Insights from mathematics

Protecting the California condor from extinction is about biology, right?

That is true only if you consider mathematics to be an essential part of biology.

This post notes 3 older examples of insights provided by mathematics into the plight of the California condor. These examples all date from the time when the condor’s future was especially bleak.

In an article published in 1971, David Mertz of the University of Illinois starts with the few facts about the California condor’s life cycle that were available at the time. He then applies mathematical theory to this limited information to better understand how the condor population might be managed to prevent its extinction.

Among Mertz’s conclusions are that:

while it is important for immature condors to survive until they reach maturity, it is more important to minimize the premature deaths of mature birds – the continuation of the species is especially dependent on adult condors living long, reproductively-active lives

the California condor as a species does not have the capacity to recover from a, in Mertz’s words, “catastrophic decimation of population numbers” – so condors must be assured of “a very stable environment”, one that is free of even infrequent threats

The title of Mertz’s article is “The Mathematical Demography of the California Condor Population”. It was published in the American Naturalist.

In a 1986 article, Lynn Maguire of Duke University applied decision analysis to several questions concerning endangered species. The author describes decision analysis as a (mathematical) “tool for guiding business decisions under uncertainty”.

As one example, the technique is employed to choose between 2 management alternatives: (a) leaving all California condors in protected habitat or (b) capturing some condors for a captive breeding program. As I am not familiar with decision analysis, I will let the author explain its value in this case:

Decision analysis can be used to explore whether opposing parties recommend management actions that are consistent with their substantive beliefs [about the condor’s circumstances] … and with their values [concerning endangered species] ….

[Applying decision analysis] simplifies the issues arising in such a case.

Maguire’s article “Using Decision Analysis to Manage Endangered Species Populations” was published in the Journal of Environmental Management.

Brian Dennis, Patricia Munholland, and J. Michael Scott collaborated to develop a new statistical method for determining the probability that an endangered species will become extinct. They applied their sophisticated mathematics to several species, including the California condor.

The researchers’ method requires knowing the number of individuals living at different points in time. Notably, the scientists were disappointed by the limited information about the size of the California condor population:

Astonishingly, no really accurate count was undertaken until the 1980s …

But based on the best available population estimates for 1965-1980 and assuming that no new actions were taken after 1980 to protect the species, the method yielded a nearly 40% probability that the California condor would be extinct by the year 2000.

01 Dennis et al 1991

Given these results, the scientists concluded:

There is little doubt that the 11th-hour decision to capture the last remaining individuals of the … California Condor [has] provided opportunities to save [the] species. [The method] strongly suggests that emergency measures [to save the condor] would have been justified some years sooner.

(There were attempts made in the 1950s to capture California condors for captive breeding, attempts that raised significant controversy.)

The article “Estimation of Growth and Extinction Parameters for Endangered Species” was published in Ecological Monographs in 1991.

As the above examples illustrate, mathematics has provided important insights into why the number of California condors was in decline during nearly all of the 20th century, and what might be done to reverse that decline. This new understanding was considered and incorporated into the plans for managing the condor population and preventing the species’ extinction.

In future posts I will note more examples of math’s contributions to the condor’s survival, including examples where the capabilities of modern computers were also required.