Sure, small patches are important, but that important?
Imagine you drive to work and you have a choice of two different roads to get there. They are the same total distance and they have the same number of intersections, each with a set of traffic lights. However, one of the roads is a major arterial road, and the traffic lights default to green. The other is a bit of a back street and the lights are usually red. You probably wouldn’t be that surprised that the first route gets you there quicker? Well, I’m going to argue that ecologists (including me) have been doing something like this since the 1980s. I’ll circle back to this – let’s talk some ecology.
Let’s say we have species lists for a group of habitat patches that differ in size. Say, all the bird species found on every island of an archipelago. We are not particularly interested in how many species we find on a single island, but in how many species we see in groups of islands for their total area. Especially when we combine groups of smaller, versus groups of larger islands. Essentially this is a question about the effects of habitat sub-division. One way it has been approached is by combining the species found on the islands in order of their size (Fig. 1), from the smallest to the largest (small-to-large) and from the largest to the smallest (large-to-small). Then we can plot the number of species we obtain as the islands are combined against the total area those islands collectively contain (hereafter SLOSS analysis).
I have a history with this particular pattern – in fact, my desire to understand them explains a lot about the direction of my PhD research. I now think I can explain them pretty well. I also think they are a classic example of how our eyes can deceive us.
It is a simple premise: if you add up the number of species in a group of small islands (or more generally, habitat patches) and there are more than you find in one or more large patches for the same total amount of area, then small patches must be important for diversity, right? While that can certainly be true, there’s two problems. First, we need to ask what difference in species number we should expect when we are comparing the number of species in habitat broken into different sized pieces. Is it reasonable to directly compare them in the way used in SLOSS analysis? Second, which species are accumulating so rapidly; are any extra species in the smaller patches just the most common species that you find everywhere, or do small and large patches contain the same mix of rare and common species? These questions were the focus of a recent paper of mine.
What should we expect to see?
Thinking about the first question (i.e., is this a reasonable comparison) the answer is a pretty clear no. For one thing, we know that sub-dividing habitat results in an expectation of more species in several small samples. The reasons are slightly technical, so I will focus instead on two other problems that arise from combining patches in reverse size order.
We know that species density (the number of species per area of habitat) decreases as you sample larger areas. The pattern we see (the number of species) changes depending on the lens through which we choose to view it (the size of the sample, or patch, or island etc.). This is an example of a phenomenon known as scale-dependence, and it is not best practice to ignore this in biodiversity comparisons because you are not comparing like with like. In SLOSS analysis, we completely ignore scale-dependence and all the highest species density (smallest), patches are combined first, with no effort made to account for how this might affect our expectation for their combined species number (I know of no other method in ecology where anything remotely like this is allowed).
Next, note that as we combine two patches, any species they share will not increase the total number of species. This becomes a problem here, because the number of species that are shared (proportionally) increases as the number of species in that patch increases. As smaller patches have fewer species, they will share fewer species (proportionally) than larger patches. This is quite intuitive when you think about it – there are only so many species in the landscape. Smaller patches contain a smaller fraction of them, so when we combine two of them, it leaves more species for the second patch to choose from without repeating the same species in the first. Put simply, large patches – just by chance – share a higher proportion of the species they contain with other large patches, smaller patches share a smaller proportion.
Now think about the SLOSS curves. In small-to-large order, the advantage of having more species per unit area in smaller patches (greater species density) compounds with every new patch we add to the curve. What’s more, of those species we do find, a smaller fraction of them are shared on average. What this means is, with no other information, the chance you encounter new species as you combine patches is greater for every patch in small-to-large order (Fig. 2). Contrast this with a typical sampling design, where all the patches are the same size – here the chance of encountering new species is the same for every patch and does not change as we combine them (‘Constant area’ in Fig. 2).
So in SLOSS analysis the same area and number of species are being combined in each order of combination – but each species ‘counts’ for more toward the total in small-to-large order. This is the ‘green light route’ in my traffic analogy. It should not then surprise us much to find out that small-to-large SLOSS curves often rise very sharply initially, while large-to-small curves have a characteristic shallow slope. This explains why in about 70% of comparisons or more, small-large order seems to accumulate so many more species. If small patches were truly this important for species diversity, it should show up in all types of comparisons between small and large patches – it doesn’t. Instead there is massive debate about the importance of small patches.
Now, anyone who has done a few of these comparisons will say ‘hey, wait a minute – sometimes the curves overlap or the large-to-small curve is above the small-to-large one!’. Quite true and there are a few reasons – including it could be a real size-dependence pattern. The problem is we can’t tell from these plots. Who wins the race to capture all the species in the dataset for the smallest total area instead depends on another influence. To introduce the idea, I’ll return to my analogy: what if the ‘red lights route’ had no speed limit and you could travel as fast as you like? You might be able to overcome the disadvantage of the constant red lights and get to work quicker (yay). Back in SLOSS analysis world, the role of the speed limit is played by the island species area relationship.
