## Surveying Natural Populations

PE review number: 1.1.1R

January 1998

**Surveying Natural Populations**, by L-A. C. Hayek and M. Buzas, Columbia University Press (http://www.columbia.edu/cu/cup), New York, 1997, xvi + 563p. ISBN 0-231-10241-0. Hb $60.00 (US), £48.00 (UK); Pb $28.00 (US), £19.00 (UK).

Every paleontologist needs to acquire a variety of quantitative skills in order to successfully pursue their profession. Even if they happen to work in one of the (now) rare areas of the discipline in which quantitative analytical techniques are not required, they will inevitably be asked to review the work of students and colleagues who do use such methods. This need for the development of quantitative analytic skills creates a problem. Given the inherently interdisciplinary nature of paleontology, along with the explosion of information in a variety of key areas (e.g., evolutionary theory, ecology, global change, molecular systematics), paleontological curricula are hard pressed to find time for traditional topics, let alone the (often misperceived) exotica of statistics and numerical analysis. In addition, many general statistics and numerical analysis courses offered by university math and statistics departments focus on methods that do not adequately treat typical paleontological data types and analytic strategies.

The most practical solution to this dilemma is for the paleontologist to regularly consult and (if possible) work their own way through one or more biometrics textbooks. As can be appreciated by those who have attempted this route to quantitative enlightenment, the task can be made either bearable (if not pleasurable) or unimaginably difficult depending on the quality of the chosen text. Access to an understandable text at an appropriate time in one’s educational or research career can literally change the direction of a young paleontologist’s career virtually overnight. Alternatively, a bad experience with quantitative analysis at a critical juncture can more-or-less foreclose all subsequent interest in such procedures. Classics in this field (e.g., Zar 1974, Sokal 1969, Sokal and Rohlf 1981,1995, Davis 1973, 1986) are worth their weight in gold for the fortunate few who have managed to enlist these authors as their self-study tutors. The importance of textbooks in the area of introductory paleontological biometrics is why the appearance of a new title is an occasion for careful scrutiny as well as guarded hope.

Lee-Ann Hayek and Marty Buzas have produced such a title. *Surveying Natural Populations* seeks to introduce students to the range of descriptive univariate statistical procedures used to characterize organismal populations and multi-species assemblages in space and time. Although primarily targeted at the conservation biology market, the nature of the subject matter make this text especially relevant to a wide range of paleontological situations. Moreover, the participation of Marty Buzas, an eminently practical paleontologist with much experience in the field of quantitative paleontological surveying, gives this volume more of a paleontological flavor that it would have otherwise had.

Perhaps the most unusual feature for a text of this scope is the authors’ use of a single dataset as a running illustration of the application of the various procedures they discuss. This dataset is the composition and spatial distribution of 663 trees in a one hectare plot of the Beni Biosphere Reserve in Bolivia (Fig. 1). While these data represent a sample of a larger statistical entity (e.g., the 90,000 hectare Beni Biosphere Reserve forest, the regional Bolivian forest, the global tropical forest), Hayek and Buzas are content to treat this sample as a population on which various sampling procedures and methods of statistical inference can be undertaken. This convention has the very desirable effect of allowing the student to compare various statistical estimates of density, distribution, and diversity within various sample types to the values of these parameters in the known population. This exercise builds the student’s confidence in sample-based statistical procedures by repeatedly demonstrating that by using appropriate methods small samples can yield a plethora of accurate data about the populations from which they are drawn. Of course, the statistical analogy between the forest sample and (say) a sample of sessile marine invertebrates is straight-forward and compelling.

The text begins with a series of chapters on primary descriptive statistics, histograms and distributions, confidence limits, and sample number estimation. These topics will be found in many introductory statistics texts. Owing to the biological orientation of the authors though, the discussions presented in this volume are especially clear and relevant to the concerns of paleontologists. Although many current statistical textbooks employ a format whereby theory and equations are presented in the text and worked examples are presented in series of boxed inserts (e.g., Sokal and Rohlf 1981, 1995, Swan and Sandilands 1995), Hayek and Buzas abandon this approach in favor of the more traditional presentation of example calculations within the body of the text. Personally, I prefer the former format for purposes of reference. Nevertheless, the calculations and resultant tables are clearly presented and the reader should have no trouble following the arguments. There are even many charming asides describing hand calculation tricks and short-cuts. One can only suppose that the authors assume spreadsheets, scientific hand calculators, and digital computer programming languages have yet to become widespread features of virtually all desktop computing environments.

Chapter 6 switches gears to introduce regression analysis via a consideration of the use of exponential curves in the analysis of spatial distributions and the estimation of optimal sample sizes. Few introductory statistics textbooks do an adequate job explaining the mysteries of regression analysis and I would have liked to see a bit more background about the concepts behind regression analysis provided before the reader was introduced to such a specific application. However, the authors constant theme of utility in practical biological situations cannot be faulted.

