The probability of extinction in a branching process and its relationship with moments of the offspring distribution 
(Seminars)
12 June 2012
11am
Venue: Room 303, B11
Contact info: Mark Holmes
Contact email: mholmes@stat.auckland.ac.nz
Department of Statistics seminar by Sterling Sawaya, University of Otago.
We model the growth of a biological population over time using a Galton-Watson (discrete) branching process. The fitness of a population can be evaluated using several statistical approaches, with the log growth being the most popular. In addition to growth, the probability of extinction can be used to measure the long-term success of any population.
Here, we will discuss the interplay between this probability and the moments of the offspring distribution. Using results from the field of decision theory we will show that the probability of extinction decreases with increasing odd moments and increases with increasing even moments, a property which is intuitively clear.
There is no closed form solution to calculate the probability of extinction, and numerical methods are often used to infer its value. Alternatively, one can use analytical approaches to generate bounds on the extinction probability. I will discuss these bounds, focusing on the theory of s-convex ordering of random variables, a method used in the field of actuarial sciences. This method utilizes the first few moments of the offspring distribution to generate "worst case scenario" distributions, which can then be used to find upper bounds on the probability of extinction. I will present these methods and discuss their merits in the field of population biology.
http://www.otago.ac.nz/crg/staff/students/otago023396.html
