139 USE OF DIVERSITY ESTIMATIONS IN THE STUDY OF SEDIMENTARY BENTHIC COMMUNITIES ROBERT S. CARNEY Department of Oceanography and Coastal Sciences, Louisiana State University, Baton Rouge, Louisiana, U.S.A. 70803 E-mail: rcarne1@lsu.edu Abstract The soft-bottom benthos covers most of the sea floor. Measurement and analysis of the species richness of these habitats are increasingly needed for studies of community regulation and for providing scientific criteria for the conservation of the ocean bottom at all depths. Diversity measures provide an evolving suite of tools that allow benthic ecologists to meet both basic and applied needs. While species diversity is now considered a fundamental aspect of communities and ecosystems, the measurement of benthic diversity did not become commonplace until the late 1960s. Prior to that communities were characterised by representative species with the implicit assumption that minor species components did not warrant detailed analysis. Use of diversity measures in benthic ecology has largely parallelled studies in other ecosystems with an emphasis upon measures that are informative when applied to large amounts of data with high species numbers. Non-parametric indices such as Simpson’s and Shannon’s are widely used along with simple species richness. Log- series and log-normal distributions have been advocated as general neutral models but receive less use. Current research is especially focused upon extrapolation of unsampled species richness and diversity relationships across spatial scales. Major contributions from benthic ecology include the rarefaction of samples to a uniform size, the development of indices that include phylogenetic relationships in diversity estimation and the extrapolation of full species richness from observed values. In meeting scientific and societal needs, benthic ecologists must apply methods that are insightful yet can be simply explained within the resource-policy arena. Introduction Justification Estimation of diversity has become an integral part of benthic ecology. There is so much recent literature and software available that review may seem unneeded. Benthic ecology is, however, now experiencing a change in the ways that species data are accessed and analytical results used that is both scientific and societal in origin. Both origins require that concepts and estimation of diversity be reconsidered. The greatest scientific change is the increasing accessibility of survey data through open Internet databases. This allows the search for geographic and temporal patterns not anticipated in the original study designs and a search across multiple studies by experts in analysis and theory who may be largely unfamiliar with benthic ecology and the taxonomy of benthic organisms. The second change is societal in the sense that international regulatory policies increasingly mandate the preservation of biological diversity in both marine and terrestrial systems. Benthic ecologists must provide regulators with estimates of diversity that can be explained and defended if these estimates are to serve agencies as the basis for conservation decisions. Thus, the intent of this review is to provide users of databases an explanation of what benthic ecologists have © 2007 by R.N. Gibson, R.J.A. Atkinson and J.D.M. Gordon ROBERT S. CARNEY 140 found and provide benthic ecologists a guide to the changes associated with the shift in terminology from diversity to biodiversity. Contraction of the term biological diversity to biodiversity seems to have originated within the U.S. government environmental management structure and was then progressively used by those ecologists especially interested in conservation biology (Harper & Hawksworth 1994). Along with development of conservation biology, biodiversity began to encompass a much broader concept than species diversity alone and now may be considered a distinct concept or suite of concepts (Hamilton 2005). One marine definition of biodiversity included the variety of genomes, species and ecosystems occurring in a defined region (National Research Council 1995) and followed a similar combination of genetic and ecological perspectives used by Norse and his colleagues (Norse et al. 1986). The official definition of biodiversity as contained in Article 2 of the Convention on Biological Diversity included “variability among living organisms from all sources … within species, between species, and of ecosystems” (United Nations Conference on Environment and Development, 1992). The view adopted in this review is that biodiversity is largely a policy term rather than scientific and its use should be avoided. Efforts to better define biodiversity from a scientific standpoint are needed and reflect conservation biologists’ duty to provide objective tools to managers faced with mandates to preserve biodiversity in marine as well as terrestrial systems (Lubchenco et al. 2003). Presently, however, policy usage of ‘biodiversity’ carries with it many assumptions that have not been proven scientifically such as a link between diversity of ecosystem health (Norse 1993) and ecosystem stability. Notable efforts in ecology