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On the use of sample indices to reflect changes in benthic fauna biodiversity
Ecological Indicators 26 (2013) 154–162
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On the use of sample indices to reflect changes in benthic fauna biodiversity Jon Barry a,∗ , Silvana Birchenough a , Beth Norris b , Suzanne Ware a a b
Centre for Environment, Fisheries and Aquaculture Science, Lowestoft Laboratory, Pakefield Road, Lowestoft, Suffolk NR33 OHT, United Kingdom School of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury CT2 7NF, United Kingdom
a r t i c l e
i n f o
Article history: Received 10 August 2012 Received in revised form 5 November 2012 Accepted 6 November 2012 Keywords: Sample indices Relative indices Biodiversity indices
a b s t r a c t This paper focuses on the difference between the value of some commonly used diversity indices (Simpson, Shannon, abundance, richness) calculated from benthic grab samples and their value in the population or region from which the samples are taken. The ability of the sample indices, as well as a recently derived relative Shannon index, to reflect change in biodiversity is examined in a short simulation study based on changing one of the diversity parameters (abundance, richness and evenness) in the population, whilst keeping the other two components constant. Our results suggest that, whilst their population equivalents do not always reflect biodiversity changes, the sample Simpson, Shannon and Richness indices perform well. We note that this will be true for any surveys where the sampling programme fails to detect many species in a population, and hence will be applicable for most benthic surveys. The use of sample indices to detect changes in biodiversity from long-running time series in the Thames and Tyne estuaries is illustrated. Crown Copyright © 2012 Published by Elsevier Ltd. All rights reserved.
1. Introduction A number of current marine policy objectives require the implementation of effective measures to monitor trends in biodiversity. These include the European Marine Strategy Framework Directive (MSFD), the Water Framework Directive and Common Standards Monitoring in support of assessing feature condition within nationally designated sites (e.g., Sites of Special Scientific Interest, Marine Conservation Zones, and Scottish Marine Protected Areas) and internationally designated sites (e.g., Special Areas of Conservation, Special Protection Areas and Ramsar sites). For benthic systems, this monitoring involves the development of indicators measuring sediment state, the role organisms play in maintaining ecosystem function and how this has been affected by human impacts. Descriptor 1 of the MSFD focuses primarily on maintaining biodiversity. This definition of maintaining biodiversity is based on the quality and occurrence of habitats and states that the distribution and abundance of species should be in line with prevailing physiographic, geographic and climatic conditions. Some of the proposed criteria for measuring biodiversity are: species distribution, population size, population condition, habitat distribution, extent and condition for the benthic community among other fauna groups (Van Hoey et al., 2010). Our focus in this study is on the application of biodiversity measurement of the benthic environment. This biodiversity is
∗ Corresponding author. Tel.: +44 1524 844113. E-mail address: [email protected] (J. Barry).
widely measured in monitoring surveys to examine the effects of impacts on seafloor communities. Examples include marine aggregate dredging (Barrio Froján et al., 2011; Birchenough et al., 2010), deposition of dredged material (Ware et al., 2010; Birchenough et al., 2006) and fishing pressure (Callaway et al., 2002). Many studies have been carried out that compare the performance of biodiversity indices (e.g., Ware et al., 2009) but little attention has been paid to how calculation of biodiversity indices from sample data reflects the values of those same measures in the population from which the samples are taken. In this paper we demonstrate that sample estimates can be misleading and should be interpreted carefully when conducting monitoring. Note that, throughout, we use ‘population’ in its statistical rather than its ecological sense. That is, by the population value of some indicator we mean the value that would be obtained if the whole of a region was sampled. Defining biodiversity can be a complicated issue. Indeed, even the name does not remain constant: ‘ecological diversity’ has now largely been replaced by ‘biological diversity’ or ‘biodiversity’ (which we use). Magurran (2004) defines biological diversity as “the variety and abundance of species in a defined unit of study”. Warwick and Clarke (2001) provide some measures that extend the concept into taxonomic distinctness – where, for example, species in the same genus are more similar than those with different genera but in the same family. Use of functional diversity is also increasingly used (Barrio Froján et al., 2011; Dimitriadis and Evagelopoulos Koutsoubas, 2012), where distinctness of species is defined by their traits rather than their biological species classification.
1470-160X/$ – see front matter. Crown Copyright © 2012 Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ecolind.2012.11.004
J. Barry et al. / Ecological Indicators 26 (2013) 154–162
In this paper, we generally follow Buckland et al.’s (2005) interpretation that biodiversity in a region or community is a function of the three components: overall abundance, number of species (richness) and evenness. Thus, a region is more biodiverse if it has more individuals, more species and if the proportions of each species as a function of total abundance are more similar (maximum evenness occurs when all species are equally abundant). Central to our work is the distinction between the biodiversity in the population being considered and in the sample. To illustrate this, for the assessment of Good Environmental Status (which needs to be obtained for all European water bodies by 2020: Van Hoey et al., 2010; Birchenough et al., 2012) under the MSFD, interest is at the subregional scale. For the UK, these sub-regions are The Greater North Sea (including the Kattegat) and the English Channel and the Celtic Seas. As in most areas of scientific investigation, our main aim is to find out properties of the population through properties of the sample. For example, we may want to use the information from the sample to tell us whether biodiversity in the population is being affected by either a natural or anthropogenically mediated pressure. As we shall see below, this is not always straightforward – indeed, biodiversity properties in the samples can be very different to biodiversity properties in the population. The problem of making inferences about populations from samples is made particularly difficult in benthic surveys by the fact that the sampling fraction (the proportion of the survey area that is measured) is generally very small. For example, a typical survey off the Norfolk coast by Kenny and Rees (1994) used five 0.25 m2 grabs over 135,000 m2 – giving a sampling fraction of 9.25926 × 10−6 . Small sampling fractions such as these mean that many species present in the population will not be present in the samples. The probability of a species being found in the sample is a function of its abundance in the population, the sampling effort (e.g., number and size of grabs), and its spatial pattern – clustered species are harder to find than more regularly distributed species (Boyd et al., 2006). These factors need to be considered when designing and interpreting benthic surveys. From the results of a benthic survey, we generally have a macrofaunal species abundance matrix with elements aij reflecting the abundance of species i at point j. These points could be in either space or time (or both) – but, for ease of explanation, we will assume here that they are in time only. Data will usually arise from a grab survey (typically employing a 0.1 m2 Day grab in soft sediments or a 0.1 m2 Hamon grab in coarse sediments). The main difference between, for example, bird surveys and benthic surveys is that the bird surveys rarely contain species with zero values and that there is a fairly small list of species that might be present at any one time in the survey area. With benthic surveys around the British Isles, there might potentially be up to 10,000 species in the survey area (UNICORNc (copyright 1995–2004 Unicomarine) database of known benthic species lists), whereas, typically, it is unusual to see more than 1000 species in all of the sample grabs. Our aims in this paper are to:
