# Surveying Natural Populations: Quantitative Tools for Assessing Biodiversity

Lee-Ann C. Hayek
Martin A. Buzas
Edition: 2
https://doi.org/10.7312/haye14620
Pages: 616
https://www.jstor.org/stable/10.7312/haye14620

1. Front Matter
(pp. i-vi)
(pp. vii-xviii)
3. PREFACE
(pp. xix-xx)
4. ACKNOWLEDGMENTS
(pp. xxi-xxiv)
5. 1 INTRODUCTION
(pp. 1-10)

Surveying natural populations is not a new endeavor for Homo sapiens. Hunters and gatherers needed to classify, find, and catch organisms in order to survive. Communication of what was edible and where it could be found were the essential bits of information necessary for the survival of primitive populations.

The problem of what still requires careful observation of animals and plants so that one group can be discriminated from another. After all, survival could depend on it. For example, strangers to the forest gather and eat mushrooms with considerable risk. Local inhabitants with taxonomic skills recognize the subtle differences required...

6. 2 DENSITY: MEAN AND VARIANCE
(pp. 11-21)

A statement such as “I found 100 clams” may be important for someone preparing a clambake, but it contains little information about the size or distribution of a clam population in nature. All organisms are distributed in space and time. The particular time at which a survey is conducted constitutes a look at the distribution of organisms at a fixed moment. In this book, however, our main concern is with distributions in space, and that space must be circumscribed. A meaningful statement for our purposes would be “There were 100 clams in Tisbury Pond on 27 December, 1943.”

Distribution in...

7. 3 NORMAL AND SAMPLING DISTRIBUTIONS FOR FIELDWORK
(pp. 22-37)

In the previous chapter we introduced 2 statistical parameters of population density: the mean, μ (Equation 2.1), and the variance, σ² (Equation 2.3). We also introduced μ̂ (Equation 2.2) and σ̂² (Equation 2.5) as statistical estimators of these parameters. These estimates are once removed from the original field observations. The summarizations they provide, however, are powerful and well worth the price. These statistical tools are, moreover, essential for much biological fieldwork, as a succinct summary.

In statistics, a random variable is a quantity that may take on any of a specified set of values. For example, human age is a...

8. 4 CONFIDENCE LIMITS AND INTERVALS FOR DENSITY
(pp. 38-52)

An arithmetic mean, such as the mean density, is a single number called a point estimate in statistics. The use of such a point estimate is common in ecology, but it has the disadvantage that we do not know how good it is. That is, a single value cannot tell us how close it is to the quantity we wish to estimate. This is why a point estimate must always be accompanied by some information upon which its usefulness as an estimate can be judged. The properties of the Normal distribution (Chapter 3) allow us to calculate such information, even...

9. 5 HOW MANY FIELD SAMPLES?
(pp. 53-68)

We now know how to estimate the mean density and its variability. By making an assumption of Normality and understanding sampling distributions, we were able to construct confidence limits and estimate precision even for small numbers of biological samples. This same knowledge, with a little manipulation, allows us to choose a sample size that will be sufficient to provide any desired degree of accuracy for surveying natural populations in the field. Because the larger the sample size, the smaller the error we can expect to make in using an estimate in place of the true value, we can select the...

10. 6 SPATIAL DISTRIBUTION: THE POWER CURVE
(pp. 69-92)

We have already discussed randomness from a sampling point of view in Chapter 2. Random sampling ensures that each of the possible samples has an equal probability of being chosen for enumeration. The procedure is strictly and quantitatively defined. Let us now examine the concept of random and nonrandom from another viewpoint; that of the individual organisms.

When we look at Figures 1.2 or 2.1, which visually portray the location of each of the 663 trees in a 1-hectare Bolivian forest plot, we notice that the individual trees represented by the dots are distributed throughout the hectare. From a qualitative...

