# Persistence or extinction: Through a mathematical lens

##### Nov 12, 2012

Scientists 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 is precarious even when Ro is less than 1," says Yakubu. "That is, independent of Ro, if the population size decreases below a certain level (the Allee index), then the individuals die faster than they reproduce."

A previous study by the authors showed that even a healthy stable population that is subject to Allee effects would succumb to a small number of infected individuals within a single location or "patch," causing the entire population to become extinct, since small perturbations can reduce population size or density to a level below or close to the Allee threshold.

Transmission of through a population is affected by local population dynamics as well as migration. Thus, when trying to understand the resilience of the ecosystem, the global survival of the species needs to be taken into account, that is, how does movement of animals between different locations affect survival when a disease affects one or more locations? Various infectious disease outbreaks, such as the West Nile virus, Phocine and distemper viruses have been seen to spread rapidly due to migrations.

In this study, the authors extend their previous research by using a multi-patch model to analyze Allee effects within the context of migration between patches. "We investigate the combined effect of a fatal disease, Allee effect and migration on different groups of the same species," Yakubu says. In their conclusions, the host population is seen to become extinct whenever the initial host population density on each patch is lower than the smallest Allee threshold. When the initial host population has a high Allee threshold, the population persists on each patch if the disease transmission rates are small and the growth rate is large. Even in the case of high Allee thresholds, the host population goes extinct if the disease transmission rate is high, and growth rate and disease threshold are small. The presence of a strong Allee effect adds the possibility of population extinction even as the disease disappears.

The research can be applied to various kinds of populations for conservation studies. "Our models and results are very general and may be applied to several declining populations," says Yakubu. "For example, the African wild dog, an endangered species, is vulnerable to fatal diseases like rabies, distemper and anthrax. Our models can be used to investigate how the Allee threshold of one subpopulation of an African wild dog pack at a geographical location is influenced by the collective migrations of several wild dog populations from different packs with different Allee thresholds."

The authors' mathematical models and rigorous analysis can be extended with the help of field data. "Future work will need to get specific field data in order to refine the model and use it to design conservation strategies for preservation of these somewhat endangered and declining populations,"says Yakubu.

Explore further: Reducing patient ER wait times mathematically

More information: Host Demographic Allee Effect, Fatal Disease, and Migration: Persistence or Extinction, Avner Friedman and Abdul-Aziz Yakubu, SIAM Journal on Applied Mathematics, 72(5), 1644–1666 (Online publish date: 25 October 2012) epubs.siam.org/doi/abs/10.1137/120861382

## Related Stories

#### From yeast, researchers learn how populations collapse

Jun 01, 2012

In the early 1990s, overfishing led to the collapse of one of the most bountiful cod fisheries in the world, off the coast of Newfoundland. Twenty years later, the cod population still has not recovered, dramatically ...

#### Study proposes a mathematical model to study malaria transmission

Jun 20, 2012

Malaria affects over 200 million individuals every year and kills hundreds of thousands of people worldwide. The disease varies greatly from region to region in the species that cause it and in the carriers that spread it. ...

#### Diversity among bird populations found to reduce threat of West Nile virus

Jun 25, 2008

A biologist and undergraduate student have discovered that what's good for an area's bird population is also good for people living nearby.

#### Researcher explores role of human behavior in infectious disease emergence

Apr 29, 2010

Wildlife scientists Kathleen Alexander examined how different human behaviors influence disease transmission between domestic dogs and the African wild dog, an endangered species.

#### Researchers demonstrate relationship between predation and extinction in small populations

Sep 03, 2010

(PhysOrg.com) -- Two ecological issues of increasing concern are the conservation of threatened and endangered species and the management of invasive species. A study by University of Georgia Odum School of Ecology postdoctoral ...

#### Wild dogs didn't go extinct in east Africa after all

Jan 23, 2012

In 1991, conservationists announced with dismay that endangered African wild dogs had gone extinct from the Serengeti-Mara region of east Africa. Now the latest genetic study reveals that this proclamation ...

