Predicting diversity in sub-divided habitat just might be ecology’s greatest theory-data fail
The question of why groups of small patches of habitat tend to contain more species than a single large patch of equal total area pretty much inspired my, recently completed, <sigh of relief> PhD research. I think I know exactly why – in fact, I think it’s almost inevitable. But I’ll save that for a later post (the answer’s in my thesis if you can’t wait). Here, I want to deconstruct the pattern a little and explore support for some possible explanations.
It is a deceptively simple question. One that has garnered some complicated explanations (that can come across a little like excuses) to account for some inconvenient evidence. When I say ‘inconvenient’ I mean contradictory. I actually think it could be one of the best examples of a head-on collision between well-validated predictive theory and sheer weight of empirical evidence in the whole of ecology. So what’s the problem?
Those ‘well-validated theories’ are largely based on demographic models (which track births, deaths, immigration and emigration over time and space to predict changes in population size). In particular, I’m thinking of island biogeography and metapopulation theory. I’ve touched on the influence of island biogeography theory (IBT) on conservation thinking before. Metapopulation models also use demographic rates (births, deaths and so on) to predict how a population of one (two, a few) species is affected as these rates are varied within and among of a bunch of spatially separated (discrete) sub-populations. That is, in a ‘population of (sub)populations’ (= a metapopulation).
Cutting a long story short, demographic theories encourage us to expect small patches of habitat will contribute little to conservation for two main reasons. First, they will contain only a select group of only the most common (and presumably therefore, low conservation interest) species. But not only that – any sub-populations of species they do support are prone to go extinct anyway, because small patches can support only a few individuals and they might all die out just by chance. It is quite reasonable to conclude from these very large bodies of well-validated theory that a single large patch will support more species than a bunch of small patches.
However, lurking uncomfortably in the shadows is the weight of evidence from dozens of published Quinn-Harrison curves, where we usually find the exact opposite pattern – it is groups of small patches that seem to contain more species. Prof. Lenore Fahrig has been an almost lone voice in pointing out this disconnect between theoretical expectation and observation on the effects of habitat subdivision (or ‘fragmentation per se’) on diversity. On reviewing evidence from Quinn-Harrison curves, Fahrig found near-universal support for small patches containing more species.
More recently, Prof. Fahrig has gone on to ask why we see this pattern at all. I think that is the right question. In my view, reducing the ‘small patches have more species’ observation to debate over reserve design skips a crucial step. Understanding. If we focus on understanding how the pattern arises, we might not only narrow the scope for debate, but – more importantly – we might even learn some very useful lessons about managing diversity in fragmented landscapes.
So – why?
There are a few theories, but not a lot of tests. One suggestion is that the species concerned are only common, widespread species. Hence it is of no relevance for conservation if small patches do have more species. I have found that when you look at the evidence there is not much to support this idea. Prof. Fahrig agrees. Still, it is probably the most common expectation among ecologists and to some extent that is reasonable. But a common-species-only argument does not answer our question.
The main theory to explain why groups of small patches contain more species than a large patch of equivalent area relates to environmental variability. Because subdividing habitat means each smaller area must be further from other small areas than if they were in a single patch, the small patches are likely to differ more in their biological and environmental conditions. So, there’s really two sides to this: biologically, you might be able to escape better competitors by just finding somewhere to live where those guys don’t; environmentally, you might have a better chance of finding the perfect set of conditions to support your growth.
I like to think of this as the ‘place for everyone’ hypothesis. And what we would expect to see is that the species found in each small patch is really quite different – at least more different than we would expect if we sampled areas of the same size from within a single large patch. This is essentially what Quinn-Harrison curves tell us – that for a given total area, species composition within and among large patches is less variable than species composition within and among small patches.
Ecologists call change in species composition between local areas ‘beta diversity’. That this increase in beta diversity is due to environmental conditions is theory # 1 for why small patches have more species (note that this really largely ignores the ‘biological’ side of things).