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2. Materials and methods 2.1. Biodiversity indices Here we consider four of the simplest and most commonly used diversity indices (many more are given in Magurran, 2004): sample richness and abundance, plus the Simpson and Shannon indices. We also use a modification to the Shannon index that was originally proposed by Buckland et al. (2005). This modification results in an index where species’ proportions at points in time are relative to the overall abundance at some reference time point (we call this the ‘relative Shannon index’). We examine the aspects of biodiversity that these five indices measure and their sample properties in terms of bias and in capturing changes in biodiversity in the population in which they are measured. The Simpson index was selected because it is known to be statistically unbiased (Section 2.3). In contrast, it is known that the Shannon index is badly biased for benthic data and we particularly wanted to contrast its performance to that of what we thought would be the improved relative Shannon index (ultimately, however, the Shannon index performed well, Section 3). Clearly, further studies could examine other indices in a similar way to the approach taken here. The standard Shannon index (Shannon and Weaver, 1949) at time j is given by S
Hj = −
pij ln(pij )
i=1
(1)
S
where pij = nij / i=1 nij = nij nj , and nij is the abundance of species i at time j. That is, pij is the proportion of species i at time j compared to the sum of the abundances of all species at time j. We should be clear about whether we are calculating this index in the sample or the population. If the former, many of the pij for unobserved species will, effectively, be estimated as zero – an under-estimate compared to their population values. The Shannon index has been applied to a variety of ecological studies including terrestrial communities, namely birds and insects (Sirami et al., 2009) as well as applications in the freshwater and marine realm (Hepp and Santos, 2009). Magurran (2004) and Pielou (1975) provide some useful background on the Shannon index. Pielou notes that two desirable properties of the index are that its maximum, S, occurs when all S species in the region have equal densities and that the index increases with number of species. Thus, the Shannon index is a function of both evenness and species richness. The relative index defined by Buckland et al. (2005) is similar to the Shannon index except that the pij term is written as qij = nij /n1 . Thus, the proportion of species i at time j is relative to the total abundance at time 1. Note that the choice of time 1 is essentially arbitrary – any sensible reference time could be used. We thus define the relative Shannon index as S
Mj = −
qij ln(qij )
(2)
i=1
1. Find indices whose sample values reflect changes in biodiversity in the wider population; 2. Use simulations to illustrate the sample bias of some indices as a function of the density of species in the population; 3. Examine how sample indices are able to reflect changes in a region’s core components of biodiversity through a simulation study; 4. Explain changes in biodiversity for long-term benthic series collected in the Thames and Tyne areas, based on the results from the simulation studies.
The Simpson index can be written as j = 1 −
S
pij 2
(3)
i=1
Simpson’s index is a function of species richness because, with more species and constant evenness, the pij will generally be smaller and hence the sum of their squared terms will also be smaller. The Simpson index also measures evenness in that its maximum value occurs when, for a given number of species, the proportions for each
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Fig. 1. Sample mean, mid 95% percentiles (solid lines), and population values (dotted lines). The x-axis reflects the density (i.e. number of individuals per m2 ) of each of the 100 species present in the simulations. The plots are: (a) richness; (b) Shannon; (c) relative Shannon; (d) Simpson; (e) abundance; (f) richness.
species are the same. Uses of Simpson’s index in the marine sciences include Ferraro and Cole (1990) and Gray (2000), undertaken in the USA and Norway respectively. We also use the sample species richness (s) as an index; this is simply the number of species found in all of the grabs. The sample abundance (n) is defined as the total number of creatures found in the grabs. To obtain an index that estimates the population abundance (N), n is multiplied by the ratio of the survey ˆ = nA/ga, where g is area to the combined area of the grabs. Thus, N the number of grabs, a is the area of each grab, and A is the area of the survey area. 2.2. Sample properties of the indices Here we are concerned with how the sample properties of the indices described above reflect the population values of those indices and, in particular, change in those population values. We start with the concept of whether the sample indices are unbiased. Statistically, the bias of a sample index is defined as its expected value minus its value in the population (the expected value is the mean value if the sampling were repeated many times). The sample index is biased if its bias is non-zero. It is clear that the sample species richness in most benthic surveys is biased because it is unlikely that all of the species in the survey area will be found. Similarly, the majority of diversity indicators that are functions of the number of species (e.g., Shannon, Margalef) will be biased for benthic surveys because many species in the population do not appear in the sample (though note that the Shannon index has a small bias even if all species are present in the sample (Hutcheson, 1970)). A notable exception is the Simpson index, which generally has negligible bias. This is because the squared proportions in the Simpson index are negligibly small for rare species. The sample species
abundance can be easily made unbiased by scaling up the sample value by the ratio of the population area to the area sampled. The bias concepts are illustrated for a simple simulation study where N species, each with a density of r individuals per m2 , are randomly placed into a population region, represented by 1 m × 1 m square. From this population, four 0.1 m2 grabs were sampled and an abundance matrix calculated from the combined grabs. Because the individuals have a random pattern, the number of individuals of a species found in the four grabs is distributed Poisson with mean 0.4r; using this fact considerably speeds up the simulations. The whole process was repeated 500 times. This allowed estimation of the sample mean together with the mid 95% range from the 2.5th and 97.5th percentiles. All computations for these simulations and those elsewhere in the paper were carried out using the statistical software R (R Development Core Team, 2010). Fig. 1 shows the sample and population values of the five diversity indices described above as a function of density. The bias of the richness (a) and Shannon (b) indices decreases with density because, as the density increases from 1 to 20, it is less likely that species will be missing from the sample. The relative Shannon index (c) has low negative bias – mainly because it is a function of abundance and not just richness. The Simpson index (d) is largely unbiased although its variability is greatest at low densities. As expected, the abundance index (e) is unbiased, although the sampling variability increases as the overall population abundance increases. Plot (f) shows the situation in which the number of species in the population decreases from 100 to 81. Up to a density of about 8, the sample richness increases even though the population value is decreasing. Thus, if sample data were used to assess changing richness over a series of yearly surveys then, for the lower densities, we would infer that the number of species was increasing when it