11. 7 FIELD SAMPLING SCHEMES
(pp. 93-123)

Expert judgment and experience are vital to the success of most fieldwork. However, before going into the field to make a determination that a sampling study is designed efficiently for the intended purposes, we must rely on some objective criteria of efficiency. Increasing the complexity of the design does not ensure its success or an increase in efficiency. The precision of the results depends heavily on how the sample is selected and how the estimated values are obtained. Choice of sample size is an important consideration, but we make the most effective use of available and usually limited resources when...

12. 8 SPECIES PROPORTIONS: RELATIVE ABUNDANCES
(pp. 124-163)

Faunas and floras are often summarized, or characterized, by the percentage of their components. The components, or categories, may range from the species level to family level or even higher in the taxonomic hierarchy. For example, a subtropical forest might be characterized by the percentage of palm trees contained therein. The marine fauna of the Arctic can often be identified by the percentage of a relatively few key species. Alternatively, interest may lie in sexual dimorphism, in proportions of adults versus larvae, or in some other community-level subdivision. Such succinct summaries of faunas and floras are important in both ecological...

13. 9 SPECIES DISTRIBUTIONS
(pp. 164-215)

One of the marvelous aspects of descriptive statistics is that, providing we know (or can assume) the statistical distribution, a large array of natural population data can be completely summarized by a few parameters. Throughout this book we have used two parameters, the arithmetic mean (for example, mean density and mean relative abundance) and the variance, as summary descriptors of a natural population. For example, the data in Appendix 1, which lists all the species and individuals within a 10-quadrat plot from the Bolivian Beni Reserve, can be condensed into the single (univariate) values of μ = 6.63 individuals per...

14. 10 REGRESSION: OCCURRENCES AND DENSITY
(pp. 216-239)

Field researchers who sample natural populations may be constrained by time or cost limitations, so that the most that can be achieved is the compilation of a species list. In addition, when observational techniques are subject to excessive variability, it may be more advantageous merely to collect presence/absence data than to attempt collecting abundance values. This is the case, for example, for many secretive or highly mobile animals, or when interobserver error is high because of unequally trained or fatigued observers. Even for initial surveys with well-behaved organisms, such as trees or sessile organisms, a compilation of a species list...

15. 11 SPECIES OCCURRENCES
(pp. 240-254)

As discussed in chapter 10, sometimes species lists may be the only available information on an area of interest. When using data from prior surveys, the investigator may find that the earlier researchers confined themselves to compiling lists of the species observed at localities that gave scant or no information on abundance. Some monographic works in systematics list the species of interest for the problem under investigation and where these species were observed, but the monographs may have ignored other members from different families in the same group. When using museum collections along with the literature and needed synonymy, researchers...

16. 12 SPECIES DIVERSITY: THE NUMBER OF SPECIES
(pp. 255-283)

Those who gather samples of natural populations for biodiversity purposes always want to know how many species actually occur in their study area. For nearly all groups of organisms, it appears that fewer species occur in the Arctic than in the tropics. The classic increase in the number of species occurring with decreasing latitude is used as the rationale for scientific investigation. Such simple but intriguing observations have led to innumerable studies and papers concerned with the number of species occurring in different areas. On grand scales covering entire regions, the number of species encountered is often referred to as...

17. 13 BIODIVERSITY: DIVERSITY INDICES USING N AND S
(pp. 284-296)

In this chapter, we present an introduction to quantitative biodiversity. We organized this presentation in a stepwise fashion based upon the categories of data collected by the researcher. That is, we first discussed in Chapter 12 how the use of only the total richness S could be used as a descriptor of the diversity of an assemblage alone and in combination with total N. Indeed, species richness is at the core of biodiversity measurement.

Because the S that is observed depends upon how many individuals, N, are counted or observed, we say that S is a function of N and...