to provide management tools were the adoption in benthic ecology of taxonomic indices that weight diversity by phylogenetic differences (Warwick & Clarke 2001) and the search for indicator species to be used in place of more comprehensive diversity assessment. As discussed in the historical review, selection of indicator species bears a strong similarity to the selection of characteristic species during the decades of benthic ecology research prior to any interest in the diversity of bottom communities. ‘Biodiversity informatics’ is the term applied to the growing development and use of databases for diversity studies and is very broadly defined to include biogeography and certain aspects of systematics. Progress and challenges for systems that will provide marine data have been outlined by Costello & Berghe (2006). There is already progress for deep-sea studies starting with data compiled by many French cruises (Fabri et al. 2006) and by many studies conducted in shallow European seas (Costello et al. 2006). Initially, these marine databases can most confidently be used for determining geographic and bathymetric ranges of individual species. As problems of incon- sistent and incorrect taxonomy are solved, however, the datasets will be extremely useful for estimating benthic diversity over a wide range of scales. Structure of the review This review takes a broad historical perspective to examine how benthic ecology has treated diversity from approximately 1870 until the present time with special attention to soft bottoms. Benthic ecologists carried out surveys as early as the 1900s that were similar to the projects of today, but lacked both the modern concepts of diversity and the computational tools to compute indices. However, there are strong similarities between the struggle of early benthic ecologists to simplify discussion of species-rich systems and the search of contemporary conservation biologists for indicator taxa that can be used in the estimation of overall community diversity (Pearson 1994). The mathematics of diversity estimation are treated herein only in sufficient detail to indicate what benthic ecologists do and have done with respect to concepts and data analysis. Only those approaches widely used in or originating in benthic ecology are considered. Texts by Hayek & © 2007 by R.N. Gibson, R.J.A. Atkinson and J.D.M. Gordon USE OF DIVERSITY ESTIMATIONS IN THE STUDY OF SEDIMENTARY BENTHIC COMMUNITIES 141 Buzas (1997) and Magurran (2004) do an excellent job of focusing upon the major concepts and methods. The former text has somewhat greater mathematical detail, while the latter text provides more information about concept development. Even these recent books are quickly outdated. Methods, concepts and large-scale patterns of diversity with respect to mud bottoms have been considered in highly informative reviews of Gray (2000, 2001, 2002). The information presented herein is intended to compliment these works by taking a broader historical perspective and tracing the use of analytical tools more than by discussing details of many individual results. Unfortunately, all reviews must choose to omit something. The two serious omissions here are (1) the use of evenness measures to compliment diversity and (2) the effect of pollution stress on benthic diversity. Both topics warrant separate treatment in the future. In concluding, recommendations are made as to a future course in benthic ecology that will allow both a better understanding of diversity and an ability to provide managers with useful information. Basics To avoid contributing to additional confusion, it is necessary to state the concept of diversity used in this review. According to a simple view of systems ecology, there are three types of information about a benthic community (Figure 1). First, an ‘inventory’ is a list of all species and their abundance. Second, a set of interactions among the component species is often represented by a matrix. Third, a set of relationships exists between the fauna and the physical environment. Sam- pling, identification and enumeration produce the inventory. Determination of fauna-environment relationships can be made through sampling designs that capture variation in sediment type, salinity, temperature, and so on. Assessment of species interactions is the most difficult information to obtain. Certainly, soft-bottom communities are impractical locations to determine the population interaction parameters required by theoretical community matrices (Levins 1968). In some cases, however, associations such as dependence on biogenic structure are obvious and a variety of tools can be used to determine at least a trophic position. The assumption is that the abundance of each species in the inventory can be explained to some extent by the interactions among species and the interactions with the environment. Of these three sets of information, diversity is an attribute of the inventory (Peet 1974). When given a mathematical definition, diversity should afford a parsimonious means of comparing the inventories of different systems. The underlying assumption is that differences in diversity reflect