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is actually deceasing (the same pattern is exhibited by the Shannon index, though not shown). Overall, using sample estimates to infer population values is not always reliable. For many indices, the difference between the sample and the population values depends on species density. Although not illustrated here, the difference also depends on the sampling effort (number of grabs) used in the survey (on average, the more grabs taken, the nearer the sample estimate will be to the population value) and the spatial pattern of the individuals (the more clustered the individuals, the further the sample estimate will be from the population value). So, rather than base inferences strictly on the population values, which often cannot be inferred from sample values, a different approach is to examine whether changes in sample indices reflect changes in population diversity. 2.3. Simulation study to assess how sample indices reflect biodiversity change For the purpose of the current study, we focus on the three components of diversity mentioned in the introduction: abundance, richness and evenness. Following the approach in Buckland et al. (2005), if any one of these indices increases/decreases, whilst the other two remain constant, then a good sample index should also increase/decrease. A simulation study was performed to examine how the five sample indices used above perform against these criteria. The simulation study was similar to the one used to illustrate sample bias in Fig. 1. As before, the simulations all involved N species, individuals from which were randomly located on the unit square. Four 0.1 m2 grabs were randomly placed onto the square and the sample indices calculated. Three types of simulation were performed; in each type changing one of the three diversity characteristics over time and keeping the other two characteristics constant. The evenness measure used to measure change in population evenness in Fig. 4(a) was proposed by Smith and Wilson (1996). This is essentially the variance of the log of the species’ abundances, transformed so that the index lies between 0 and 1. Specifically, at time j, the index is
⎧ ⎡ ⎤2 ⎫ ⎪ ⎪ S S ⎨ ⎬ 2 1 ⎣ ⎦ Ej = 1 − arctan ln(nij ) − ln(nij ) /S S ⎪ ⎪ ⎩ i=1 ⎭ j=1
(4)
2.4. Thames and Tyne time series We used the values of the sample indices – Simpson, Shannon, richness, abundance and evenness (Eq. (4)) – to try to explain real time series of benthic abundance from yearly surveys in the Tyne (1984–2006) and the Thames (1986–2006) estuaries. We introduced the evenness measure because it can help explain changes in richness. We did not use the relative Shannon index as it was out-performed by the Shannon and Simpson indices in the simulation study for detecting changes in richness and evenness. The three Tyne stations are part of a long-term monitoring programme started in the 1980s to ascertain the changes resulting from sewage sludge disposal in this area. The stations RN and RS were used as reference stations, DG was the disposal station. Further analysis in relation to natural variability and recovery of these stations was conducted by Rees et al. (2006) and Birchenough and Frid (2009) respectively. Similarly the Thames area has also been monitored since the 1980s to assess the effects of sewage sludge disposal (MAFF, 1993). The station BD was located in the centre of the disposal ground and MD was used as a reference station. Although four or five 0.1 m2 Hamon grabs were used in some years,
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for comparability between years, we have combined the counts from three grabs in each year. 3. Results 3.1. Simulation study to assess biodiversity change The pattern of the changing diversity characteristic in the population is shown in the top left hand plot of each of Figs. 2–4. This is the pattern that we want the sample indices to reflect. When describing the simulations, we first describe how the indices are affected in the population and then how their sample values change – these sample changes are shown graphically in plots (b)–(f) in each of Figs. 2–4. 3.1.1. Changing population abundance, keeping richness and evenness constant 3.1.1.1. Population. The number of species is fixed at N = 75. By changing the species density, the overall mean abundance moves from 150 to 300 and then back to 150 at the end of the series (Fig. 2(a)). In the population, the proportion of each species at any one time does not change. Thus, the standard Shannon and Simpson indices will also not change over time. However, the relative Shannon index will change because its base abundance is fixed at time 1. Thus, in the population, the relative Shannon index is a good indicator of changing abundance biodiversity. 3.1.1.2. Sample. The way that the sample indices change tells a different story to their population equivalents (Fig. 2). Because the change in population abundance means that the numbers of species found in the samples will reflect this change (i.e. more species will be found as their density increases), the sample richness (b), Shannon (c) and Simpson (e) indices all reflect the population change in abundance fairly well. The relative Shannon index (d) also performs well and provides a sharper reflection of the change in abundance. Note also from Fig. 2 that the change in the index on the y-axis is much larger for the relative Shannon index than for the standard one. However, it is also evident that the standard Shannon index shows the correct pattern of change – which, in practice, is what would be required of it. 3.1.2. Changing population richness, keeping abundance and evenness constant 3.1.2.1. Population. The population richness was increased from 50 to 100 and then back to 50 again by the end of the series (Fig. 3(a)). Overall mean abundance was set at 300. The proportion of each species was identical at each time point so that evenness was at its maximum value at all time points. In the population, the Simpson, Shannon and relative Shannon indices will all reflect this change. 3.1.2.2. Sample. The sample Shannon (c), Simpson (e) and richness (b) indices all show the change in population richness well. The relative Shannon index (d) does reflect the changes in richness, but not as tightly as the standard indices. Other simulations (not shown) show that the relative index performs better as overall abundance is increased (and hence more species are likely to be detected). 3.1.3. Changing population evenness, keeping abundance and richness constant 3.1.3.1. Population. The process by which the evenness is changed is as follows. At maximum evenness (in the middle of the series), all of the 75 species have the same density r = 300/75, where the overall mean abundance is set at 300 throughout. At one time-step away from maximum evenness, one species is allocated a density r∗ = r/3. The density of the remaining species is then adjusted so that the sum of the 75 densities remains at 300. This process is
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Fig. 2. Plot (a) shows the change in abundance in the population over time (with constant richness and evenness). Plots (b)–(f) show the mean and mid 95% range sample indices for: (b) richness; (c) Shannon; (d) relative Shannon; (e) Simpson; (f) abundance.
Fig. 3. Plot (a) shows the change in richness in the population over time (with constant abundance and evenness). Plots (b)–(f) show the mean and mid 95% range sample indices for: (b) richness; (c) Shannon; (d) relative Shannon; (e) Simpson; (f) abundance.
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Fig. 4. Plot (a) shows the change in evenness in the population over time (with constant abundance and richness). Plots (b)–(f) show the mean and mid 95% range sample indices for: (b) richness; (c) Shannon; (d) relative Shannon; (e) Simpson; (f) abundance.
