Conservation Math
DB: This is Earth and Sky – on what engineering and the study of differential equations have to do with the conservation of jaguars in Costa Rica.
JB: Ecologists and mathematicians from Texas A&M University are working together on a sort of “mathematical theory of landscape” to predict how deforestation affects Costa Rica’s jaguar population.
DB: Their process starts with information from biologists – such as how much forest a jaguar needs to find food and mate – how far jaguars will forage – and how much agricultural land they can tolerate. The researchers count jaguars and analyze satellite maps showing patches of forest and the distances between the patches. Mathematical tools are used to put these data into equations that model a variety of scenarios of deforestation – and show how each scenario might affect jaguar populations.
JB: These scientists are focusing now on the pattern of deforestation – whether forested patches are connected chains, or isolated. The models indicate that as landscape becomes more fragmented, the risk of extinction for jaguars rises. The researchers hope their models will help predict which conservation policies will work – and which corridors of land should be left alone – to enhance jaguar survival.
DB: Our thanks today to the National Fish and Wildlife Foundation – and to the U.S. Forest Service. We’re Block and Byrd for Earth and Sky.
The following people were interviewed for today’s program. Our thanks to:
Thomas E. Lacher, Jr.
Caesar Kleberg Chair in Wildlife Ecology Department of Wildlife and Fisheries Sciences Texas A&M University
College Station, TX
Paulo Lima-Filho
Department of Mathematics
Texas A&M University
College Station, TX
Dr. Michael Pilant
Professor
Department of Mathematics
Texas A&M University
College Station, TX
Dr. Peter Stiller
Professor
Department of Mathematics
Texas A&M University
College Station, TX
Dr. Jay Walton
Professor
Department of Mathematics
Texas A&M University
College Station, TX
The following books, articles and web sites were used in preparing this script:
““New mathematical model predicts conservation’s success”“:http://enn.com/news/enn-stories/2001/10/10232001/model_45329.asp, Environmental News Network, October 23, 2001
More information from Dr. Thomas E. Lacher, Jr, Department of Wildlife and Fisheries Sciences, Texas A&M University:
“Another example is the application of the mathematics of continuum mechanics to ecosystem processes. Most existing ecosystem models consider only total population numbers or total biomass for each species within an ecosystem, possibly including age or size structure, but not considering spatial distribution patterns. When spatial information is included, it is usually based upon unrealistic assumptions about what causes creatures to move about their environment leading to diffusive models of motion similar to those modeling the diffusion of heat in a material. We are addressing a long standing goal within mathematical ecology to develop a comprehensive, mechanistic framework for ecosystem modeling general enough to cover all types of organisms(plants, grazing species, predators, even bacteria if need be),accounting for all possible mechanisms of locomotion or movement and all relevant behaviors (feeding, reproduction, growth, etc).The theory is modeled after classical continuum physics which provides a minimal set of fundamental axioms and balance laws all ecosystems must obey.
“In particular, we are developing a theory for modeling the behavorial choices species make (e.g. plants ``decide’‘ whether to expend energy growing or producing seeds or storing energy in roots, etc, and animals ``decide’‘ whether to graze or hunt, mate, migrate, etc). The behavior theory borrows its inspiration from continuum thermodynamics, but unlike inert materials which move or deform based upon external forces, many creatures have a brain that mediates between external and internal environmental conditions and behavioral choices. Our behavior theory attempts to account for this decision process. The underlying premise of this theory is that while the behavioral choices an individual creature makes might appear to be more like a biased random walk through ``behavior space’‘ (i.e. the set of all possible behaviors to creature could choose to do at any particular time), the average behavior observed for large populations of creatures can be modeled deterministically. Knowledge about the spatial patterns within the ecological landscape, as discussed above, provides crucial input into the mechanistic models of the species occupying the ecological system. For example, with jaguar model postulated above, jaguars finding themselves trapped on landscape patches too small to their liking, might ``decide’‘ not to mate, which naturally would lead to a catastrophic decline in their numbers. Or if the prey upon which jaguars feed decide not to mate because the landscape patch is not to their liking, then again the jaguar population would be catastrophically affected. All of these possible scenarios can easily be modeled within our theoretical framework.
“ There are four basic aspects of models. They should maximize generality, reality, precision, and simplicity. Clearly one cannot do all of these things simultaneously. If one maximizes reality the model will likely be extremely complex, rather than simple. If one wants general explanations of ecological patterns, then the precision of those predictions for specific situations is likely to be very low. Thus, models are always some compromise among these attributes. A very general answer to your question is that you include or delete things based upon what you want the model to accomplish. Lets return to the jaguar scenario. Jaguars use lots of kinds of habitats with different frequencies. There are also many different forest types in Costa Rica, based upon species composition, degree of human disturbance, etc. A specific model of the impact of human disturbance on jaguar movements should include all of this information, but we can probably get a pretty good idea of how we affect jaguars simply by considering forest versus non-forest cover. We have excluded a lot of information on jaguar biology that is available, but it would make the model extremely complex and probably not generate a much different answer. We can then add factors to add more precision for a specific location, but we decrease the generality. For some species, we lack data on how far they might disperse. We can use information from a similarly sized organism as an estimate. We can then test the sensitivity of the model to error in that particular bit of information by tweaking the number and seeing how a change in 10 or 20percent will affect the predictions of the model. This is called sensitivity analysis, precisely because it allows us to determine how sensitive the model is to certain variables.”
