Defining the population

To use species richness in practice, we need first to define the group of individual organisms included. We usually limit it to a particular taxonomic group (eg. birds) and a particular place (eg Bako NP). Often we specify a trophic level (eg. insectivores) or a guild (eg. understorey gleaners).

Richness estimation means counting the number of species, treating all species equally, whether they are endangered endemics or invasive weeds, top predators or primary producers. This is only reasonable if the population is defined so that species are actually reasonably similar.

Invariably there will be population boundaries defined by your sampling method (eg. susceptible to capture in a 40mm mesh mist net extending from 1m to 3m above the ground from 7am to 7pm); results can only be compared if the same sampling methods are used, and the method is an important part of the definition.

Many of the "rare" species we encounter are actually "edge species", on the boundary of our defined groups of organisms, eg. birds that rarely enter Bako NP, or are rarely captured in mist nets. Deciding which to include can be difficult, as it implies knowing what species ought to be present!

Species accumulation curves

Once the population is defined, we want to know the number of species within it. Sampling is unlikely to capture all the species present, so the number of species observed, S_obs, will usually be too low. We can plot some graphs which will give us an idea of how much too low.

You could draw a simple "collector's curve" by plotting the number of species vs the number of individuals as you collected more samples: the black line in the graph on the left is such a curve for bats trapped in Loagan Bunut NP in Malaysia.

Provided the samples are independent, the order is not important; our collector's curve would look different if the order of samples was different. The smooth red curve was drawn by shuffling the order of the samples 100 times and averaging the curves obtained. We used computer software to do the shuffling, and also to calculate the 95% confidence intervals indicated by the dashed lines.

You can use EstimateS to calculate smoothed species accumulation curves and estimates of species richness (see below). A Lab Guide to a worked example using the Loagan Bunut bat data is here, and you can download the data file here.

The species accumulation curve starts climbing rapidly, then flattens out. If we collected enough samples so that we had picked up all the species present, it would level off. For the Loagan Bunut bats we still have a way to go. Estimating where it would level off is an extrapolation problem, and those are always difficult.

 Estimating richness

A number of methods have been suggested to estimate the true species richness:

1. Jackknife and bootstrap methods examine the sampling process, asking, "How many species which we know are there would we have missed if we had taken fewer samples, or different samples?" This is then used to estimate the number missing from the actual set of samples.
    
2. Anne Chao's methods consider the number of species which are so rare that they only occur once or twice in the sample, and try to estimate how many are even rarer, so didn't turn up in the sample at all. ACE and ICE use the same approach but using species which occur 1-10 times in the sample.
    
3. Some people try to fit a mathematical equation to the species accumulation curve, and use this to predict the number of species where the curve levels off. A favourite is the Michaelis-Menton equation, which describes an enzyme-catalyzed chemical reaction: it's not clear what that might correspond to when sampling animals or plants!
    
4. Rennolls and Laumonier (2006), working with tree species in Sumatra, assume the rare species in their plots are a random sample of equally rare species in the whole forest, and try to estimate how many 'shadow' species there are.
    
5. Recently Royle and Dorazio (2008) have developed a method which allows detection probabilities to vary among species and they use Bayesian software to compute the estimated total of species.

Various methods in Groups 1-3 are implemented in EstimateS and the Lab Guide explains how to use this with data for bat trapping in Loagan Bunut. More details for these estimators are in the documentation for EstimateS, and I won't repeat them here. Many authors have recommendations for the choice of estimator, and a survey is here.

Species accumulation gives us a way to judge how well the various species richness estimators work for our data. The ideal estimator would be a straight horizontal line (green in the graph on the right) at the level where the species accumulation curve (black) will level off. In practice, we might expect a good estimator to give crazy answers when we have only a few samples, but to settle down to a steady value as we get more samples: the blue line in the graph would be fine. The red curve, which gradually goes up and up as we get more samples - and record more species - is not much help, but estimators often give a result like this.

Comparing species richness between sites

Very often the important question is not "How many species…?" but "Are there more species at… than…", either comparing two sites or the same site at two points in time. Here we can make inferences based on interpolation, which is much safer than extrapolation.

Some harp-trapping has been done in peat swamp forests at Maludam National Park, about 450 km from Loagan Bunut. Unlike Loagan Bunut, Maludam was used for timber production before being established as a national park.

In Maludam, 81 bats from 11 species were caught. In Loagan Bunut NP we caught 174 bats from 22 species. Does that mean that Loagan Bunut has more species of bats which can be trapped in harp-traps?

We can’t compare the species totals – 11 vs 22 – directly, because the number of bats caught in Maludam is less than half the number caught in Loagan Bunut. If we had carried on trapping at Maludam, we would almost certainly have found more species but, as we’ve seen, it’s difficult to estimate how many more. However, we can estimate how many species we would expect to find at Loagan Bunut if we only trapped 81 individuals. We use a subset of the data we collected at Loagan Bunut, with a process known as “rarefaction”. This involves taking samples at random from the Loagan Bunut set until we have approximately 81 individuals, and noting how many species we have found. We do this many times, and average the number of species.

In fact, the smoothing process for the species accumulation curve also uses random selections from the samples, and ‘Randomization Curve’ is an alternative name for the smoothed species accumulation curve. The graph on the left shows the species accumulation curves for Loagan Bunut (black) and Maludam NP (red). If we only collected 82 bats at Loagan Bunut we'd expect to record 17 species. So Loagan Bunut really is richer than Maludam in harp-trappable bats (though if we look at the confidence intervals, we see that they overlap: the difference could have arisen by chance, it is not statistically significant).

To summarize...

Species richness is intuitively the "right" way to estimate species diversity.

However, it is almost impossible to measure, and estimates based on extrapolation are often unreliable unless we have huge samples.

Although we may not be able to estimate the true species richness of our sites, we can use interpolation (rarefaction) to compare richness at two or more sites.