The island species area relationship tells us about how the number of species we see changes in smaller or larger independent habitat patches. ‘Independent’ here roughly means isolated – the patches are far enough apart that the composition of one has little to no influence on the composition of those nearby. We can think of it as how a random sample from all the species that live in the region (the regional species pool) changes depending on the size of the sample we take (represented by the area of the patch). If the slope of the island species area relationship is shallow, there is not much difference between small and large patches and the ‘green light’ advantage means the small-to-large curve is likely to lie above the large-to-small curve. If the slope is high enough, large patches contain so many more species it doesn’t matter that small patches share a smaller fraction of species (because we can drive faster between lights).
Most power-law island species area relationships have a slope (aka z-value) of about 0.25 or less. Turns out we have to get to about 0.35 or greater before the large-to-small curve reliably gets it’s nose above the small-to-large curve. Because more datasets have a shallower slope, so more SLOSS analysis comparisons favour small-to-large order. This is what scientists call a ‘confounding factor’ – an effect that influences the outcome (the slope of the island species area relationship) but is not related to what we want to test (the effect of patch-size on species accumulation when combining patches). We might see a result, but we can’t say for certain why.
Are all patches created equal?
I mentioned I was interested in both the strength of evidence that the SLOSS analysis approach offers and the question of which species accumulate more rapidly in the smaller patches. I answered both of these questions using a null model. This is an approach where you create a bunch of simulated datasets that are like the one from the community you are analysing. However, you randomize how species are assigned to samples in each simulated dataset so you remove any structure in the dataset. Each of your simulated datasets is analysed the same way as in the observed data. From the datasets simulated under your null model, you know how the effect you are interested in would look like if it happened at random. That way if you see a bigger (or smaller) effect in the real data, then you have some evidence it would not happen at random. The null model I used predicted how many species we should see in groups of patches if patch size had no effect (you can see the null model in Fig. 2 – it is the smooth line). Here I randomised the patches that species were found in but kept the total number of times they were recorded the same.
Then, instead of comparing the small-to-large and large-to-small curves with each other, I compared each of them with themselves; that is, to their respective simulated curves. For every patch on each curve, I took the difference between the observed proportion of species and the expected (average value) from all the simulated communities. I then averaged these differences. If there were no effect, this value would be zero. If the average difference was positive, then when patches were accumulated in that particular order (either large-to-small or small-to-large), they contained more species than expected (negative meaning less). I interpreted a positive effect in large-to-small order (more species in the data than the expected value) as meaning that some species either preferred or required large habitat patches. Vice versa for small patches. I ran the analysis on 202 published datasets I have collected from the literature for three different habitat types: ‘true’ islands (i.e., archipelagoes), fragments of formerly continuous habitat, and ‘habitat’ islands – those which naturally occur as different size habitat patches in some non-habitat landscape (like wetlands, lakes and sky islands).
To explore patch size dependence for each dataset, I tested for a statistical difference between the small-to-large and large-to-small effect sizes. Over all 202 datasets I had available to run the model, the difference was -0.027. This I roughly equate to meaning for a given amount of habitat area accumulated, 2.7% of species would prefer you chose the largest patches. This value differed quite a lot between habitat types though (Fig. 5). It was strongest for archipelagos (~5% preference for larger islands), weaker for fragments (~1.5% preference for larger fragments) and there was no statistical evidence for any patch-size effect for habitat islands.
So, what do I conclude from all this? First, it is worth noting that the ecological effects of breaking habitat apart are much harder to detect than those due to the loss of habitat area (which is always bad news for biodiversity). Where present, the effects of breaking habitat apart are typically small in magnitude and can work in either direction. This is consistent with this analysis but contrasts with SLOSS analysis, which more often than not seems to imply small patches are collectively amazingly diverse. Despite the modest effect size with these data, this analysis suggests that small and large patches do not usually support all of the same species. It is likely that in most cases a subset of species require (or at least prefer) larger patches to persist.
Getting a little more specific, it was interesting to see the lack of clear evidence for large patch size dependence in species of habitat islands. I also note there were instances in all habitat types where a preference for small patches was evident. Unfortunately, the datasets where this was the case were not revealed through SLOSS analysis. In other words, the method doesn’t even reliably detect situations where small patches are preferred by more species than large patches after controlling for the problems I discuss above. On a personal note, after more than five years messing around with them in one form or another, I do not feel anything useful can be learned from SLOSS analysis about the effects of sub-dividing habitat (or anything else to be honest). Best avoided.