Another thing that could result in a difference in species number between small and large patches is if they differ in the way that individuals are divided up among species – their abundances, relative to one another. In nature, a few species are common, and lots of species are pretty rare. We quantify these differences using a diversity property called ‘evenness’. If every species had the same number of individuals, a common measure of evenness (proposed by the awesome quantitative ecologist E.C. Pielou) would assign this a value of 1. But it is usually (read, ‘always’) the case that species differ in their number of individuals; a highly uneven distribution would have an evenness value close to 0. The figure below illustrates the basic idea.
To show why evenness matters, let’s ask what might happen if two birds died from each of the assemblages in figure 1. What effect would that have on the number of species? Well, for the panel on the left it could remove half the species if you were unlucky; but in the assemblage on the right, it could never remove any species completely.
Conversely, if you grabbed (say) three individuals at random, the right panel would, on average, yield more species. We can estimate this using a formula derived by Stuart Hurlbert. Here, if we grabbed 3 individuals at random from the left panel, we’d expect 1.74 species; from the right panel it is 2.5 species.
The take home is that both extinction risk, and the number of species we expect, depends not only on how many species there are, but also on how many of each species there are as well. This is true whether the habitat is sub-divided or not. If small and large patches have the same number of individuals, but the small patches have a more even distribution of abundance among species, then they should also contain more species.
This is illustrated in the next figure.
There’s a twist though: recall that we measure change in species composition using beta diversity? Well, this also depends on evenness – but in the opposite direction to species richness. So, samples from more uneven distributions will result in higher beta diversity. This is interesting because, as we discuss above, higher beta diversity is the main explanation for more species in those small patches.
So rather than asking about beta diversity, in some ways it makes more sense to ask whether and how species evenness changes for patches of different size. Because that will tell us about both the number of species and beta diversity. Typically we expect abundances in any single small patch will be very uneven. However, if evenness increases in groups of small patches (which some people have found), it should decrease beta diversity. The key point here, is that despite reducing beta diversity, increased evenness in small patches could still potentially result in more species in several small, than a single large patch (as Figure 2 shows).
There’s another possibility that has been sort of acknowledged in the literature but not directly tested: what if the pattern is only due to a sampling error? Think about how much easier it is to count the number of birds in a backyard compared to a large urban park. Maybe (probably) we do not count the species in the large patches as well as we do in the small patches. Because of that bias, we might miss more species in the large patch. So it might seem that the small patches have more species, because we just didn’t count the large patches properly. If you have the right kind of data, you can control for this (but that is not usually the type of data available to build Quinn-Harrison curves).
Finally, if we want to find a general explanation, we need to consider how possible differences among the different types of animals and plants will influence the patterns. For example, birds are very mobile, other animals not so much – would we expect to see different taxonomic groups like insects and mammals with the same pattern of richness? Some animals eat plants, others eat other animals, will they have similar area requirements? Clearly we need to account for this potential source of variation and test for differences among taxa as a sub-question of asking why small patches contain more species.
Recently, we combined all of the above ideas (beta diversity, evenness, sampling error and taxonomic group) into a single model – called a structural equation, or confirmatory path analysis model. We used the model to test how much influence each of these possibilities has on the difference in species number between a single large patch and a group of small patches. We used a bunch of published data to do this, but because our data had some nuances requiring special treatment we used a fairly new kind of path analysis called piecewise structural equation modelling (See here for some excellent background on the method, which is under ongoing development led by ecologist, Jon Lefchek).
The figure below sets out the hypothesized paths we tested and how they relate to one another. The thing we are interested in is the difference in species number between groups of small and a single large patch (the dashed line in Figure 2; ‘Difference in species number’ in Figure 3). If small patches have more species, this number is positive, if the large patch has more species, it’s negative.
What figure 3 essentially shows is how we imagine the different influences might affect the number of species in small vs. large patches. The cool thing about path models is they are graphically based with the ‘graph’ representing the relationships you are portraying. This forces you to think carefully about the causal influence of the different factors included in the model.