differences in species interactions. Common questions in benthic ecology have been directed to whether ubiquitous gradients of diversity exist with depth, with latitude and with anthropogenic stress. In each case, diversity is a convenient indicator of ecosystem differences. Terminology varies greatly in the larger ecological literature, but most authors take the position advocated by Hill (1973) and Hurlbert (1971). Measures of species diversity (the variety of the inventory) are based on two simple attributes: the number of species (species richness) and the pro- portional abundances. An effective means of describing the variability of proportional abundance is evenness (i.e.,departure from equal proportions). Using these two attributes, indices can be calcu- lated and used as an overall measure of heterogeneity (Magurran 2004). A somewhat unsettling aspect about species diversity is that all species are treated equally, making no use of additional knowledge about biotic or abiotic interactions and life histories. Failure to treat some species as more important would seem to make a traditional species diversity measure poorly suited to be used for conservation decisions about which communities should be afforded special protections. A partial solution is seen in a recent development in benthic ecology, use of indices of taxonomic distinctness (Warwick & Clarke 2001). Still an attribute of the inventory, these indices make use of additional information about taxonomic position of the component species. The adoption of these indices marks a major change in benthic community analysis. © 2007 by R.N. Gibson, R.J.A. Atkinson and J.D.M. Gordon ROBERT S. CARNEY 142 History From Forbes zones to Petersen communities When benthic studies from the late 1800s through the mid-1900s are reviewed a peculiar situation emerges about use of species diversity. Early hints of interest in diversity existed prior to the advent Figure 1 Basic nature of soft-bottom benthic survey data. Ecology theory takes the position that population levels of individual species in a community are influenced by interactions with the environment, including resource utilisation, and pairwise relationships among species. In application, benthic surveys produce quan- titative species-by-sample data according to designs that nest replicates with stations within larger ocean areas. Interactions of species with the environment are often expressed as correlation coefficients and are limited to the few factors included in the sampling design. An actual matrix of the relationships among pairs of species is rarely known, but statistical associations are sometimes developed as substitutes from the species-sample data. Traditionally, species diversity has been seen as a property of the species-by-sample data alone, ignoring the other two types of data. x 1,1 x 2,1 x 3,1 x 4,1 x 5,1 x 6,1 … x i,1 ρ 1,1 ρ 2,1 ρ 3,1 ρ 4,1 ρ 5,1 ρ 6,1 … x i,1 ρ 1,2 ρ 2,2 ρ 3,2 ρ 4,2 ρ 5,2 ρ 6,2 … x i,2 ρ 1,3 ρ 2,3 ρ 3,3 ρ 4,3 ρ 5,3 ρ 6,3 … x i,3 ρ 1,4 ρ 2,4 ρ 3,4 ρ 4,4 ρ 5,4 ρ 6,4 … x i,4 ρ 1,5 ρ 2,5 ρ 3,5 ρ 4,5 ρ 5,5 ρ 6,5 … x i,5 ρ 1,6 ρ 2,6 ρ 3,6 ρ 4,6 ρ 5,6 ρ 6,6 … x i,6 ρ 1,7 ρ 2,7 ρ 3,7 ρ 4,7 ρ 5,7 ρ 6,7 … x i,7 ρ 1,8 ρ 2,8 ρ 3,8 ρ 4,8 ρ 5,8 ρ 6,8 … x i,8 ρ 1,m ρ 2,m ρ 3,m ρ 4,m ρ 5,m ρ 6,m … x i,m x 1,2 x 2,2 x 3,2 x 4,2 x 5,2 x 6,2 … x i,2 x 1,3 x 2,3 x 3,3 x 4,3 x 5,3 x 6,3 … x i,3 x 1,4 x 2,4 x 3,4 x 4,4 x 5,4 x 6,4 … x i,4 x 1,5 x 2,5 x 3,5 x 4,5 x 5,5 x 6,5 … x i,5 x 1,6 x 2,6 x 3,6 x 4,6 x 5,6 x 6,6 … x i,6 x 1,7 x 2,7 x 3,7 x 4,7 x 5,7 x 6,7 … x i,7 x 1,8 x 2,8 x 3,8 x 4,8 x 5,8 x 6,8 … x i,8 x 1,9 x 2,9 x 3,9 x 4,9 x 5,9 x 6,9 … x i,9 x 1,10 x 2,10 x 3,10 x 4,10 x 5,10 x 6,10 … … x i,10 x 1,k x 2,k x 3,k x 4,k x 5,k x 6,k … x i,k Species 1 Species i Species 6 Species 5 Species 4 Species 3 Species 2 Factor 6 Factor m Depth Sediment Factor 8 Factor 7 Factor 5 Salinity Te mp erature Speciesenvironment factor interactions … … … … … … … … … … … … … … … … … … … … … … … Sample 6 Sample k Sample 1 Sample 9 Sample 2 Sample 8 Sample 7 Sample 5 Sample 4 Sample 3 Sample 10 Species 1 Species i Species 6 Species 5 Species 4 Species 3 Species 2 Species-by-sample quantitative data Species 1 α 2,1 α 3,1 α 4,1 α 5,1 α 6,1 … α i,1 1 α 1,2 α 3,2 α 4,2 α 5,2 α 6,2 … α i,2 1 α 1,3 α 2,3 α 4,3 α 5,3 α 6,3 … α i,3 1 α 1,4 α 2,4 α 3,4 α 5,4 α 6,4 … α i,4 1 α 1,5 α 2,5 α 3,5 α 4,5 α 6,5 … α i,5 1 α 1,6 α 2,6 α 3,6 α 4,6 α 5,6 … α i,6 1 α 1,j α 2,j α 3,j α 4,j α 5,j … 1 α 6,j Species i Species 6 Species 5 Species 4 Species 3 Species 2 Species 1 Species i Species 6 Species 5 Species 4 Species 3 Species 2 Speciespair relation matrix © 2007 by R.N. Gibson, R.J.A. Atkinson and J.D.M. Gordon USE OF DIVERSITY ESTIMATIONS IN THE STUDY OF SEDIMENTARY BENTHIC COMMUNITIES 143 of community ecology, but then there was surprisingly little interest during early formative years of community ecology. Finally tremendous new interest began in the 1950s as niche theory and easy computation facilitated inquiry. Certainly, benthic surveys produced inventories in which a few species were common and many more rare, but comments as to this fact are largely absent from about 1900 to 1960. With so much emphasis