Magurran does not shrink from making tough judgments and recommendations that go against 'tradition' in this field.
I expect the 'new Magurran' to become an essential reference on researchers' bookshelves and required reading for advanced students in biodiversity studies. It will be a useful reference book and educational tool for years to come for those interested in the measurement of biological diversity. It will be an indispensable guide for any researcher engaged in measuring species diversity or in comparing the richness of different species assemblages. It is, above all, a practical book, clearly laid out, with concise descriptions and worked examples. Measuring Biological Diversity Anne E. Added to Your Shopping Cart.
Description This accessible and timely book provides a comprehensive overview of how to measure biodiversity. The book highlights new developments, including innovative approaches to measuring taxonomic distinctness and estimating species richness, and evaluates these alongside traditional methods such as species abundance distributions, and diversity and evenness statistics.
Helps the reader quantify and interpret patterns of ecological diversity, focusing on the measurement and estimation of species richness and abundance. Explores the concept of ecological diversity, bringing new perspectives to a field beset by contradictory views and advice. Discussion spans issues such as the meaning of community in the context of ecological diversity, scales of diversity and distribution of diversity among taxa Highlights advances in measurement paying particular attention to new techniques such as species richness estimation, application of measures of diversity to conservation and environmental management and addressing sampling issues Includes worked examples of key methods in helping people to understand the techniques and use available computer packages more effectively.
About the Author Anne E.
Review of Magurran's "Measuring Biological Diversity"
She is interested in the measurement, evolution, and conservation of biological diversity. Her research is focused on the behavior and ecology of freshwater fish in the neotropics the Brazilian Amazon, Trinidad, and Mexico and in Britain. Permissions Request permission to reuse content from this site. Unfortunately this box contains misleading information. The criticisms below are organized according to the item numbers in Magurran's box. Magurran wisely encourages students to think about the aspects of diversity they need to measure, and she correctly argues that it is not good to calculate many different diversity indices and then pick the one that gives the most attractive answer.
Nevertheless, different indices of diversity place different emphases on the common or rare species of a sample, and it is therefore legitimate even recommendable to present more than one diversity. Best is to present a continuous graph of the Hill numbers see Magurran p. If sample size is small, it is best to present just the diversities of order 0, 1, and 2 N0, N1, and N2 in Magurran's notation and to calculate each of these using Chao estimators discussed for N0, which is species richness, in Magurran p. It may be possible to derive a continuous estimator of the Hill numbers; Anne Chao is currently working on this problem with me.
If we are able to solve it, then it would be possible and desireable to plot a continuous graph of Hill numbers even when sample size is small. Such a graph contains complete information about the diversity of the system under study; the value of any standard diversity index can be calculated from such a graph. Magurran's second recommendation, that sample size be large enough to support the planned analysis, is of course correct. So is her third recommendation, that samples be replicated if possible. Her fourth point is that an estimate of species richness will often be the most appropriate measure of diversity.
This is a common opinion in ecology but in fact species richness should always be a last resort, unless presented alongside frequency-based measures as described above. As Lande shows and Magurran herself shows in the first chapters of the book , species richness is the diversity measure that is slowest to converge to a definite value as sample size increases, and indeed it often does not approach an asymptote at all see graph below. Also, when repeated samples are drawn from the same ecosystem, species richness shows more variability than any other measure of diversity.
More important, estimates of species richness are the least ecologically meaningful measures of diversity, because they give vagrants and very rare residents the same weight as the dominant species. An ecosystem with ten equally common species is much more diverse in terms of ecological interactions than a system with one dominant species and nine vagrant species, yet species richness assigns both ecosystems the same diversity.
Measures which take into account the frequencies of the species are much more meaningful ecologically than species richness. Many ecologists are suspicious of frequency-based indices of diversity because these seem difficult to interpret. Conversion of these indices to effective number of species, as described elsewhere on this website, gives them many of the same intuitive properties as species richness, and should help in breaking down this prejudice.
This is a common opinion but it is not good advice. All Simpson indices emphasize the most common species disproportionately compared to their frequencies in the sample. When they are converted to N2, the Hill number or diversity of order 2, they are useful to include alongside N1 and N0. But they should not be the sole diversity index used in a study unless the focus is particularly on the most dominant species, or on the probabilities of interspecific encounters.
Measuring Biological Diversity
Another argument against Simpson measures is that they cannot generally be decomposed into meaningful independent alpha and beta components. Her recommendation that the log-series parameter alpha be used as a diversity index even when the species do not follow a log-series distribution seems unwise though she is not alone in making this recommendation.
There seem to be strong reasons to avoid this index for general use. The log-series alpha depends only on n the number of individuals sampled and S the number of species in the sample. When the data is not log-series distributed this index throws away almost all the information in the sample since it depends only on the sample size and the number of species in the sample, not the actual species frequencies and gives counterintuitive results. For example, a sample containing ten species with abundances [91, 1, 1, 1, 1, 1, 1, 1, 1, 1] has the same diversity, according to this index, as a sample containing ten species with abundances [10, 10, 10, 10, 10, 10, 10, 10, 10, 10], whereas ecologically and functionally the second community is much more diverse than the first.
Magurran's recommendation to avoid Shannon measures reveals a common prejudice shared by many ecologists. The arguments presented are not logical. Magurran says "Given its sensitivity to sample size there appear to be few reasons for choosing it over species richness. See the graph below, taken from Kempton The sensitivity of Shannon measures to sample size can be corrected using the same techniques that Magurran discusses for correcting species richness; see Chao and Shen for comparisons of different methods.
