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The fitness of the strongest individual in the subcritical GMS model. (English) Zbl 1336.60145
Summary: We derive the strongest individual fitness distribution on a variation for a species survival model proposed by H. Guiol et al. [Markov Process. Relat. Fields 17, No. 2, 253–258 (2011; Zbl 1325.60157)]. We point out to the fact that this distribution relies on the Gauss hypergeometric function and when $$p=\frac{1} {2}$$ on the hypergeometric function type I distribution.

##### MSC:
 60J20 Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) 60G50 Sums of independent random variables; random walks 33C05 Classical hypergeometric functions, $${}_2F_1$$
##### Keywords:
GMS model; random walk; Gauss hypergeometric function
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