upon diversity today, it is informative to consider a historical period of very active benthic surveying when the concept seems to have been missing or unimportant. Estimation of species diversity is now associated with quantitative benthic sampling. Toward the end of the 1800s, seafloor studies began the transition from the description of faunal zones based upon qualitative trawl and dredge sampling (Forbes 1859, Mills 1978, Carney 2005) to more quantitative grab and core surveys. Interest in species diversity during qualitative sampling can be seen from the criticism of the C HALLENGER Expedition (1872–1876) by Anton Stuxburg (1883). Stuxburg complained about the lack of synthesis in the largely taxonomic works and specifically suggested that the number of species and the proportions of each be presented trawl by trawl. Possibly accepting these suggestions, the summary of the expedition issued 12 yr later carefully noted that deep samples contained a greater variety of megafauna species that showed lower numerical dominance than shallow samples in spite of the numerically smaller catch (Murray 1895). No explanation of this higher deep diversity was presented, and the observation was largely forgotten, possibly due to the much greater emphasis upon quantitative shallow water studies that soon followed. Contemporary surveys of soft bottom benthic communities are distinguished by a strong emphasis on numerical analysis of truly quantitative samples of the fauna in a known volume of sediment lying under a similarly known area of the sea floor. The origin of this type of surveying is generally attributed to the work of pioneering fisheries ecologist, C.G.J. Petersen (Petersen 1918), The method was developed during the course of ecologically comprehensive fish stock assessment begun in the late 1880s. Petersen-type surveys producing species inventories were widely adopted. Local surveys were conducted around Great Britain at such locations as in the vicinity of the Plymouth Marine Laboratory (Ford 1923, Smith 1932) and Scotland (Stephen 1928, 1934, Clark & Milne 1955). Numerous surveys took place along other west European coasts such as off Iceland and in the Mediterranean. By the 1900s larger scale surveys were conducted in the English Channel (Holme 1966). In North America, Allee (1923) surveyed the benthos in the vicinity of Woods Hole. Possibly most influential were benthic surveys in Puget Sound on the Pacific coast by Shelford (1935) who was a strong proponent of the super-organism view of community structure and function. Similar surveys were spread across the Arctic from the 1920s onward, and were summarised in English by Zenkevitch (1963). The techniques were also adopted along the Japanese coast in the 1930s and 1940s by Miyada (cited by Thorson 1957). These many Petersen-type surveys were all quite similar although sampling gear and sediment processing evolved over the course of the studies (Spärck 1935, Thorson 1955). The general trend was towards larger areas of sampling and more reliable penetration of the bottom. Statistical analyses were minimal, and results were often presented as a map of both faunal assemblages and oceanographic conditions. Assemblages were inventoried in detail, then described and named on the basis of the two characteristic species. Graphics were used to portray the relative abundance of dominant species. Diversity, as an aspect of the species inventories, was neither discussed nor analyzed in studies into the 1960s. This was despite the availability of useful indices since the 1940s, and their widespread use terrestrially for both plant and insect surveys. In addition these early workers considered themselves to be studying communities as interacting systems. However, hints exist that questions about species diversity were beginning to be formulated. In the survey by Smith (1932) of the Eddystone grounds species richness was presented with singletons and more abundant species © 2007 by R.N. Gibson, R.J.A. Atkinson and J.D.M. Gordon ROBERT S. CARNEY 144 carefully noted. Possibly reflecting growing ideas and better calculators, more sophisticated analyses began to appear such as the dispersion of species across samples (Clarke & Milne 1955). By the time of the English Channel survey (Holme 1966), the Petersen tradition of naming assemblages after two characteristic species had been dropped due to the finding that species composition varied greatly within such assemblages. The surprisingly little interest in species diversity or in any related characterisation of species inventories probably had several causes. The three most likely are a lack of practical utility, a lack of relevant concepts, and a lack of computational tools. With respect to utility, many of these benthic surveys were associated with fisheries studies making community productivity the parameter of interest. The apparent lack of ideas about species diversity may be related to the immaturity of the community concept. In the early 1900s, mapping of communities and characterisation of their component species was the major activity, and not a careful investigation of community structure and function that