-term persistence.
However, due to a lack of actual field data on persistence, accurate estimates of persistence-time are difficult to make for a particular species. One must also assume that there are no irreversible or systematic changes in the environment, such as a climatic shift or the introduction of a new species.
The effectiveness of management strategies can be evaluated in terms of persistence-time.
Take, for example, the simple management strategy of removing individuals from the population when the population exceeds a maximum level (to prevent deterioration of the habitat). Or a researcher might simply notice the habitat is improved because the population has fallen below a critical level (that is, the death rate is greater than the birth rate). If the population level is less than 10,000 individuals, and the birth rate is 0.28, with a death rate of 0.42, then the persistence of the population over time would theoretically be 62.1 years. If management techniques decreased the death rate to 0.335, the persistence-time would be 14,300 years. Think about it - a difference in the death rate by only 55 lizards per 1000 has dramatic effects.
The long-term persistence of the Texas Horned Lizard is influenced by many factors.
Here are some requirements for the long-term persistence of the Texas Horned Lizard:
1. A viable harvester ant population, which is about 66% of the Texas horned lizard diet according to E. R. Pianka and W. S. Parker [Copeia (1975)];
2. A large land area [persistence time is proportional to the maximum population size, which in turn is proportional to habitat area ]
3. No changes in the environment that may increase the ratio of death rate to birth rate.
Unfortunately, irreversible changes in the environment may occur that could decrease the persistence time of the Texas Horned Lizard.
For example, increased agricultural expansion in semi-arid regions can reduce horned lizard habitat. There are new or improved drought-resistant plants that may affect land usage in West Texas. Also, invading species, such as fire ants, can negatively affect harvester ant and horned lizard populations. And research shows that fire ants appear to be adapting to the drier climate of West Texas [Sherman Phillips, Texas Tech University (1993)].
However, an appropriate management strategy can significantly increase persistence time. Recall that persistence-time can increase dramatically – if the management strategy successfully decreases the ratio of death rate to birth rate. (In the earlier example, persistence time increased from 62 years to 14,300 years.)
This model shows that there are some simple strategies that deserve examination.
1. Relocation of individuals from a population, if the population exceeds a maximum level, to prevent deterioration of the habitat. The flip side of this action is noticing that when the population falls below a critical level, that the habitat is improved, which theoretically decreases the ratio of death rate to birth rate.
2. Rearing of young horned lizards: The death rate for juvenile horned lizards is about 70%, but it is only about 35% for adult horned lizards [E. R. Pianka and W. S. Parker, in Copeia (1975)]. By improving survivorship of young to adulthood could have a dramatic impact.
3. Improve the habitat for harvester ants – perhaps by providing desirable colony sites.
In conclusion, continuing environmental and agricultural changes can significantly reduce the persistence time of the Texas Horned Lizard in Texas.
But management strategies may be used to increase the persistence time. For example, one might improve harvester ant habitat. Or promote harvester ants as beneficial to rangeland. Harvester ants improve the tilth, fertility, and aeration of the soil and also are useful as scavengers and predators of insects [G. C. Wheeler and J. N. Wheeler, The Ants of Nevada (1986)]. Or one might raise or protect young horned lizards to reduce the population death rate. Unfortunately, the rearing of young horned lizards is extremely difficult in captivity.