## Recommended for you

#### Gender identity and single-sex schools

2 hours ago

Newspaper headlines worldwide tout the benefits of single-sex schools: Girls 75% more likely to take math if they go to a single-sex private school, Will boys learn better if girls aren't allowed? Single-sex education is ...

#### Pregnant job applicants can act to dispel discriminatory stereotypes

3 hours ago

Pregnant women are more likely to experience discrimination in the job search process than nonpregnant women, but they can minimize bias by addressing negative pregnancy stereotypes in the application process, according to ...

#### Women's presence in science is not reflected in peer-review authorship or citations

4 hours ago

After reviewing the authorship of 5.4 million peer-reviewed articles, University of Montreal information scientist Prof Vincent Larivière and colleagues from UQAM and University of Indiana have established that women are ...

#### Social exclusion and consumer product preference: Drink Pepsi to fit in, but fly American to stand out?

5 hours ago

Social networks are commonplace in this day and age, and how we fit in may depend on anything from political affiliation, to religion, to even our own personality traits. According to a new study published in the Journal of ...

#### Colleges pay attention: How do top 10 rankings influence applications?

5 hours ago

Ranked lists are everywhere. If you want to pick out a college, restaurant, hotel, or doctor, chances are there's a Top 10 list that can tell you which ones are the best. According to a new study in the Journal of Consumer Re ...

#### Mounting challenges undermine parenting

5 hours ago

New findings from a long-running study of nearly 1300 rural children by UNC's Frank Porter Graham Child Development Institute (FPG) reveal that parenting deteriorates when families face a number of risk factors ...

##### Tausch
1 / 5 (1) Nov 24, 2012
All life goes extinct.
Or rewrite physics.
##### RazorsEdge
1 / 5 (1) Nov 26, 2012
Send more money is the theme. I don't see any consideration that there could be no conservation strategy that can save a declining species.

## More news stories

#### Colleges pay attention: How do top 10 rankings influence applications?

Ranked lists are everywhere. If you want to pick out a college, restaurant, hotel, or doctor, chances are there's a Top 10 list that can tell you which ones are the best. According to a new study in the Journal of Consumer Re ...

#### Nutrients in food vital to location of early human settlements

Research led by the University of Southampton has found that early humans were driven by a need for nutrient-rich food to select 'special places' in northern Europe as their main habitat. Evidence of their activity at these ...

#### Game theory used to explain evolution of 'third party punishment'

You're shopping for holiday gifts when you spot someone pocketing a nice pair of leather gloves. What do you do?

#### Office holiday parties highlight racial dissimilarities and fail to promote team unity

With the holiday season upon us, companies across the country are excitedly coordinating holiday office parties to celebrate a year's worth of work and provide a social setting that can build stronger bonds among employees. ...

#### Women's presence in science is not reflected in peer-review authorship or citations

After reviewing the authorship of 5.4 million peer-reviewed articles, University of Montreal information scientist Prof Vincent Larivière and colleagues from UQAM and University of Indiana have established that women are ...

#### Even without a concussion, blows to head may affect brain, learning and memory

New research suggests that even in the absence of a concussion, blows to the head during a single season of football or ice hockey may affect the brain's white matter and cognition, or memory and thinking abilities. The study ...

#### New system allows for high-accuracy, through-wall, 3-D motion tracking (w/ Video)

Imagine playing a video game like Call of Duty or Battlefield and having the ability to lead your virtual army unit while moving freely throughout your house.

#### Clay-like minerals found on icy crust of moon Europa

(Phys.org) —A new analysis of data from NASA's Galileo mission has revealed clay-type minerals at the surface of Jupiter's icy moon Europa that appear to have been delivered by a spectacular collision with ...

#### Repairing mitochondria in neurodegenerative disease

(Medical Xpress)—The relationship between fine-scale structure and function in the brain is perhaps best explored today by the study of neurodegenerative disease. Disorders like Rett syndrome may be considered developmental in origin—and defined by exotic mechanisms in ...

#### Study identifies new way to predict prognosis for heart failure patients

Johns Hopkins researchers have identified a new way to predict which heart failure patients are likely to see their condition get worse and which ones have a better prognosis. Their study is one of the first to show that ...