Not magic, but necessary

18 10 2011

In April this year, some American colleagues of ours wrote a rather detailed, 10-page article in Trends in Ecology and Evolution that attacked our concept of generalizing minimum viable population (MVP) size estimates among species. Steve Beissinger of the University of California at Berkeley, one of the paper’s co-authors, has been a particularly vocal adversary of some of the applications of population viability analysis and its child, MVP size, for many years. While there was some interesting points raised in their review, their arguments largely lacked any real punch, and they essentially ended up agreeing with us.

Let me explain. Today, our response to that critique was published online in the same journal: Minimum viable population size: not magic, but necessary. I want to take some time here to summarise the main points of contention and our rebuttal.

But first, let’s recap what we have been arguing all along in several papers over the last few years (i.e., Brook et al. 2006; Traill et al. 2007, 2010; Clements et al. 2011) – a minimum viable population size is the point at which a declining population becomes a small population (sensu Caughley 1994). In other words, it’s the point at which a population becomes susceptible to random (stochastic) events that wouldn’t otherwise matter for a small population.

Consider the great auk (Pinguinus impennis), a formerly widespread and abundant North Atlantic species that was reduced by intensive hunting throughout its range. How did it eventually go extinct? The last remaining population blew up in a volcanic explosion off the coast of Iceland (Halliday 1978). Had the population been large, the small dent in the population due to the loss of those individuals would have been irrelevant.

But what is ‘large’? The empirical evidence, as we’ve pointed out time and time again, is that large = thousands, not hundreds, of individuals.

So this is why we advocate that conservation targets should aim to keep at or recover to the thousands mark. Less than that, and you’re playing Russian roulette with a species’ existence. Read the rest of this entry »

Classics: Effective population size ratio

27 04 2011

Here’s another concise Conservation Classic highlighted in our upcoming book chapter (see previous entries on this book). Today’s entry comes from a colleague of mine, Dick Frankham, who has literally written the book on conservation genetics. I’ve published with Dick a few times – absolutely lovely chap who really knows his field more than almost any other. It is a great pleasure to include one of his seminal works as a Conservation Classic.

This entry is highly related to our work on minimum viable population size, and the controversial SAFE index (more on that later).

Although it had long been recognized that inbreeding and loss of genetic diversity were accentuated in small, isolated populations (Charlesworth & Charlesworth, 1987), genetic hazards were generally considered to be of less consequence to extinction risk than demographic and environmental stochasticity. Frankham (1995) helped overturn this viewpoint, using a meta-analysis to draw together comprehensive evidence on the ratio of genetically effective to actual population size (Ne:N). Read the rest of this entry »

Species’ Ability to Forestall Extinction – AudioBoo

8 04 2011

Here’s a little interview I just did on the SAFE index with ABC AM:

Not a bad job, really.

And here’s another one from Radio New Zealand:

CJA Bradshaw

Classics: demography versus genetics

16 03 2011

Here’s another short, but sweet Conservation Classic highlighted in our upcoming book chapter (see previous entries on this book). Today’s entry comes from long-time quantitative ecology guru, Russ Lande, who is now based at the Silwood Park Campus (Imperial College London).


In an influential review, Lande (1988) argued that

“…demography may usually be of more immediate importance than population genetics in determining the minimum viable size of wild populations”.

It was a well-reasoned case, and was widely interpreted to mean that demographic and ecological threats would provide the ‘killer blow’ to threatened species before genetic factors such as inbreeding and fitness effects of loss of genetic diversity had time to exert a major influence on small population dynamics.

Read the rest of this entry »

S.A.F.E. = Species Ability to Forestall Extinction

8 01 2011

Note: I’ve just rehashed this post (30/03/2011) because the paper is now available online (see comment stream). Stay tuned for the media release next week. – CJAB

I’ve been more or less underground for the last 3 weeks. It has been a wonderful break (mostly) from the normally hectic pace of academic life. Thanks for all those who remain despite the recent silence.


But I’m back now with a post about a paper we’ve just had accepted in Frontiers in Ecology and Environment. In my opinion it’s a leap forward in how we measure relative threat risk among species, despite some criticism.

I’ve written in past posts about the ‘magic’ minimum number of individuals that should be in a population to reduce the chance of extinction from random events. The so-called ‘minimum viable population (MVP) size’ is basically the abundance of a (connected) population below which random events take over from factors causing sustained declines (Caughley’s distinction between the ‘declining’ and ‘small’ population paradigms).

Up until the last few years, the MVP size was considered to be a population- or species-specific value, and it required very detailed demographic, genetic and biogeographical data to estimate – not something that biologists tend to have at their fingertips for most high-risk species. However, several papers published by our group (Minimum viable population size and global extinction risk are unrelated, Minimum viable population size: a meta-analysis of 30 years of published estimates and Pragmatic population viability targets in a rapidly changing world) have shown that there is in fact little variation in this number among the best-studied species; both demographic and genetic data support a number of around 5000 to avoid crossing the deadly threshold.

Now the fourth paper in this series has just been accepted (sorry, no link yet, but I’ll let you all know as soon as it is available), and it was organised and led by Reuben Clements, and co-written by me, Barry Brook and Bill Laurance.

The idea is fairly simple and it somewhat amazes me that it hasn’t been implemented before. The SAFE (Species Ability to Forestall Extinction) index is simply the distance a population is (in terms of abundance) from its MVP. In the absence of a species-specific value, we used the 5000-individual threshold. Thus, Read the rest of this entry »

Faraway fettered fish fluctuate frequently

27 06 2010

Hello! I am Little Fish

Swimming in the Sea.

I have lots of fishy friends.

Come along with me.

(apologies to Lucy Cousins and Walker Books)

I have to thank my 3-year old daughter and one of her favourite books for that intro. Now to the serious stuff.

I am very proud to announce a new Report in Ecology we’ve just had published online early about a new way of looking at the stability of coral reef fish populations. Driven by one of the hottest young up-and-coming researchers in coral reef ecology, Dr. Camille Mellin (employed through the CERF Marine Biodiversity Hub and co-supervised by me at the University of Adelaide and Julian Caley and Mark Meekan of the Australian Institute of Marine Science), this paper adds a new tool in the design of marine protected areas.

Entitled Reef size and isolation determine the temporal stability of coral reef fish populations, the paper applies a well-known, but little-used mathematical relationship between the logarithms of population abundance and its variance (spatial or temporal) – Taylor’s power law.

Taylor’s power law is pretty straightforward itself – as you raise the abundance of a population by 1 unit on the logarithmic scale, you can expect its associated variance (think variance over time in a fluctuating population to make it easier) to rise by 2 logarithmic units (thus, the slope = 2). Why does this happen? Because a log-log (power) relationship between a vector and its square (remember: variance = standard deviation2) will give a multiplier of 2 (i.e., if xy2, then log10x ~ 2log10y).

Well, thanks for the maths lesson, but what’s the application? It turns out that deviations from the mathematical expectation of a power-law slope = 2 reveal some very interesting ecological dynamics. Famously, Kilpatrick & Ives published a Letter in Nature in 2003 (Species interactions can explain Taylor’s power law for ecological time series) trying to explain why so many real populations have Taylor’s power law slopes < 2. As it turns out, the amount of competition occurring between species reduces the expected fluctuations for a given population size because of a kind of suppression by predators and competitors. Cool.

But that application was more a community-based examination and still largely theoretical. We decided to turn the power law a little on its ear and apply it to a different question – conservation biogeography. Read the rest of this entry »

Fanciful mathematics and ecological fantasy

3 05 2010

© flickr/themadlolscientist

Bear with me here, dear reader – this one’s a bit of a stretch for conservation relevance at first glance, but it is important. Also, it’s one of my own papers so I have the prerogative :-)

As some of you probably know, I dabble quite a bit in population dynamics theory, which basically means examining the mathematics people use to decipher ecological patterns. Why is this important? Well, most models predicting extinction risk, estimating optimal harvest rates, determining minimum viable population size and metapopulation dynamics for species’ persistence rely on good mathematical abstraction to be realistic. Get the maths wrong, and you could end up overharvesting a species (e.g., 99.99 % of fisheries management), underestimating extinction risk from habitat degradation, and getting your predictions wrong about the effects of invasive species. Expressed as an equation itself, (conservation) ecology = mathematics.

A long-standing family of models known as ‘phenomenological’ models (i.e., because they deal with the phenomenon of population size which is an emergent property of the mechanisms of birth, death and immigration) has been used to estimate everything from maximum sustainable yield targets, temporal abundance patterns, wildlife management interventions, extinction risk to epidemiological patterns. The basic form of the model describes the growth response, or the relationship between the population’s rate of change (growth) and its size. The simplest form (known as the Ricker), assumes a linear decline in population growth rate (r) as the number of individuals increases, which basically means that populations can’t grow indefinitely (i.e., they fluctuate around some carrying capacity if unperturbed). Read the rest of this entry »