Moments for a bivariate beta distribution

A common choice for a probability distribution of a probability is the beta distribution. It has the required support between 0 and 1, and with its two parameters we can obtain a pretty wide qualitative range for the probability density function. What should we do if we want to create correlated probabilities? We might look for some kind of multivariate generalisation of the beta distribution, … Continue reading Moments for a bivariate beta distribution

Comparing E/MSY and Chisholm method

Historical data (e.g. sighting records) can be used to estimate historical extinction rates in a variety of ways. The Chisholm et al. (2016) method (earlier post) uses the data to estimate yearly extinction probabilities. The extinctions per million species-years (E/MSY) approach (Pimm et al., 2014) estimates they extinction probability averaged over species-years. Below, I use two small examples to illustrate the similarities and differences between … Continue reading Comparing E/MSY and Chisholm method

The method of confidence belts illustrated

What is a confidence interval, really? We all learnt in undergrad how to find CIs for a standard distribution, but plugging numbers into equations never gave me a deep intuition for what was really going on. A worded definition is probably more helpful. Paraphrasing a bit from Wikipedia, we can think of the meaning of the confidence interval in terms of the procedure that we … Continue reading The method of confidence belts illustrated

Estimating undetected extinctions

The purpose of this blog post is to give a simplified account of how the Chisholm et al. (2016) method works for estimating undetected extinctions. To estimate the historical extinction rate within a taxonomic group, a naive approach would be to divide the number of species known to be extinct by the total number of species. However, this does not account for the historical process … Continue reading Estimating undetected extinctions

Understanding the neigbour-modulated inclusive fitness approach

The goal is to understand Equation 4.2 of Rodrigues and Kokko (2016). To understand the technique, I read through Taylor et al. (2007), and Taylor and Frank (1996), specifically examples 4, 4a and 4b. Very briefly, we begin with a matrix \( A = [w_{i,j} ] \) whose elements represent the genetic contribution of class \( j \) to class \( i \). Then for … Continue reading Understanding the neigbour-modulated inclusive fitness approach

Evolution of parochialism

Previously I was reading about identity in Singapore, and I found that the government project of creating a national identity is focused upon creating a cosmopolitan mindset (i.e. one of openness and tolerance of difference), and that this interacts in different ways with the two main groups of foreigners, the ‘foreign talent’ and the ‘foreign worker’. The literature review that I did there was focused … Continue reading Evolution of parochialism

Identity in Singapore, the Internet, and connections to game theory

The following is a literature summary that I undertook as part of my broader interest in modelling social systems, using identity in Singapore as a case study. I should preface all of this by saying that the ideas below are not ‘my own’ as such, but rather my attempt to synthesise the literature and opinions of experts in Singapore. Identity in Singapore Since independence, the … Continue reading Identity in Singapore, the Internet, and connections to game theory

Termite eusociality

Termites are eusocial by possessing two subfertile or sterile castes, the worker and the soldier. The consensus is that eusociality in termites is the result of a suite of factors (Thorne, 1997), though the relative importance accorded to each in the literature has shifted over time (Howard and Thorne, 2011). For the purpose of a quick review, I have not looked into mechanisms that appear … Continue reading Termite eusociality

Network structural uncertainty in Qualitative Modelling

Background Imagine a situation in which we want to model the behaviour of a food web, but we don’t know what the species interaction strengths are, and we’re not 100 percent sure what the structure of the food web is, either. For example, in the figure below, experts are are uncertain about whether or not there is a direct interaction between species 4 and 5, … Continue reading Network structural uncertainty in Qualitative Modelling