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The fitness of a biological strategy is typically measured by its expected reproductive rate, the first moment of its offspring distribution. However, strategies with high expected rates can also have high probabilities of extinction. A similar situation is found in gambling and investment, where strategies with a high expected payoff can also have a high risk of ruin. We take inspiration from the gamblers ruin problem to examine how extinction is related to population growth. Using moment theory we demonstrate how higher moments can impact the probability of extinction. We discuss how moments can be used to find bounds on the extinction probability, focusing on s-convex ordering of random variables, a method developed in actuarial science. This approach generates best case and worst case scenarios to provide upper and lower bounds on the probability of extinction. Our results demonstrate that even the most fit strategies can have high probabilities of extinction.
How should dispersal strategies be chosen to increase the likelihood of survival of a species? We obtain the answer for the spatially extend
When a population inhabits an inhomogeneous environment, the fitness value of traits can vary with the position in the environment. Gene flow caused by random mating can nevertheless prevent that a sexually reproducing population splits into differen
The Ebola virus is spreading throughout West Africa and is causing thousands of deaths. In order to quantify the effectiveness of different strategies for controlling the spread, we develop a mathematical model in which the propagation of the Ebola v
Antibodies, an essential part of our immune system, develop through an intricate process to bind a wide array of pathogens. This process involves randomly mutating DNA sequences encoding these antibodies to find variants with improved binding, though
Microorganisms live in environments that inevitably fluctuate between mild and harsh conditions. As harsh conditions may cause extinctions, the rate at which fluctuations occur can shape microbial communities and their diversity, but we still lack an