The reason for Chapter 6’s seemingly odd placement becomes evident in Chapter 7 where the authors take up the subject of field sampling. To some this ordering of topics may sound like placing the cart before the horse, but there is method to the apparent madness and an important lesson to be learned. One of the banes of every quantitative paleontologist’s life is having a student or colleague bring him/her a dataset that took much time, effort (and in many cases money) to assemble and request that the biometrician magically conjure “the answer” out of the numbers. In order to be maximally useful data must be collected with the eventual analysis program in mind. Otherwise much of the investigator’s time and effort are likely to be wasted making unnecessary and/or inappropriate observations. By presenting their discussion of sampling theory in the middle, rather than at the beginning of their book Hayek and Buzas (no doubt veterans of many such requests) make the implicit point that the sampling strategy cannot be designed until at least the rudiments of statistical characterization required by the project have been understood. In addition, Hayek and Buzas use this chapter to emphasize the importance of using quadrats and collecting replicate samples in order to address the question of inter-sample variability and data reproducibility. As has been seen in various recent “blind” tests (e.g., Zachariasse et al. 1978, Ginsburg 1997), paleontologists often seriously overestimate the inherent variability of their data. Routine replicate sampling strategies—of the type advocated by Hayek and Buzas—can provide quantitative error estimates for a variety of paleontological variables and it would be in the interests of all paleontologists to make more use of these sampling techniques.

The statistics of species’ relative abundances, distribution patterns, occurrence patterns, and diversity comprises the remainder of the book. Though aspects of these methods are covered in most introductory statistical texts, each is treated here in much more detail with numerous example analyses drawn from the Beni Reserve data as well as the odd supplementary example drawn from the authors’ research programs. The chapter on species relative abundances is particularly useful owing to the popularity of this data type (especially with micropaleontologists) along with the analytical and interpretative complications engendered by forcing variables to a constant sum.

The capstone of this section (and indeed the entire book), however, is the last chapter in which Hayek and Buzas introduce the concept of *SHE Analysis*. *SHE* stands for the number of species or the species richness (*S*), the species assemblage’s diversity estimate (*H*), and the evenness of the species’ abundance distribution (*E*). Ecologists have long known that these parameters are inter-related, but until now they have been unable to (1) separate the effects of richness and evenness in the calculation of diversity, and (2) consistently characterize assemblages drawn from different species’ distributions using any of these three parameters. Hayek and Buzas present an extended discussion and example of their proposed solution to these problems. In addition, the authors point out that even at this very early stage in the application of *SHE Analysis*, there are tantalizing hints that suggest unexpected complexities in patters of similarity and difference among biotic species assemblages. It may well be that *SHE Analysis* offers a new way of looking at biodiversity structure in both modern and fossil contexts which might contribute to the formulation of a much needed theoretical bridge between the fields of modern and paleo-ecology.

To sum up, Hayek and Buzas’ *Surveying Natural Populations* is a welcome addition to the list of recommended texts for anyone interested in constructing a paleontological or biotic field sampling program or analysis of the resulting descriptive, spatial, abundance, occurrence and/or diversity data. The text is well-written and contains numerous relevant example analyses with discussions of possible biological interpretations of the results. A very low level of mathematical knowledge is assumed by the authors; who take great pains to patiently introduce and explain all necessary mathematical concepts within the text. While appropriate for a semester-long course in quantitative paleontological field surveying methods, my own feeling is that this book will make its largest impact as a self-study tool for those who need an authoritative guide in this area. Lee-Ann Hayek and Marty Buzas have produced a rare classic in the field of quantitative biological-paleontological analysis. If you collect paleontological data in the field, if you analyse such data in the office, or if you are asked to review such work, you need a copy of this book.

**REFERENCES**

Davis, J.C. 1973. **Statistics and Data Analysis in Geology**. John Wiley & Sons, New York.

Davis, J.C. 1986. **Statistics and Data Analysis in Geology, Second Edition**. John Wiley, New York.

Ginsburg, R.N. 1997. An attempt to resolve the controversy over the end-Cretaceous extinction of planktic foraminifera at El Kef, Tunisia using a blind test. Introduction: background and procedures. **Marine Micropaleontology**, 29:67–68.

Sokal, R.R. 1969. **Biometry: The Principles and Practice of Statistics in Biological Research**. W. H. Freeman and Company, San Francisco.

Sokal, R.R., and Rohlf, F.J. 1981. **Biometry: The Principles and Practice of Statistics in Biological Research, Second Edition**. W. H. Freeman and Co., San Francisco.

Sokal, R.R., and Rohlf, F.J. 1995. **Biometry: The Principles and Practice of Statistics in Biological Research, Third Edition**. W. H. Freeman, New York.

Swan, A.R.H., and Sandilands, M. 1995. **Introduction to Geological Data Analysis**. Blackwell Science, Oxford.

Zachariasse, W.J., Riedel, W.R., Sanfilippo, A., Schmidt, R.R., Brolsma, M.J., Schrader, H.J., Gersonde, R., Drooger, M.M., and Brokeman, J.A. 1978. Micropaleontological counting methods and techniques — an excersize on an eight meters section of the Lower Pliocene of Capo Rossello, Sicily. **Utrecht Micropaleontological Bulletins**, 17:1–265.

Zar, J.H. 1974. **Biostatistical Analysis**. Prentice Hall, Englewood Cliffs.