repeated at two steps away where two species are allocated the reduced density, and so on. Thus, as one moves further away from the middle of the series, the evenness is reduced (Fig. 4(a)). The Simpson, Shannon and relative Shannon indices will reflect the evenness change in the population (the relative Shannon index is identical to the Shannon index in the population as abundance is constant) as they are all functions of evenness. 3.1.3.2. Sample. The sample Shannon (c), Simpson (e) and richness (b) indices pick up the change in population evenness well. However the relative Shannon index (d) reflects the change quite poorly (the same effect was noted in many repeat runs of these simulations with different abundances and values of N). 3.2. Thames and Tyne time series Fig. 5 shows the indices plotted for each of the three Tyne stations RN, DG and RS (columns 1–3). Fig. 6 shows the same plots but for the Thames stations BD and MD. The smoothed trend is shown on all plots for which it was statistically significant (p < 0.05) against the null hypothesis of ‘no trend’. The trend was fitted using a Generalised Additive Model (GAM) with the R package mgcv. We used thin plate regression splines to smooth the data and the degree of smoothing was determined by generalised cross validation, but with a maximum of four degrees of freedom (Wood, 2006). The Tyne RN station seems to have fairly constant biodiversity until around 2002 but then experiences a sharp decline at the very end of the series. For example, richness remained quite constant until a big fall in 2005 – from 124 species in 2004 to 31 and 34 species in 2005 and 2006 respectively. Abundance also fell
dramatically. Reasons for this reduction will be reported in further studies. At the DG site, there is a slight increase in biodiversity as measured by the Simpson and Shannon indices, with richness remaining fairly constant apart from a large drop in 2005. The overall abundance, however, declined over the time period. This suggests that population richness is increasing because sample richness remains constant despite abundance decreasing (i.e. even though it is harder to detect species, sample richness does not decline). One possible reason for the non-decline of sample richness towards the end of the series is that evenness increases from around 2000. Over the whole series, Tyne RS shows increasing diversity as measured by the Shannon and Simpson and indices, with richness increasing from the late 1990s. Sample abundance remains quite constant. However, the increase in diversity could be explained by increasing evenness as this also goes up throughout the series. At the Thames BD site (Fig. 6), abundance dropped throughout the 1980s and then stayed fairly constant until about 2003, when there is a suggestion that it increased again. The Shannon, Simpson and richness indices show a peak of biodiversity around 1995, followed by a decline, with an increase in sample richness from about 2000 (which probably also reflects a similar change in population richness as this increase is not explained by abundance or evenness). Note that the 1999 richness value of 31 is unusual with respect to the other observations and was not used when fitting the GAM trend. For Thames MD, there is a fall in the sample Simpson, Shannon and richness indices in the late 1990s, probably caused by a fall in population richness. There is a steady decline in abundance and then a possible slight increase towards the end of the series.
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Fig. 5. Plots of Simpson, Shannon, richness, abundance and evenness indices (rows, from top to bottom) for RN, DG and RS sites (columns, left to right) in the Tyne.
4. Discussion This study has demonstrated that some sample biodiversity indices can be misleading in terms of representing changes in the population from which they are sampled. However, we have also shown that common indices such as richness, Shannon and Simpson can be good indicators of changes of biodiversity for benthic data, where many species are undetected in samples. Our simulations are necessarily simplistic in that they examine changes in only one of the three diversity elements at a time. In practice, as demonstrated by the real time series from the Tyne and the Thames, biodiversity will change in a complicated way. However, by also calculating the abundance and evenness measures, we submit that it is possible to gain a better understanding of what is happening to population biodiversity. However, clearly, knowledge of outside influences is also very important in telling the whole story. It is recognised that univariate summaries of a benthic community may not be the only way to assess changes over time. In particular, multivariate summaries may help to elicit further information about how the community is developing. For example, the work developed by Van Den Brink et al. (2009) used principal response curves in support of bio-monitoring of time series. These analyses helped to evaluate environmental status and trends. Our brief analysis of the Thames and Tyne data sets was carried out mainly to illustrate our methods for the univariate indices – and
we recognise that more extensive analyses should be done in order to bring out a fuller picture. As opposed to using sample indices, another approach is to estimate the population values directly. Chao (2005), and Gotelli and Colwell (2010) give reviews for estimating population richness; Chao and Shen (2003) describe a method to estimate the population value of the Shannon index. However, these methods do not take into account factors such as spatial clustering that are highly prevalent for benthic species. Generally, we do not consider these methods to be robust enough for our purposes – we prefer using the raw sample indices when the aim is to detect changes in diversity rather than estimates of actual diversity. Additionally, the scale at which biodiversity is measured should also receive consideration. Clearly, we can only make inferences about larger units from smaller units in terms of the diversity that is measured at the smaller units. Gray (2000) and Gray and Elliot (2009) discuss further issues of spatial scale. Similarly, when data is obtained from several grabs or other sampling units, we need to decide whether to analyse measures by individual grab or from the combined sample. Here, we have chosen the latter approach because estimates of richness (and indices that are a function of richness) are better for the larger sampling units. Conversely, one advantage of breaking down index measurements into smaller units, however, is that it allows a measure of variation of the index. This could give further clues about apparent patterns of biodiversity.
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Fig. 6. Plots of Simpson, Shannon, richness, abundance and evenness indices (rows, from top to bottom) for BD and MD sites (columns, left to right) in the Thames.
A tool that can help in the choice of sample scale is rarefaction (Gotelli and Colwell, 2010). Rarefaction curves plot the number of species found against number of grabs sampled, averaged over all possible combinations of grab ordering. This averaging gives a smooth estimate of the number of species for increasing levels of sampling effort. Whilst the emphasis of this paper is on benthic surveys, many of the ideas and conclusions will translate to any surveys in which many fewer species are detected in the sample than in the population.
used in situations where most species will be detected in the surveys – an unusual situation in benthic survey sampling. We also believe that measuring sample abundance is important – because it can help to explain apparent changes in richness as well as giving an unbiased estimate of population abundance. Similarly, we think that it is useful to have a sample measure of pure evenness (i.e. one that is not also affected by abundance or sample richness) such as the Smith and Wilson (1996) index that was calculated above. Not only does this index show how evenness is changing, it also gives information on what might be driving changes in sample richness.
5. Conclusions Acknowledgement The overall conclusions from our simulations are that the Simpson, Shannon and richness indices are useful indicators of changes in biodiversity in the population. The relative Shannon index is best
We thank two referees for suggestions which improved the structure and wording of the paper.
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Gray, J.S., Elliot, M., 2009. Ecology of Marine Sediments: From Science to Management. Oxford University Press, Oxford. Hepp, L.U., Santos, S., 2009. Benthic communities of streams related to different land uses in a hydrographic basin in southern Brazil. Environ. Monit. Assess. 157, 305–318. Hutcheson, K., 1970. A test for comparing diversities based on the Shannon formula. J. Theor. Biol. 29, 151–154. Kenny, A.J., Rees, H.L., 1994. The effects of marine gravel extraction on the macrobenthos: early post-dredging recolonisation. Mar. Pollut. Bull. 28, 442–447. Magurran, A.E., 2004. Measuring Biological Diversity. Blackwell Publishing, Oxford. MAFF, 1993. Analysis and interpretation of benthic community data at UK sewage sludge disposal sites. Aquatic Environment Monitoring Report, MAFF Directorate of Fisheries Research, Lowestoft, No. 37. Pielou, E.C., 1975. Ecological Diversity. Wiley, London. R Development Core Team, 2010. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria, ISBN 3900051-07-0 http://www.R-project.org Rees, H.L., Pendle, M.A., Limpenny, D.S., Mason, C.E., Boyd, S.E., Birchenough, S., Vivian, C.M.G., 2006. Benthic responses to organic enrichment and climatic events in the western North Sea. J. Mar. Biol. Assoc. UK 86, 1–18. Shannon, C.E., Weaver, W., 1949. The Mathematical Theory of Communication. University of Illinois Press, Urbana. Sirami, C., Seymour, C., Midgley, G., Barnard, P., 2009. The impact of shrub encroachment on savannah bird diversity from local to regional scale. Divers. Distrib. 15, 948–957. Smith, B., Wilson, J.B., 1996. A consumer’s guide to evenness measures. Oikos 76, 70–82. Van Den Brink, P.J., Den Besten, P.J., De Vaate, A.B., Ter Braak, C.J.F., 2009. Principal response curves technique for the analysis of multivariate biomonitoring time series. Environ. Monit. Assess. 152, 271–281. Van Hoey, G., Borja, A., Birchenough, S.N.R., Degraer, S., Fleischer, D., Magni, P., Muxika, I., Reiss, H., Rumohr, H., Schröder, A., Zettler, M., 2010. The use of benthic indicators in Europe: from the Water Framework Directive to the Marine Strategy Framework Directive. Mar. Pollut. Bull. 60, 2187–2196. Ware, S.J., Rees, H.L., Boyd, S.E., Birchenough, S.N., 2009. Performance of selected indicators in evaluating the consequences of dredged material relocation and marine aggregate extraction. Ecol. Indic. 9, 704–718. Ware, S.J., Bolam, S.G., Rees, H.L., 2010. Impact and recovery associated with the deposition of capital dredging at UK disposal sites: lessons for future licensing and monitoring. Mar. Pollut. Bull. 60, 79–90. Warwick, R.M., Clarke, K.R., 2001. Practical measures of marine biodiversity based on relateness of species. Oceanogr. Mar. Biol. Annu. Rev. 39, 207–231. Wood, S.N., 2006. Generalized Additive Models: An Introduction with R. Chapman and Hall/CRC, London.
