My Math Forum  

Go Back   My Math Forum > Math Forums > Math

Math General Math Forum - For general math related discussion and news


Reply
 
LinkBack Thread Tools Display Modes
July 12th, 2019, 05:08 PM   #1
Newbie
 
Joined: Jul 2019
From: USA

Posts: 1
Thanks: 0

Simulating Birth-Death Processes at Small Populations

In birth-death processes for populations, what are solutions for preventing the same individual from both giving birth and dying simultaneously (meaning the same time-step) in your model?
I'll provide some context:

Let's say the timestep is a year. You might say - A certain percentage of individuals of a certain age will give birth and a certain percentage will die, and so I don’t need to care if any particular individual does one, both or neither; it’s the percentages that matter.

The problem with looking out for what happens after a year is that it potentially under-estimates the rate of extinction. This happens because a population size of zero is a special case that we need to treat differently. For example, let's look at a population of rabbits of size 1. Let's say they have averaged rates of 10 births/year and 5 deaths/year. In a population of size 1, clearly, the extinction rate is > 1/3 since there's is a 33.3% chance a death occurs first and there is a non-zero chance extinction occurs even if growth occurs first. However if we calculate Pois(10)-Pois(5) as a realization of the population size change, that value is less than zero 7.4% of the time. This gives a completely wrong extinction percent (>33.% vs 7.4%) since it is not taking into account the fact that anything that reaches a zero population size is extinct regardless of whatever is simulated to happen afterwards.

Another way to put this issue is that the distribution of the change in population size becomes skewed at small sizes since you can't treat size zero normally. The question I want answered is how I simulate this distribution.

Last edited by skipjack; July 12th, 2019 at 06:02 PM.
Iceman is offline  
 
Reply

  My Math Forum > Math Forums > Math

Tags
birth-death, birthdeath, poisson, populations, processes, simulating, small, statistics



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Linear birth and death process calypso Advanced Statistics 1 November 13th, 2016 02:26 PM
some Markov chain questions in Brownian Motion and Birth-Death power3173 Advanced Statistics 0 March 5th, 2015 03:09 PM
Samples and Populations jhon13 Advanced Statistics 1 May 24th, 2012 12:40 AM
A man's age is 1/29 of the year of his death... westworld Elementary Math 6 January 25th, 2012 08:46 PM
Samples, Populations and Problems mmmmxxx Advanced Statistics 1 November 13th, 2011 07:39 AM





Copyright © 2019 My Math Forum. All rights reserved.