Filed Under #undiscovered_extinctions

Estimating undiscovered extinctions

Estimating undiscovered extinctions Have you ever wondered how many species were lost before we had the chance to discover them? In a paper now out in Conservation Biology, we estimated just that, for plant species in Singapore. This paper follows from the Chisholm Lab’s related work on Singapore birds and butterflies. The orchid species Grammatophyllum speciosum has not been recorded in Singapore since 1918. Photo credit: Cerlin Ng All over the world, many species remain undiscovered while both known and unknown species continue to go extinct. This is particularly true in the tropics, where biodiversity is high and development continues apace. Singapore provides...

Extinction of undiscovered butterflies + tutorial

Extinction of undiscovered butterflies + tutorial Meryl Theng just had a new paper published in Biological Conservation, where she estimated that 46% of Singapore’s butterfly species have been extirpated since 1854. The special thing about this estimate is that it includes all species that existed, including species that went extinct before we had a chance to discover them. The trick to estimating undiscovered extinctions is the SEUX model. There is a nice write-up about the paper on Ryan’s blog. The paper has also received a good response in the press - The Straits Times and The Star have covered it - and it is generating some...

Relationship between species discovery and extinction probability

What is the relationship between a plant’s historical probability of having being discovered and its probability that it went extinct? All else being equal, species with low abundance are less likely to be collected, and low abundance is both theoretically (e.g. McCarthy et al., 2014) and empirically cited as a good predictor of extinction probability. The empirical relationship has been observed both in general (McKinney, 1997) and specifically for plants (Sutton and Morgan, 2009; Matthies et al., 2004). It has also been found in the context of habitat fragmentation (Table 2 of Henle et al., 2004), which is particularly relevant...

Moments for a bivariate beta distribution

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, one that can describe pretty flexible correlation between the variables. The generalised Dirichlet distribution allows us to describe correlated probabilities, however it has some restrictions on the support of the joint probability density function that...

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 them. Chisholm \(=\) E/SY when extinction constant Consider the example in the table below, where the extinction probability \(\mu_t\) is the same in every year. discovered year \( t \)extant \( S_t \)extinct \(E_t\)discoveries \(...

The method of confidence belts illustrated

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 used to construct it. If this procedure for constructing confidence intervals is repeated on many samples, then the fraction of times that the true parameter value will fall within the different intervals will approach \(\gamma\)....

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 of species discovery and temporal fluctuations in the extinction rate. The approach can be improved by estimating the cumulative probability of persistence over the time period of interest. This is equivalent to accounting for species...