might be implied from the species inventory. Jones (1950) reviewed the status of benthic studies in the context of community theory and concluded that many workers accepted the idea that they were studying integrated systems in which biological interactions were important. Few, however, seemed to fully embrace the idea that benthic communities were superorganisms passing through biologically controlled successive states until a certain climax was reached. Indeed, the distribution of benthic assemblages was always explained in terms of control by physical conditions such as depth, sediment type, salinity, etc. One notable exception was Shelford, who was one of the framers of the climax community and biome concepts (Clements & Shelford 1939). He divided the oceans into a series of biomes largely associated with depth and geographic position without reference to species richness. Another ecology pioneer was Allee (1934), a strong proponent of benthic communities functioning as superorganisms, tracing the idea back to Verrill. At the end of Petersen era In 1957, the state of knowledge about benthic ecology was compiled by international experts in a twenty nine-chapter memoir and published by the Committee on Marine Ecology and Paleoecology of the Geological Society of America (Hedgepeth 1957). Of particular relevance to the concept of diversity was the paper on bottom communities by Thorson (1957). This paper clearly marks a transition from the era of naming communities to one of discussing diversity patterns. The level mud bottom was correctly seen as one of the largest, and apparently homogenous, environments on Earth. Due to the strong dependence upon oceanographic conditions, bottom communities with similar taxonomic structure should be found over very large areas. These parallel communities were viewed as having relatively minor differences around the world. More importantly, Thorson compiled species richness data on selected taxa and found an increase from pole to tropics for epifauna and no gradient for infauna. Strongly influenced by physiological explanations, the increase was attributed to greater thermal stability in the tropics. A different view of benthic community stability emerged based upon ‘Thorson’s Rule’, a generalisa- tion about increased occurrence of pelagic larvae in the tropics seen as having many exceptions but some general validity (Laptikhovsky 2006). It was then suggested that the tropical benthos would show greater spatial and temporal variation in species composition because of a large variation in survival to settlement in the plankton. Higher latitudes should have a more stable community structure due to the prevalence of direct development. The strong emphasis on parsimoniously characterising multispecies communities in a manner suitable for mapping without actual mathematical analyses lead early benthic ecologists to depend on nomenclature, or the naming of communities. A reading of the very detailed “ideal rules” of Thorson (1957) indicates how subjective the process actually was. Recommendations on how to © 2007 by R.N. Gibson, R.J.A. Atkinson and J.D.M. Gordon USE OF DIVERSITY ESTIMATIONS IN THE STUDY OF SEDIMENTARY BENTHIC COMMUNITIES 145 select characteristic species would be of only historical interest if a similar need did not exist today to simply describe benthic communities for conservation planning. Later in this review it will be shown that naming Petersen communities is similar to picking indicator species and assigning greater importance to some species than others. The primary task of naming communities was to identify within the collected fauna those species that are ‘characteristic’ of the community. The five rules of Thorson paraphrased here were. First, more than one such species should be selected. Second, short life-span species should be avoided because their numbers fluctuate too much to be consistently characteristic. Third, highly mobile animals and predators should be avoided as being be too transient. Fourth, characteristic species should be big enough and abundant enough to be immediately conspicuous and have good identification traits without consultation with a specialist. Fifth, biomass and/or density can be used an indicator of abundance as long as they are not misleading due to large brood sizes or very large specimens. Even within the mundane task of picking names for communities, an interest in diversity can be seen. Thorson divided the species inventory into four categories or orders based on abundance and fidelity of association with a particular community. A first-order characteristic species should be conspicuous, found throughout the range of the community in at least 50% of the samples, and at least 5% of the biomass and restricted to that community. A second-order characteristic species should have a similar frequency of occurrence and biomass dominance, but limited to only portions of the range. A third-order species would be found in other communities as well as in at least 70% of the units and at least 10% biomass. A fourth-order of ‘associated animals or influents’ would be in at least 25% of the units and as much as 2% of the