18. 14 BIODIVERSITY: DIVERSITY MEASURES USING RELATIVE ABUNDANCES
(pp. 297-319)

In chapter 12 we saw that when more individuals, N, are added to the sample or accumulated by observation or collection, the number of species, S, encountered also gets larger. This phenomenon, when plotted on Cartesian coordinates, often is called the collectors or effort curve. The number of species is a function of (depends on) the number of individuals, N, and we write S = f(N) as done in Chapter 13.

As shown in Chapters 12 and 13, simple measures, either S alone, or those composed of N and S, can be calculated easily, but no single such number will...

19. 15 BIODIVERSITY: DOMINANCE AND EVENNESS
(pp. 320-336)

Clearly, relative abundances from different communities form distinct patterns when they respond differently to external environmental, compositional, or other changes that alter both absolute and relative abundances of the constituent species. Therefore, the most useful quantitative diversity measures used in biodiversity studies, as we have seen in the previous chapters (Chapters 12 through 14), should incorporate information on species richness, S, as well as N and especially p.

Thus far in our treatment of biodiversity measurement we have learned that the set of values of the species proportions that are contained in p; that is, {pi}, compose what is termed...

20. 16 BIODIVERSITY: UNIFYING DIVERSITY AND EVENNESS MEASURES WITH CANONICAL EQUATIONS
(pp. 337-341)

In chapters 12 through 15 we present the development of a family of measures that adequately summarize the attributes or characteristics of the RSAV, p. We showed that the most useful of these measures were based upon information theory as developed by Shannon, Renyi, Hill, and others. In addition, we tied together most of the widely accepted measures, showed how they could be viewed in sets with common characteristics. We then examined characteristics of each member of each set in light of usage in the biodiversity literature and finally discussed rules and properties of each set that made certain of...

21. 17 BIODIVERSITY: SHE ANALYSIS AS THE ULTIMATE UNIFICATION THEORY OF BIODIVERSITY WITH THE COMPLETE BIODIVERSITYGRAM
(pp. 342-353)

This chapter in combination with Chapter 18 composes the culmination of the chapters on quantitative biodiversity assessment. Here we introduce SHE analysis, the information–theoretic approach to obtaining a comprehensive biodiversity analysis. We show how SHE allows us to dissect our families of measures into components useful for powerful inferential statements; we elucidate the cogent aspects and give the fundamental properties of this technique. In addition, we explain how this new synthesis in biodiversity analysis can be used as a distribution-free methodology and considerably more. Strong inferences with SHE are enhanced by the addition of knowledge of an appropriate statistical...

22. 18 BIODIVERSITY: SHE ANALYSIS FOR COMMUNITY STRUCTURE IDENTIFICATION, SHECSI
(pp. 354-382)

In chapter 16, we introduce the reader to the decomposition into richness and evenness of information or information-based diversity via the canonical equations. We connected all biodiversity measures mathematically. In Chapter 17, we explain how information measures calculated from the RSAV, p, actually have an associated distribution, which has a parameter called entropy. Entropy can be designated as the expected value of H, and written as E(H). In this chapter we introduce equations for E(H), unique for each of the major and most commonly used distributions in ecological analysis. We then illustrate further depths of SHE analysis with the data...

23. APPENDIX 1: Number of Individuals per 100 m² Quadrats of the Beni Biosphere Reserve Plot 01, N = 100
(pp. 383-398)
24. APPENDIX 2: Number of Individuals per 400 m² Quadrats of the Beni Biosphere Reserve Plot 01, N = 25
(pp. 399-404)
25. APPENDIX 3: Table of Random Numbers
(pp. 405-406)
26. APPENDIX 4: Values of the Log Series Parameter α for a Given Number of Individuals (N) and Species (S)
(pp. 407-514)
27. APPENDIX 5: Subset of Bat Counts from Venezuela
(pp. 515-522)
28. APPENDIX 6: Answers to Chapter Problems
(pp. 523-554)
29. REFERENCES
(pp. 555-562)
30. INDEX
(pp. 563-592)