Contents lists available at SciVerse ScienceDirect
Ecological Indicators journal homepage: www.elsevier.com/locate/ecolind
On the use of sample indices to reflect changes in benthic fauna biodiversity Jon Barry a,∗ , Silvana Birchenough a , Beth Norris b , Suzanne Ware a a b
Centre for Environment, Fisheries and Aquaculture Science, Lowestoft Laboratory, Pakefield Road, Lowestoft, Suffolk NR33 OHT, United Kingdom School of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury CT2 7NF, United Kingdom
a r t i c l e
i n f o
Article history: Received 10 August 2012 Received in revised form 5 November 2012 Accepted 6 November 2012 Keywords: Sample indices Relative indices Biodiversity indices
a b s t r a c t This paper focuses on the difference between the value of some commonly used diversity indices (Simpson, Shannon, abundance, richness) calculated from benthic grab samples and their value in the population or region from which the samples are taken. The ability of the sample indices, as well as a recently derived relative Shannon index, to reflect change in biodiversity is examined in a short simulation study based on changing one of the diversity parameters (abundance, richness and evenness) in the population, whilst keeping the other two components constant. Our results suggest that, whilst their population equivalents do not always reflect biodiversity changes, the sample Simpson, Shannon and Richness indices perform well. We note that this will be true for any surveys where the sampling programme fails to detect many species in a population, and hence will be applicable for most benthic surveys. The use of sample indices to detect changes in biodiversity from long-running time series in the Thames and Tyne estuaries is illustrated. Crown Copyright © 2012 Published by Elsevier Ltd. All rights reserved.
1. Introduction A number of current marine policy objectives require the implementation of effective measures to monitor trends in biodiversity. These include the European Marine Strategy Framework Directive (MSFD), the Water Framework Directive and Common Standards Monitoring in support of assessing feature condition within nationally designated sites (e.g., Sites of Special Scientific Interest, Marine Conservation Zones, and Scottish Marine Protected Areas) and internationally designated sites (e.g., Special Areas of Conservation, Special Protection Areas and Ramsar sites). For benthic systems, this monitoring involves the development of indicators measuring sediment state, the role organisms play in maintaining ecosystem function and how this has been affected by human impacts. Descriptor 1 of the MSFD focuses primarily on maintaining biodiversity. This definition of maintaining biodiversity is based on the quality and occurrence of habitats and states that the distribution and abundance of species should be in line with prevailing physiographic, geographic and climatic conditions. Some of the proposed criteria for measuring biodiversity are: species distribution, population size, population condition, habitat distribution, extent and condition for the benthic community among other fauna groups (Van Hoey et al., 2010). Our focus in this study is on the application of biodiversity measurement of the benthic environment. This biodiversity is
∗ Corresponding author. Tel.: +44 1524 844113. E-mail address: [email protected] (J. Barry).
widely measured in monitoring surveys to examine the effects of impacts on seafloor communities. Examples include marine aggregate dredging (Barrio Froján et al., 2011; Birchenough et al., 2010), deposition of dredged material (Ware et al., 2010; Birchenough et al., 2006) and fishing pressure (Callaway et al., 2002). Many studies have been carried out that compare the performance of biodiversity indices (e.g., Ware et al., 2009) but little attention has been paid to how calculation of biodiversity indices from sample data reflects the values of those same measures in the population from which the samples are taken. In this paper we demonstrate that sample estimates can be misleading and should be interpreted carefully when conducting monitoring. Note that, throughout, we use ‘population’ in its statistical rather than its ecological sense. That is, by the population value of some indicator we mean the value that would be obtained if the whole of a region was sampled. Defining biodiversity can be a complicated issue. Indeed, even the name does not remain constant: ‘ecological diversity’ has now largely been replaced by ‘biological diversity’ or ‘biodiversity’ (which we use). Magurran (2004) defines biological diversity as “the variety and abundance of species in a defined unit of study”. Warwick and Clarke (2001) provide some measures that extend the concept into taxonomic distinctness – where, for example, species in the same genus are more similar than those with different genera but in the same family. Use of functional diversity is also increasingly used (Barrio Froján et al., 2011; Dimitriadis and Evagelopoulos Koutsoubas, 2012), where distinctness of species is defined by their traits rather than their biological species classification.