biomass but of little diagnostic value due to a wide distribution crossing other communities. Beginning of a new era While formative elements of modern ecological theory may be found in many lines of early population research, ecological questions about niche filling, resource utilisation, and competitive exclusion were first expressed by G.E. Hutchinson and his students and colleagues in the 1960s (Maurer 1999). The “diversity of a species inventory” was modelled as a balance achieved through competition, resource specialisation, habitat complexity, resource availability, and history (Mac- Arthur 1972). The details of community structure and function were being examined with mathe- matical tools, and species diversity was a parameter of great interest. The transition to the new view is most evident in a series of benthic studies begun in shallow estuaries (Sanders 1960) and then extended to abyssal depths (Sanders et al. 1965). Initially, com- munities were still named on the basis of characteristic species such as the Nephthys incisa – Nucula proxima community, and diversity indices were not calculated (Sanders 1960). By 1965, descriptive habitat names were used in place of characteristic species, and new diversity tools were proposed. There was obvious interest in species richness and proportions, the large number of rarer species, and the quantitative analysis of recurrent groups using trellis diagrams. Sanders’ benchmark com- parative study of marine benthic diversity (Sanders 1968) marked the beginning of an adoption of niche theory and analytical methods by benthic ecologists worldwide that persists to this day. This comprehensive paper by Sanders made four major contributions. First, it objectively examined the use of several diversity measures, and found that the information-based Shannon’s index was adequate, but species richness was preferred. Secondly, rarefaction, a procedure for estimating species richness in computationally reduced samples was presented to reduce the effect of sample size. Third, Thorson’s infauna versus epifauna latitude gradients were challenged and regional oceanographic conditions considered to be of greater importance in controlling diversity highs and lows. Fourth, the high diversity of deep-sea macrofauna was noted for the first time since © 2007 by R.N. Gibson, R.J.A. Atkinson and J.D.M. Gordon ROBERT S. CARNEY 146 the C HALLENGER Expedition and proposed as a general ocean feature. A stability-time hypothesis was proposed as a general model for all benthic environments. In this explanation physical instability was predicted to cause low diversity and biological accommodation would cause high diversity where physical conditions were stable. Sanders was extremely careful about making a distinction between measurements of diversity that are reflective of species number (species diversity) and those reflective of proportional abun- dance (dominance diversity). Although categorising several indices as being of one or the other category, Sanders employed his own method of using species number per sample size for species diversity. His method of calculating dominance diversity was to first plot a species accumulation curve for each sample. He then compared that curve at reduced sample sizes (arrived at by rarefaction) with a baseline curve representing maximum equitability with all species having the same proportional abundance. Unfortunately, full details of the method were omitted. Sanders proceeded to examine the behaviour of species diversity versus dominance diversity in eight benthic habitats reducing the sample size artificially through rarefaction. A graphical means was employed to track changes in rank of diversity as samples were rarefied. The ranks determined by species number were found to be fairly consistent upon rarefaction, while ranks determined by dominance were very inconsistent. He concluded that species number was the more conservative measure of diversity while dominance was more variable due to the physical environment. Influx of indices The 1960s and 1970s saw a rapid adoption of diversity measures and multivariate approaches to the analysis of benthic data. This adoption was due to a more fully developed niche theory, a better access to computers, and a dissatisfaction with the subjectivity of Petersen-like community descrip- tion (Lie personal communication). The origins of the indices, however, preceded adoption by benthic ecologists by a decade or more. The inventories, lists and counts of species, found in benthic or any other type of survey sampling are categorical data in which individual specimens are assigned to a species category. Linguists also deal with categorical data, and pioneers like Zipf (1935) and Yule (1944) developed quantitative methods of comparing texts. They counted the frequency of words in various texts, ordered those frequencies by rank and noted recurrent curves reflecting the fact that a few words were very common and many rare. At roughly the same time period, R.A. Fisher (Fisher et al. 1943) proposed the use of a logarithmic series for examination of species categorical data. Influ- enced by the linguistic indices, Simpson (1949) proposed use of a ‘concentration’ index, and Shannon (1948) developed Information Theory that would be embraced by ecologists following a suggestion by Margalef (1958). The literature on how diversity should be measured continues to grow rapidly. Works in general ecology published in the 1960s through 1980s tend to fall into a either a category dealing with niche-theory models or a more practical category trying to improve the utility of indices. Benthic studies of diversity fit into both categories, but place emphasis on practical aspects. The emphasis on practical aspects stems from the increased number of surveys required to address environmental problems. Both theoretical and practical works are now on an upsurge. Increased theoretical interest has been generated by the proposal by Hubbell (2001) of the “unified theory of biodiversity and biogeography” and by multinational interest in the preservation of the European coastal seas. The ‘unified theory’ has inspired considerable controversy (Whitfield 2002) and renewed examination of diversity models (Pueyo 2006). Preservation of the coastal seas of many European nations requires standardised measures of diversity that are both scientifically meaningful and useful for policy and management decisions. © 2007 by R.N. Gibson, R.J.A. Atkinson and J.D.M. Gordon USE OF DIVERSITY ESTIMATIONS IN THE STUDY OF SEDIMENTARY BENTHIC COMMUNITIES 147 Compared with terrestrial studies, the use of diversity measures by benthic ecologists has been relatively conservative in terms of restricting the types of indices proposed and applied. This can be attributed to the nature of benthic survey data, that is, a collection of many thousands of individuals and several hundred species. The taxonomy for many of the benthic groups is poorly developed and often in need of revision. Many species are rare. Compounding these problems, attempts at larger-scale syntheses are hindered by inconsistent sampling methods and great natural variation in sample size. Therefore, benthic ecologists have always needed measures that were robust when data were not ideal and which simplified the task of interpretation. Most studies have made use of just a few diversity measures based either upon fitting abundance distribution models or calculating an index. Most of these measures were well described by Gray (1981a) in benthic terms. In the context of this review, use of a distribution means fitting and calculation of the parameters that generate the distribution. Use of an index means the combining of two or more characteristics of species-abundance distributions to produce a single value on a scale that allows comparison among communities. Indices make no assumptions about the underlying distribution, but carry with them implicit definitions of diversity. Use of distributions always allows for signif- icance testing. For all common indices statistical properties have been developed and formal testing is also possible. Traditional approaches Diversity measures are so widely applied and improved measures are so actively sought that a division into traditional versus newer approaches is somewhat artificial. Old approaches are con- stantly being reconsidered. That acknowledged, there are some approaches that have been in use a long time and have been quite extensively discussed. These shall be presented first. Then some of the more recent developments are considered. Log-series and log-normal abundance distributions From a statistical perspective the most parsimonious means of describing diversity and conducting rigorous comparisons among communities is to first identify the underlying species abundance distribution, and fit the model and estimate the parameters that characterise the distribution. Several such distributions have been used in diversity studies (Hayek & Buzas 1997, Magurran 2004), but the two oldest have had the greatest usage in benthic ecology. These are the log-series (Fisher et al. 1943) and log-normal (Preston 1948) distributions. The finding that either one or the other of these distributions fitted a wide variety of terrestrial and marine data was once considered to reflect profound aspects about ecosystem structure (Odum et al. 1960), and that studies of pattern alone could definitively identify the causative processes. It has now been realised, however, that such distributions may simply reflect the outcome of many complex processes, especially when there are a large number of species and individuals are present (May 1975, Pueyo 2006). Indeed, information on species abundance alone is insufficient to select among alternate ecological theories of causation (McGill 2003). Many different processes can generate the same distribution. Explanation of distributions, the process of fitting, and the determination of parameters is substantially more complex than a discussion of diversity indices. Hayek & Buzas (1997) provide an excellent detailed account, but these authors are strong advocates for the wide application of the log-series. The log-series can be characterised using only a single parameter Fisher’s α. Computing α requires an interactive computation. When data