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Persistence or extinction: Through a mathematical lens
Date:11/12/2012

Philadelphia, PAScientists have estimated that there are 1.7 million species of animals, plants and algae on earth, and new species continue to be discovered. Unfortunately, as new species are found, many are also disappearing, contributing to a net decrease in biodiversity. The more diversity there is in a population, the longer the ecosystem can sustain itself. Hence, biodiversity is key to ecosystem resilience.

Disease, destruction of habitats, pollution, chemical and pesticide use, increased UV-B radiation, and even the presence of new species are some of the causes for disappearing species. "Allee effect," the phenomenon by which a population's growth declines at low densities, is another key reason for perishing populations, and is an overriding feature of a paper published last month in the SIAM Journal on Applied Mathematics.

Authors Avner Friedman and Abdul-Aziz Yakubu use mathematical modeling to analyze the impact of disease, animal migrations and Allee effects in maintaining biodiversity. Some Allee effect causes in smaller and less dense populations are challenges faced in finding mating partners, genetic inbreeding, and cooperative behaviors such as group feeding and defense. The Allee threshold in such a population is the population below which it is likely to go extinct, and above which persistence is possible. Declining populations that are known to exhibit Allee effects currently include the African wild dog and the Florida panther.

Author Abdul-Aziz Yakubu explains how disease can alter the behavior of populations that exhibit Allee effects. In infectious disease studies, the reproduction number or Ro is defined as the expected number of secondary infections arising from an initial infected individual during the latter's infectious period. For regular populations, the disease disappears in the population if (and only if) the Ro is less than 1. "In the present paper, we deal with a population whose survival i
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Contact: Karthika Muthukumaraswamy
karthika@siam.org
267-350-6383
Society for Industrial and Applied Mathematics
Source:Eurekalert

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