1470-160X/$ – see front matter. Crown Copyright © 2012 Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ecolind.2012.11.004
J. Barry et al. / Ecological Indicators 26 (2013) 154–162
In this paper, we generally follow Buckland et al.’s (2005) interpretation that biodiversity in a region or community is a function of the three components: overall abundance, number of species (richness) and evenness. Thus, a region is more biodiverse if it has more individuals, more species and if the proportions of each species as a function of total abundance are more similar (maximum evenness occurs when all species are equally abundant). Central to our work is the distinction between the biodiversity in the population being considered and in the sample. To illustrate this, for the assessment of Good Environmental Status (which needs to be obtained for all European water bodies by 2020: Van Hoey et al., 2010; Birchenough et al., 2012) under the MSFD, interest is at the subregional scale. For the UK, these sub-regions are The Greater North Sea (including the Kattegat) and the English Channel and the Celtic Seas. As in most areas of scientific investigation, our main aim is to find out properties of the population through properties of the sample. For example, we may want to use the information from the sample to tell us whether biodiversity in the population is being affected by either a natural or anthropogenically mediated pressure. As we shall see below, this is not always straightforward – indeed, biodiversity properties in the samples can be very different to biodiversity properties in the population. The problem of making inferences about populations from samples is made particularly difficult in benthic surveys by the fact that the sampling fraction (the proportion of the survey area that is measured) is generally very small. For example, a typical survey off the Norfolk coast by Kenny and Rees (1994) used five 0.25 m2 grabs over 135,000 m2 – giving a sampling fraction of 9.25926 × 10−6 . Small sampling fractions such as these mean that many species present in the population will not be present in the samples. The probability of a species being found in the sample is a function of its abundance in the population, the sampling effort (e.g., number and size of grabs), and its spatial pattern – clustered species are harder to find than more regularly distributed species (Boyd et al., 2006). These factors need to be considered when designing and interpreting benthic surveys. From the results of a benthic survey, we generally have a macrofaunal species abundance matrix with elements aij reflecting the abundance of species i at point j. These points could be in either space or time (or both) – but, for ease of explanation, we will assume here that they are in time only. Data will usually arise from a grab survey (typically employing a 0.1 m2 Day grab in soft sediments or a 0.1 m2 Hamon grab in coarse sediments). The main difference between, for example, bird surveys and benthic surveys is that the bird surveys rarely contain species with zero values and that there is a fairly small list of species that might be present at any one time in the survey area. With benthic surveys around the British Isles, there might potentially be up to 10,000 species in the survey area (UNICORNc (copyright 1995–2004 Unicomarine) database of known benthic species lists), whereas, typically, it is unusual to see more than 1000 species in all of the sample grabs. Our aims in this paper are to:
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2. Materials and methods 2.1. Biodiversity indices Here we consider four of the simplest and most commonly used diversity indices (many more are given in Magurran, 2004): sample richness and abundance, plus the Simpson and Shannon indices. We also use a modification to the Shannon index that was originally proposed by Buckland et al. (2005). This modification results in an index where species’ proportions at points in time are relative to the overall abundance at some reference time point (we call this the ‘relative Shannon index’). We examine the aspects of biodiversity that these five indices measure and their sample properties in terms of bias and in capturing changes in biodiversity in the population in which they are measured. The Simpson index was selected because it is known to be statistically unbiased (Section 2.3). In contrast, it is known that the Shannon index is badly biased for benthic data and we particularly wanted to contrast its performance to that of what we thought would be the improved relative Shannon index (ultimately, however, the Shannon index performed well, Section 3). Clearly, further studies could examine other indices in a similar way to the approach taken here. The standard Shannon index (Shannon and Weaver, 1949) at time j is given by S
Hj = −
pij ln(pij )
i=1
(1)
S
where pij = nij / i=1 nij = nij nj , and nij is the abundance of species i at time j. That is, pij is the proportion of species i at time j compared to the sum of the abundances of all species at time j. We should be clear about whether we are calculating this index in the sample or the population. If the former, many of the pij for unobserved species will, effectively, be estimated as zero – an under-estimate compared to their population values. The Shannon index has been applied to a variety of ecological studies including terrestrial communities, namely birds and insects (Sirami et al., 2009) as well as applications in the freshwater and marine realm (Hepp and Santos, 2009). Magurran (2004) and Pielou (1975) provide some useful background on the Shannon index. Pielou notes that two desirable properties of the index are that its maximum, S, occurs when all S species in the region have equal densities and that the index increases with number of species. Thus, the Shannon index is a function of both evenness and species richness. The relative index defined by Buckland et al. (2005) is similar to the Shannon index except that the pij term is written as qij = nij /n1 . Thus, the proportion of species i at time j is relative to the total abundance at time 1. Note that the choice of time 1 is essentially arbitrary – any sensible reference time could be used. We thus define the relative Shannon index as S
Mj = −
qij ln(qij )
(2)
i=1
1. Find indices whose sample values reflect changes in biodiversity in the wider population; 2. Use simulations to illustrate the sample bias of some indices as a function of the density of species in the population; 3. Examine how sample indices are able to reflect changes in a region’s core components of biodiversity through a simulation study; 4. Explain changes in biodiversity for long-term benthic series collected in the Thames and Tyne areas, based on the results from the simulation studies.
The Simpson index can be written as j = 1 −
S
pij 2
(3)
i=1
Simpson’s index is a function of species richness because, with more species and constant evenness, the pij will generally be smaller and hence the sum of their squared terms will also be smaller. The Simpson index also measures evenness in that its maximum value occurs when, for a given number of species, the proportions for each
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Fig. 1. Sample mean, mid 95% percentiles (solid lines), and population values (dotted lines). The x-axis reflects the density (i.e. number of individuals per m2 ) of each of the 100 species present in the simulations. The plots are: (a) richness; (b) Shannon; (c) relative Shannon; (d) Simpson; (e) abundance; (f) richness.