Each arrow is really a hypothesis; if the arrow ends at the ‘Difference in species number’ box, it is called a ‘direct’ effect. If the arrow points to something else, then that points to ‘Difference in species number’, we call that an indirect effect. An indirect effect will influence the difference in species number because it affects the something else and it is that something else that influences the outcome of interest.
In words, we thought the difference in species number (our response variable) would be directly and positively affected by beta diversity (more beta diversity means a larger positive difference in species), directly and positively affected by evenness (more even abundance in small patches means more positive difference), directly affected by taxonomic group (more of a control than a hypothesis) and directly and negatively affected by sampling error (more sampling effort should decrease the difference in species number).
The main indirect effect we hypothesized was the negative influence of evenness on beta diversity, although we thought taxonomic group would probably also have an indirect effect, albeit we were not as certain what direction it might go.
After we tested the hypotheses (using data from 44 published studies), we found support for most of the paths. This is shown in the next figure, where we only draw an arrow where we found an effect (the hypothesis was supported). The size of the arrows roughly shows the relative strength of that effect, while the number beneath or above the arrow (the path coefficient) quantifies its strength, and shows the direction of the effect (positive or negative).
The first thing to note is that we were able to explain nearly 70% of the variation in species number between small and large patches using our causal model. In ecology, that’s pretty respectable, but it’s not a huge sample size, so nothing to get too caught up in. Next thing is that the direction of the effect for all direct and indirect hypotheses in the model were as we predicted, which is much more satisfying. Though a number of the paths (hypotheses) were not supported by the data (compare the missing arrows in the two path diagrams).
Also, while most of the variation was explained by differences among taxonomic groups, the main model predicts that we should, on average, always expect small patches to contain more species than a single large patch, irrespective of taxonomic group. Is it possible for a single large patch to have more species? Sure. But should we expect that for any taxonomic group based on this analysis. No. However, the sample size (44 is not many data points for an analysis like this – few researchers are generous enough to make this type of data freely available) means we need to be cautious in drawing any general conclusions.
So then, what’s the main take homes from this analysis? Taxonomy matters the most, then beta diversity. In other words, small patches matter for all animals, but some a lot more than others. After accounting for the type of animal, evenness really has a big effect on species number both indirectly – via effects on beta diversity – and directly where increasing evenness increases the Difference in species number. But because it is opposite in direction, the overall effect is quite weak.
What we can say, is the greatest difference in species number between groups of small patches and a single large patch occurs when both beta diversity and evenness are high. We should expect to see that when:
- the taxonomic group we are interested in finely divides the environment into different niches – typically this will be small things like invertebrates (and also plants, which seem to respond in a similar way to invertebrates); and,
- each patch presents contrasting environmental conditions – for example, where there are clear gradients in soil texture or nutrient concentrations; and,
- it is not easy for individuals to move from one patch to another (lots of dispersal means that the same species that are the most prolific reproducers can reach every patch)
Basically the lower two points are conditions where the ‘place for everyone’ hypothesis should hold up well.
It is a pretty general set of conclusions, and quite what it means for managing landscapes with patchy habitats will depend on the circumstances and the type of animal or plant that you are interested in. But to me, it at least makes a lot of sense in explaining the high beta diversity I have seen in seasonal wetland plant communities (which vary greatly in hydrology, soil type, land use etc – see a Quinn-Harrison curve here) and also why their species composition becomes more similar when lots of those wetlands are found close together (because this increases dispersal).
Do I think a group of small reserves will preserve more species than a single large reserve? No. Not really. But the landscapes I have worked in tend to be productive landscapes and the notion of designing a bespoke conservation reserve network is little more than a fantasy. In those landscapes, it gives me great hope that in at least some situations, groups of small patches do seem to provide a ‘place for everyone’. At least for now. The questions then become: how viable are those species’ populations; and, how can we best help them to persist as part of a functional, productive landscape.