actually fit the log-series, α is approximately the number of species represented by a single specimen (singletons). © 2007 by R.N. Gibson, R.J.A. Atkinson and J.D.M. Gordon ROBERT S. CARNEY 148 An especially successful use of the log-series in benthic systems was an application to archived foraminiferan data from five coastal regions ranging from the Arctic into the Caribbean (Buzas & Culver 1989). Fisher’s α provided a highly useful measure of diversity and indicated a strong geographic trend with the highest diversities in the tropical Caribbean and lowest in the Arctic. An unusual aspect of that analysis was that log-series rarefaction was used (Hayek & Buzas 1997) to produce equivalency, and that occurrence among samples was used as a measure of abundance rather than counts within a sample. The log-normal refers to abundances that are normally distributed about a mean once the data have been log transformed. As for any normal distribution, it is characterised by two parameters — mean and variance, which can be used as indicators of diversity. The log-normal has a rich history of usage in ecology since first recognised as a widespread pattern (Preston 1948). An early application in benthic ecology was the re-examination by Gage & Tett (1973) of benthic data from two lochs that had been previously analyzed using rarefacted species richness (Gage 1972). The log-normal distribution was fitted, and resulting means and variances used to search for patterns associated with the salinity differences of two lochs, salinity gradient within each loch, and sediment type. In the authors’ opinion, the two log-normal parameters provided a more informative picture than rarefacted species richness. The actual goodness of fit, however, can be questioned since single- tons were excluded before analysis. The complete data may have been better fitted with the log-series. The most extensive use of the log-normal distribution in benthic ecology can be found in the studies of John Gray and his colleagues. Gray (1981a) noted that benthic assemblages containing many singletons generally fit the log-series distribution, but the common assemblage in which most species were represented by a few individuals fit the log-normal. The log-normal distribution has proven useful in identifying pollution impacts on benthic diversity (Gray 1981b, 1983, 1985). The log-normal has been proposed as a neutral model for soft bottom macrofauna assemblages in the sense that it is the expected outcome of certain ubiquitous processes of immigration, emigration, and resources partitioning (Ugland & Gray 1982, 1983). In a renewed discussion about the genera- tion of species abundance patterns by neutral models, the appropriateness of the log-normal has been criticised (Williamson & Gaston 2005). Grey et al. (2006a), however, considered both a terrestrial and a marine system, and argue that many systems may be effectively modelled as compound log-normals in which two or more distributions are mixed. Ecologically, it seems quite feasible that benthic samples will include several suites of species for which the abundances reflect separate and distinct histories. Additional investigation is required. Species richness and its rarefaction Species richness is defined as the number of species in the samples of interest. Those samples may represent replicates from a single location or from larger spatial scales. The notation and nomen- clature of Gray (2000) serves to avoid confusion with other symbols and ambiguity as to scale. ‘SR’ denotes species richness with subscripts applied to indicate spatial extent. It is the most easily explained of all measures of diversity, and for a large segment of the concerned community it is synonymous with biodiversity. In his classification of indices (Hill 1973), “SR” is viewed as giving equal weight to species of any abundance since it ignores those abundances completely. Recognising that SR is a function of sample size N, SR is often normalised through division by N or area sampled. Additionally, relationships of SR with sample size and abundance can be examined through regression with the slope of a regression serving as a index of diversity. These approaches are well covered by Hayek & Buzas (1997) and Magurran (2004). Species richness is often plotted against sampling effort represented by counts, number of samples, or area sampled as an indication of the completeness of the species inventory. In the case of a complete inventory, the curve becomes asymptotic. © 2007 by R.N. Gibson, R.J.A. Atkinson and J.D.M. 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An important advancement was an independent derivation by Ugland et al. (2003) and Colwell et al. (20 04) of an analytical method of calculating the mean and variance. 1923, Smith 1932) and Scotland (Stephen 1928, 19 34, Clark & Milne 1955). Numerous surveys took place along other west European coasts such as off Iceland and in the Mediterranean. By the 1900s. of an analogy between transmission systems and temporal changes in ecosystems. Very simplified, temporal changes are like a noisy channel between the structure of an ecosystem at one time and another