Magurran goes on to say that converting Shannon entropy to effective number of species the exponential of Shannon entropy, which is N1, the diversity or Hill number of order 1 "does not overcome the fundamental problems of this measure". She misses the point of taking the exponential. As I have shown in my Oikos paper, Entropy and diversity , and as Hill showed in his paper and as MacArthur showed in his article, taking the exponential of Shannon entropy makes it behave intuitively in comparisons and ratios.
Please see Effective numbers of species for additional explanation on this point. Converting any diversity index to effective number of species makes it behave intuitively in comparisons and ratios. It is especially unfair for Magurran to recommend the log-series parameter alpha over the exponential of Shannon entropy.
I have explained above that the log-series parameter alpha can only be given a reasonable interpretation when the species distribution is log-series distributed. Even in that case, when a species distribution does follow a log series, the log-series parameter alpha has no advantage over the exponential of Shannon entropy-- in that case the log-series alpha and the exponential of Shannon entropy are related by a simple transformation. It is worth pointing out that Shannon entropy and its exponential are the near-universal measures of uncertainty and diversity in physics, chemistry, information theory, and computer science.
They are the only measures of diversity that weigh all species proportionately to their frequencies in the sample, rather than favoring common or rare species as Simpson indices or species richness do. This alone is reason enough to select them as the best general-purpose diversity measures. Shannon measures are also the only measures which can be decomposed into meaningful independent alpha and beta diversities when applied to a region with multiple unequal-sized communities.
No other diversity measures can be used to measure regional alpha and beta diversity. This is also reason enough to select them as the best measures for general use. Lande's decomposition of non-Shannon measures into "alpha" and "beta" does not yield a beta that is independent of alpha; see the counterexample in Diversity and similarity. If just one number must be chosen to characterize the diversity of an ecosystem, the exponential of Shannon entropy is the most reasonable choice by far.
Incidentally, the Shannon measures do not need to be borrowed from other disciplines but can be derived within biology by a careful consideration of the properties required of an ideal diversity measure. I show this in my upcoming paper on the mathematics of beta diversity. The Berger-Parker index throws away all frequency information except that of the single most abundant species, so it can give misleading ideas of dominance when there are two or three almost-equally dominant species. Dominance can be nicely read from the shape of a graph of Hill numbers as recommended in 1 above.
A horizontal graph indicates complete evenness. A value of unity indicates complete equitability and a value near zero indicates high dominance. Parametric measures of diversity p. Magurran's treatment of parametric measures of diversity gives the impression that these are generally useful measures.
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However, log series alpha and log normal lambda cannot generally be interpreted if the species distributions are not log series or log normally distributed. The work she cites in support of these measures, that of Kempton and collaborators, involves data that are nearly log-series distributed, and their goal is slightly different from that of most investigators using diversity indices. They therefore search for parameters that emphasize a particular time-invariant aspect of their samples. While it is interesting to search for characteristics of a sample that are invariant with respect to year-to-year variation, a general-purpose diversity index should neutrally describe the sample at hand without making implicit hypotheses about the underlying structure of the sample.
If an objective characterization of the diversity of a particular sample is the goal, nonparametric measures corrected for small-sample bias are superior. They are capable of interpretation even when the distributions of species are not log-series or log normal. The Q statistic is actually a nonparametric index, as Magurran notes. Nonparametric measures of diversity p. For most users of Magurran's book this is an important section. The organization of the section and the book as a whole reflects the common view that there are many unrelated diversity indices in ecology.
Yet the standard diversity indices those based on sums of powers of the species frequencies, or limits of such sums are all closely related and vary only in their emphasis on common or rare species. All of these, in spite of their apparent differences, lead to the same expression for the effective number of species, as explained in Entropy and diversity. This expression, which unites all these diversity measures, has a single free parameter, q, which determines its sensitivity to common or rare species.
This section would have been more profound had this unity been used as an organizing principle. As I have already explained in my review of Magurran's Box 4. She cites some critics of Shannon measures in support of her opinion, but the articles cited are not very well thought out. Many of these criticisms focus on the fact that for small samples, Shannon measures show a consistent negative bias. As I mention above, this bias is much smaller than that of the commonly-recommended species richness index, and this bias can be almost completely removed by using the methods suggested in Chao and Shen In any case, sampling properties should not be the primary criteria for choosing a measure.
Shannon measures are the only standard diversity indices that do not disproportionately favor either common or rare species, and are the only measures that correctly capture the concepts of alpha and beta diversity when community weights are unequal. Magurran mentions the various logarithmic bases that have been used with the Shannon index. Base 2 is used not just for historical reasons; it has some interesting advantages.
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When the Shannon entropy is expressed in logs to the base 2, it gives the mean depth of the maximally-efficient key to the species of the ecosystem being studied. Still, in general the base is unimportant, as Magurran says. The really meaningful number is not the value of the Shannon entropy, which depends on the base used, but rather the value of the exponential of the entropy, and since the exponential is taken to the same base as the logarithm, the two cancel out and the final diversity is independent of the choice of base.
The most convenient base is the base of the natural logarithm, e. She then notes that some investigators "sidestep the problem" her words by taking the exponential of H, but she thinks this still does not shed much light on the question. Like most ecologists, she has not appreciated MacArthur's and Hill's insight that conversion to effective number of species e.
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This is the key "blind spot" that burdens the field of diversity analysis. It is possible to prove mathematically that effective numbers of species regardless of the index on which they are based possess a reasonable and intuitive doubling property, so that the proportional difference between two effective numbers of species really reflects the proportional difference in an intuitively-defined diversity.
This is explained in Hill and elsewhere on my website: