*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 deviation^{2}) will give a multiplier of 2 (i.e., if *x* ~ *y*^{2}, then log_{10}*x* ~ **2**log_{10}*y*).

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.

Our hypotheses went like this. Following MacArthur & Wilson’s predictions from island biogeography, we expect populations in small habitat patches isolated from source populations to have a higher probability of extinction (i.e., fewer stabilising niches and species interactions; fewer immigrants to ‘rescue’ declining populations). In other words, their temporal abundance should be relatively higher than in populations found in larger, better connected habitat patches. Therefore, one can hypothesise that the slope of Taylor’s power law for populations on small, isolated patches should be > 2, and those on large, well-connected ones to be < 2. Simple, but where’s the empirical evidence?

We found it. Based on possibly the most extensive and temporally expansive coral reef fish survey in the world (15 years over43 reefs on the Great Barrier Reef), the Australian Institute of Marine Science’s ‘Long Term Monitoring Programme’ (LTMP) was an ecological goldmine to test the hypotheses. Camille used some rather fancy sliding window analyses and generalised linear models to show that in fact, as reef size increases, so does the slope of its Taylor’s power law (< 2); likewise, as reefs become more and more isolated, their slopes increase (> 2). Very cool.

Not only that, the combined effects of size and isolation compounded the change in power law slope in the expected directions (e.g., very small and isolated reefs had much higher-than-expected temporal variance in fish abundance). Very, very cool.

Still, this might only appeal to the true theoretical ecologists and not have many practical applications. Not so, say we! Taking the relationships derived from the 43 sampled reefs, we can now extend the algorithm to predict the expected temporal variance in fish populations across the entire Great Barrier Reef (the largest fringing reef in the world). Now we have a map of expected fish population fluctuations, or put more simply, a map of expected ‘resilience’ to change. Why? We know now that more temporally variable populations tend to fall below their minimum viable population size more frequently, and so are more likely to go extinct. Thus, we now have a map of ‘susceptibility’ (at least for fish) across the entire reef!

Of course, this isn’t the only information layer one would use to identify the best areas to conserve on coral reef complexes, but we argue it’s an essential piece in the marine planning puzzle. Hopefully we’ll be able to do this for other reefs around the world as datasets become available.

Mellin, C., Huchery, C., Caley, M.J., Meekan, M.G., & Bradshaw, C.J.A. (2010). Reef size and isolation determine the temporal stability of coral reef fish populations Ecology DOI: 10.1890/10-0267.1

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