Estimating Animal Abundance

Figure 1.1 shows the result of survey conducted to estimate the number of plants in a 50m by 100m field. The dots represent detected plants. An eighth of the survey region (the shaded rectangles) was searched so if we were sure every plant in the shaded rectangles was detected, it would be reasonable to assume that about an eighth of the plants in the field were detected. This would lead us to estimate that there were 200 plants present.

It is often easier to understand how abundance estimation methods work if we can check our estimates against the true population after estimating abundance, to see how well we did. This is impractical with real populations, so we will be using examples with artificial populations for illustration.

Throughout this book we formulate the problem of estimating animal abundance in terms of state models and observation models. This gives a common framework and allows many different estimation methods to be viewed as variants on the same basic theme. It also provides a natural link to more complicated methods for open populations, which we discuss briefly in this book, but which are crucial for the management of wildlife populations.

In Chapter 2, we introduced maximum likelihood estimation for the case where abundance (N) was unknown, but detection probability (p) was known (or at least assumed). In Chapter 4, we dealt with the only wildlife survey methods in which p is known — and is equal to 1. In this chapter we consider for the first time the more common scenario in which neither N not p are known. We again use the data from our example population to illustrate the problem and the methods.

With data from one survey only, we can’t estimate abundance without making strong assumptions about capture probability. In the case of plot surveys, we assume we know it, and with distance sampling methods (Chapter 7) we assume “capture” is certain on the line or point. Depending on the application, these assumptions may be quite reasonable; when they are not, removal or mark-recapture methods can be useful. With mark-recapture methods, animals continue to contribute information about capture probability after they have been initially captured; with removal methods, they do not. Recapture data allow us to estimate capture probability without the assumptions of plot or distance sampling methods and without removing animals from the population.

With distance sampling we can estimate abundance from a single survey because the method involves a strong (but often reasonable) assumption about detection probability. Distance sampling comprises several related methods which involve measuring or estimating distances of detected animals from a line or point. The two main methods are line transect sampling and point transect sampling (sometimes called variable circular plots). Both are extensions of plot sampling, in which only incomplete counts of animals within the covered region are made. The key assumption about detection probability is that all animals that are located on the line or at the point are certain to be detected. Detection probability p(x) is assumed to fall off in a smooth way out to some distance x = w from the line or point.

In nearest neighbour sampling, objects within the survey region are randomly sampled, and the distances to their nearest neighbour are measured. In point-to-nearest-object sampling, points within the survey region are randomly sampled, and the distance from each point to the nearest object is measured. If we assume that objects are independently and uniformly distributed throughout the survey region, then the distribution of nearest-object distances is the same under both approaches.

We concentrate on model-based methods of estimating abundance in this book. There are advantages and disadvantages to doing this. If you were interested in the process determining the population state (the spatial distribution of animals, for example), this would be a reason to use model-based methods. Model-based methods can also lead to substantial improvement in precision, because some of the variation in density is “explained” by the model instead of being assigned to variance. The main reason you might not want to use model-based inference is that you never know the true process determining the population state, and if the state model you assume is not a good approximation to it, inferences may be biased. With the availability of flexible state models and adequate diagnostics, this is much less of a problem than it used to be, although there are still sometimes difficulties. In particular, the independence assumptions implicit in many state models can be unrealistic, and modelling dependence can be difficult. Unless care is taken, this can result in model-based estimates of variance that are too small and corresponding confidence intervals that are too narrow. A compromise approach is to use model-based methods for point estimation, and nonparametric, and essentially design-based methods for interval estimation.

In this chapter, we consider model-based estimation of animal distribution when all animals in the covered region are detected. We look at estimation of

We use the term “heterogeneity” to refer to differences in capture or detection probability at the level of individual animals or groups of animals. For our purposes, a heterogeneous population is one in which individuals or groups in the covered region are not equally detectable even when exactly the same survey effort is applied to them. (Note that heterogeneity in this sense is a product of both the physical properties of the population and the survey method: the same population might be heterogeneous with one survey method but not with another.)

The theme of this chapter is integration. We describe three models that involve integration of some models covered in previous chapters, and very briefly suggest some others.

We concentrate on closed populations in this book and provide only a brief introduction to open population models for two reasons. First, adequate coverage of integrated modelling for open populations requires a book in its own right. Second, the tools to fit such integrated models have only recently been developed, and more research is needed to explore their potential.

We have met a wide range of techniques for estimating the abundance of closed populations. When should we use which method? We give a few guidelines here. In any one field, one or two methods tend to dominate. For example, line transect sampling is the most commonly used method for estimating abundance of cetaceans and large terrestrial mammals; line and point transects for birds; mark-recapture and removal methods for small mammals; CPUE and other “harvest” methods for fisheries.