species are the same. Uses of Simpson’s index in the marine sciences include Ferraro and Cole (1990) and Gray (2000), undertaken in the USA and Norway respectively. We also use the sample species richness (s) as an index; this is simply the number of species found in all of the grabs. The sample abundance (n) is defined as the total number of creatures found in the grabs. To obtain an index that estimates the population abundance (N), n is multiplied by the ratio of the survey ˆ = nA/ga, where g is area to the combined area of the grabs. Thus, N the number of grabs, a is the area of each grab, and A is the area of the survey area. 2.2. Sample properties of the indices Here we are concerned with how the sample properties of the indices described above reflect the population values of those indices and, in particular, change in those population values. We start with the concept of whether the sample indices are unbiased. Statistically, the bias of a sample index is defined as its expected value minus its value in the population (the expected value is the mean value if the sampling were repeated many times). The sample index is biased if its bias is non-zero. It is clear that the sample species richness in most benthic surveys is biased because it is unlikely that all of the species in the survey area will be found. Similarly, the majority of diversity indicators that are functions of the number of species (e.g., Shannon, Margalef) will be biased for benthic surveys because many species in the population do not appear in the sample (though note that the Shannon index has a small bias even if all species are present in the sample (Hutcheson, 1970)). A notable exception is the Simpson index, which generally has negligible bias. This is because the squared proportions in the Simpson index are negligibly small for rare species. The sample species
abundance can be easily made unbiased by scaling up the sample value by the ratio of the population area to the area sampled. The bias concepts are illustrated for a simple simulation study where N species, each with a density of r individuals per m2 , are randomly placed into a population region, represented by 1 m × 1 m square. From this population, four 0.1 m2 grabs were sampled and an abundance matrix calculated from the combined grabs. Because the individuals have a random pattern, the number of individuals of a species found in the four grabs is distributed Poisson with mean 0.4r; using this fact considerably speeds up the simulations. The whole process was repeated 500 times. This allowed estimation of the sample mean together with the mid 95% range from the 2.5th and 97.5th percentiles. All computations for these simulations and those elsewhere in the paper were carried out using the statistical software R (R Development Core Team, 2010). Fig. 1 shows the sample and population values of the five diversity indices described above as a function of density. The bias of the richness (a) and Shannon (b) indices decreases with density because, as the density increases from 1 to 20, it is less likely that species will be missing from the sample. The relative Shannon index (c) has low negative bias – mainly because it is a function of abundance and not just richness. The Simpson index (d) is largely unbiased although its variability is greatest at low densities. As expected, the abundance index (e) is unbiased, although the sampling variability increases as the overall population abundance increases. Plot (f) shows the situation in which the number of species in the population decreases from 100 to 81. Up to a density of about 8, the sample richness increases even though the population value is decreasing. Thus, if sample data were used to assess changing richness over a series of yearly surveys then, for the lower densities, we would infer that the number of species was increasing when it
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is actually deceasing (the same pattern is exhibited by the Shannon index, though not shown). Overall, using sample estimates to infer population values is not always reliable. For many indices, the difference between the sample and the population values depends on species density. Although not illustrated here, the difference also depends on the sampling effort (number of grabs) used in the survey (on average, the more grabs taken, the nearer the sample estimate will be to the population value) and the spatial pattern of the individuals (the more clustered the individuals, the further the sample estimate will be from the population value). So, rather than base inferences strictly on the population values, which often cannot be inferred from sample values, a different approach is to examine whether changes in sample indices reflect changes in population diversity. 2.3. Simulation study to assess how sample indices reflect biodiversity change For the purpose of the current study, we focus on the three components of diversity mentioned in the introduction: abundance, richness and evenness. Following the approach in Buckland et al. (2005), if any one of these indices increases/decreases, whilst the other two remain constant, then a good sample index should also increase/decrease. A simulation study was performed to examine how the five sample indices used above perform against these criteria. The simulation study was similar to the one used to illustrate sample bias in Fig. 1. As before, the simulations all involved N species, individuals from which were randomly located on the unit square. Four 0.1 m2 grabs were randomly placed onto the square and the sample indices calculated. Three types of simulation were performed; in each type changing one of the three diversity characteristics over time and keeping the other two characteristics constant. The evenness measure used to measure change in population evenness in Fig. 4(a) was proposed by Smith and Wilson (1996). This is essentially the variance of the log of the species’ abundances, transformed so that the index lies between 0 and 1. Specifically, at time j, the index is
⎧ ⎡ ⎤2 ⎫ ⎪ ⎪ S S ⎨ ⎬ 2 1 ⎣ ⎦ Ej = 1 − arctan ln(nij ) − ln(nij ) /S S ⎪ ⎪ ⎩ i=1 ⎭ j=1
(4)
2.4. Thames and Tyne time series We used the values of the sample indices – Simpson, Shannon, richness, abundance and evenness (Eq. (4)) – to try to explain real time series of benthic abundance from yearly surveys in the Tyne (1984–2006) and the Thames (1986–2006) estuaries. We introduced the evenness measure because it can help explain changes in richness. We did not use the relative Shannon index as it was out-performed by the Shannon and Simpson indices in the simulation study for detecting changes in richness and evenness. The three Tyne stations are part of a long-term monitoring programme started in the 1980s to ascertain the changes resulting from sewage sludge disposal in this area. The stations RN and RS were used as reference stations, DG was the disposal station. Further analysis in relation to natural variability and recovery of these stations was conducted by Rees et al. (2006) and Birchenough and Frid (2009) respectively. Similarly the Thames area has also been monitored since the 1980s to assess the effects of sewage sludge disposal (MAFF, 1993). The station BD was located in the centre of the disposal ground and MD was used as a reference station. Although four or five 0.1 m2 Hamon grabs were used in some years,
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for comparability between years, we have combined the counts from three grabs in each year. 3. Results 3.1. Simulation study to assess biodiversity change The pattern of the changing diversity characteristic in the population is shown in the top left hand plot of each of Figs. 2–4. This is the pattern that we want the sample indices to reflect. When describing the simulations, we first describe how the indices are affected in the population and then how their sample values change – these sample changes are shown graphically in plots (b)–(f) in each of Figs. 2–4. 3.1.1. Changing population abundance, keeping richness and evenness constant 3.1.1.1. Population. The number of species is fixed at N = 75. By changing the species density, the overall mean abundance moves from 150 to 300 and then back to 150 at the end of the series (Fig. 2(a)). In the population, the proportion of each species at any one time does not change. Thus, the standard Shannon and Simpson indices will also not change over time. However, the relative Shannon index will change because its base abundance is fixed at time 1. Thus, in the population, the relative Shannon index is a good indicator of changing abundance biodiversity. 3.1.1.2. Sample. The way that the sample indices change tells a different story to their population equivalents (Fig. 2). Because the change in population abundance means that the numbers of species found in the samples will reflect this change (i.e. more species will be found as their density increases), the sample richness (b), Shannon (c) and Simpson (e) indices all reflect the population change in abundance fairly well. The relative Shannon index (d) also performs well and provides a sharper reflection of the change in abundance. Note also from Fig. 2 that the change in the index on the y-axis is much larger for the relative Shannon index than for the standard one. However, it is also evident that the standard Shannon index shows the correct pattern of change – which, in practice, is what would be required of it. 3.1.2. Changing population richness, keeping abundance and evenness constant 3.1.2.1. Population. The population richness was increased from 50 to 100 and then back to 50 again by the end of the series (Fig. 3(a)). Overall mean abundance was set at 300. The proportion of each species was identical at each time point so that evenness was at its maximum value at all time points. In the population, the Simpson, Shannon and relative Shannon indices will all reflect this change. 3.1.2.2. Sample. The sample Shannon (c), Simpson (e) and richness (b) indices all show the change in population richness well. The relative Shannon index (d) does reflect the changes in richness, but not as tightly as the standard indices. Other simulations (not shown) show that the relative index performs better as overall abundance is increased (and hence more species are likely to be detected). 3.1.3. Changing population evenness, keeping abundance and richness constant 3.1.3.1. Population. The process by which the evenness is changed is as follows. At maximum evenness (in the middle of the series), all of the 75 species have the same density r = 300/75, where the overall mean abundance is set at 300 throughout. At one time-step away from maximum evenness, one species is allocated a density r∗ = r/3. The density of the remaining species is then adjusted so that the sum of the 75 densities remains at 300. This process is
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Fig. 2. Plot (a) shows the change in abundance in the population over time (with constant richness and evenness). Plots (b)–(f) show the mean and mid 95% range sample indices for: (b) richness; (c) Shannon; (d) relative Shannon; (e) Simpson; (f) abundance.
Fig. 3. Plot (a) shows the change in richness in the population over time (with constant abundance and evenness). Plots (b)–(f) show the mean and mid 95% range sample indices for: (b) richness; (c) Shannon; (d) relative Shannon; (e) Simpson; (f) abundance.
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Fig. 4. Plot (a) shows the change in evenness in the population over time (with constant abundance and richness). Plots (b)–(f) show the mean and mid 95% range sample indices for: (b) richness; (c) Shannon; (d) relative Shannon; (e) Simpson; (f) abundance.
repeated at two steps away where two species are allocated the reduced density, and so on. Thus, as one moves further away from the middle of the series, the evenness is reduced (Fig. 4(a)). The Simpson, Shannon and relative Shannon indices will reflect the evenness change in the population (the relative Shannon index is identical to the Shannon index in the population as abundance is constant) as they are all functions of evenness. 3.1.3.2. Sample. The sample Shannon (c), Simpson (e) and richness (b) indices pick up the change in population evenness well. However the relative Shannon index (d) reflects the change quite poorly (the same effect was noted in many repeat runs of these simulations with different abundances and values of N). 3.2. Thames and Tyne time series Fig. 5 shows the indices plotted for each of the three Tyne stations RN, DG and RS (columns 1–3). Fig. 6 shows the same plots but for the Thames stations BD and MD. The smoothed trend is shown on all plots for which it was statistically significant (p < 0.05) against the null hypothesis of ‘no trend’. The trend was fitted using a Generalised Additive Model (GAM) with the R package mgcv. We used thin plate regression splines to smooth the data and the degree of smoothing was determined by generalised cross validation, but with a maximum of four degrees of freedom (Wood, 2006). The Tyne RN station seems to have fairly constant biodiversity until around 2002 but then experiences a sharp decline at the very end of the series. For example, richness remained quite constant until a big fall in 2005 – from 124 species in 2004 to 31 and 34 species in 2005 and 2006 respectively. Abundance also fell
dramatically. Reasons for this reduction will be reported in further studies. At the DG site, there is a slight increase in biodiversity as measured by the Simpson and Shannon indices, with richness remaining fairly constant apart from a large drop in 2005. The overall abundance, however, declined over the time period. This suggests that population richness is increasing because sample richness remains constant despite abundance decreasing (i.e. even though it is harder to detect species, sample richness does not decline). One possible reason for the non-decline of sample richness towards the end of the series is that evenness increases from around 2000. Over the whole series, Tyne RS shows increasing diversity as measured by the Shannon and Simpson and indices, with richness increasing from the late 1990s. Sample abundance remains quite constant. However, the increase in diversity could be explained by increasing evenness as this also goes up throughout the series. At the Thames BD site (Fig. 6), abundance dropped throughout the 1980s and then stayed fairly constant until about 2003, when there is a suggestion that it increased again. The Shannon, Simpson and richness indices show a peak of biodiversity around 1995, followed by a decline, with an increase in sample richness from about 2000 (which probably also reflects a similar change in population richness as this increase is not explained by abundance or evenness). Note that the 1999 richness value of 31 is unusual with respect to the other observations and was not used when fitting the GAM trend. For Thames MD, there is a fall in the sample Simpson, Shannon and richness indices in the late 1990s, probably caused by a fall in population richness. There is a steady decline in abundance and then a possible slight increase towards the end of the series.
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Fig. 5. Plots of Simpson, Shannon, richness, abundance and evenness indices (rows, from top to bottom) for RN, DG and RS sites (columns, left to right) in the Tyne.
4. Discussion This study has demonstrated that some sample biodiversity indices can be misleading in terms of representing changes in the population from which they are sampled. However, we have also shown that common indices such as richness, Shannon and Simpson can be good indicators of changes of biodiversity for benthic data, where many species are undetected in samples. Our simulations are necessarily simplistic in that they examine changes in only one of the three diversity elements at a time. In practice, as demonstrated by the real time series from the Tyne and the Thames, biodiversity will change in a complicated way. However, by also calculating the abundance and evenness measures, we submit that it is possible to gain a better understanding of what is happening to population biodiversity. However, clearly, knowledge of outside influences is also very important in telling the whole story. It is recognised that univariate summaries of a benthic community may not be the only way to assess changes over time. In particular, multivariate summaries may help to elicit further information about how the community is developing. For example, the work developed by Van Den Brink et al. (2009) used principal response curves in support of bio-monitoring of time series. These analyses helped to evaluate environmental status and trends. Our brief analysis of the Thames and Tyne data sets was carried out mainly to illustrate our methods for the univariate indices – and
we recognise that more extensive analyses should be done in order to bring out a fuller picture. As opposed to using sample indices, another approach is to estimate the population values directly. Chao (2005), and Gotelli and Colwell (2010) give reviews for estimating population richness; Chao and Shen (2003) describe a method to estimate the population value of the Shannon index. However, these methods do not take into account factors such as spatial clustering that are highly prevalent for benthic species. Generally, we do not consider these methods to be robust enough for our purposes – we prefer using the raw sample indices when the aim is to detect changes in diversity rather than estimates of actual diversity. Additionally, the scale at which biodiversity is measured should also receive consideration. Clearly, we can only make inferences about larger units from smaller units in terms of the diversity that is measured at the smaller units. Gray (2000) and Gray and Elliot (2009) discuss further issues of spatial scale. Similarly, when data is obtained from several grabs or other sampling units, we need to decide whether to analyse measures by individual grab or from the combined sample. Here, we have chosen the latter approach because estimates of richness (and indices that are a function of richness) are better for the larger sampling units. Conversely, one advantage of breaking down index measurements into smaller units, however, is that it allows a measure of variation of the index. This could give further clues about apparent patterns of biodiversity.
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Fig. 6. Plots of Simpson, Shannon, richness, abundance and evenness indices (rows, from top to bottom) for BD and MD sites (columns, left to right) in the Thames.
A tool that can help in the choice of sample scale is rarefaction (Gotelli and Colwell, 2010). Rarefaction curves plot the number of species found against number of grabs sampled, averaged over all possible combinations of grab ordering. This averaging gives a smooth estimate of the number of species for increasing levels of sampling effort. Whilst the emphasis of this paper is on benthic surveys, many of the ideas and conclusions will translate to any surveys in which many fewer species are detected in the sample than in the population.
used in situations where most species will be detected in the surveys – an unusual situation in benthic survey sampling. We also believe that measuring sample abundance is important – because it can help to explain apparent changes in richness as well as giving an unbiased estimate of population abundance. Similarly, we think that it is useful to have a sample measure of pure evenness (i.e. one that is not also affected by abundance or sample richness) such as the Smith and Wilson (1996) index that was calculated above. Not only does this index show how evenness is changing, it also gives information on what might be driving changes in sample richness.
5. Conclusions Acknowledgement The overall conclusions from our simulations are that the Simpson, Shannon and richness indices are useful indicators of changes in biodiversity in the population. The relative Shannon index is best
We thank two referees for suggestions which improved the structure and wording of the paper.
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