Using Species Proportions to Quantify Turnover in Biodiversity

Perhaps appropriately, there is a great diversity of measures for quantifying biodiversity (Pielou 1975; Krebs 1989; Magurran 2004). Choice of measure depends both on the type of data available and on the questions being asked. Maurer and McGill (2010) reviewed a large number of indices to measure species diversity, and gave a list of indices to measure different aspects of diversity, such as richness, evenness, dominance and rarity. This paper concentrates on temporal turnover, which we define as the change in species proportions over time, taking into account species identity. Thus, if a community is to exhibit zero turnover, then each species should represent a constant proportion of the community. We propose families of turnover measures in this paper, and link some of them to the metrics summarized by Martín-Fernández et al. (1998). We further study their properties in the context of measuring turnover, and provide transformation and modification for general applications. Although we focus on temporal turnover, these measures can also be used for quantifying spatial turnover between two neighbouring locations.

Spatial turnover is closely related to the concept of beta diversity. If we consider total diversity of a region (termed gamma diversity), we can partition it into alpha diversity, which measures average diversity at locations within the region, and beta diversity, which reflects spatial heterogeneity in diversity (Lande 1996). Thus, a region with high beta diversity has a diverse range of communities, perhaps reflecting a wide variety of habitats, while a region with low beta diversity has a relatively homogeneous community of species across the region. We refer to spatial turnover as the dissimilarity between pairs of locations that are neighbours, whereas beta diversity does not require this, and can be used to compare multiple assemblages. Beta diversity covers a broader range of objectives than the spatial turnover we discuss here. Jøst et al. (2010) reviewed a number of indices used for measuring similarities between assemblages in the context of beta diversity. Here, we concentrate on the dissimilarity of species composition. Measuring turnover, whether spatial or temporal, is about assessing the changes between two species compositions, and such change is measured by dissimilarity, which is also referred to as differentiation, divergence or distance in different scientific fields, such as probability theory, mathematical geology and cluster analysis. Given species proportions, we propose four different families of turnover measure, all of which can be used to quantify either spatial or temporal change in diversity.

There is no simple relationship between species turnover and other measures of diversity such as richness and evenness. For example, one assemblage can have complete turnover (no species in common between two time points), but its evenness might stay the same (the species proportions might remain the same, even though they relate to different species for the two time points). The relationship between richness and turnover is more complicated; both negative and positive relationships between spatial turnover and richness have been observed in studies on spatial turnover using species–area relationships (Clarke and Lidgard 2000; Stevens and Willig 2002; Koleff et al. 2003; Lennon et al. 2001; Lyons and Willig 2002). Quantifying changes in species diversity over time or space provide valuable insights into understanding biodiversity trends.

Traditionally, turnover usually refers to spatial turnover, and is usually measured from species presence–absence data (Rodrigues et al. 2000; La Sorte and Boecklen 2005). However, if available, it is more informative to use species abundance distributions to measure the compositional change over time (Magurran 2010). Measures based on the species abundance distribution or on species proportions are more informative and sensitive to biodiversity changes than measures based on presence/absence data. When we use species abundance distributions to measure turnover, turnover is evaluated by quantifying the rate at which individuals of one species are being replaced by individuals of another species.

The U.K. Breeding Bird Survey (BBS, Risely et al. 2013) has been conducted annually since 1994 on a stratified random sample of 1 km squares. Sites are surveyed twice a year by volunteers walking along two parallel 1 km transect lines, and recording any adult birds detected. Harrison et al. (2014) fitted models to these data to allow estimation of abundance in any 1 km square on the British mainland for any species with adequate data. We use those estimates for farmland species to estimate temporal turnover in the British farmland bird community, and study how it varies spatially. The BBS is undertaken by the British Trust for Ornithology (BTO) and jointly funded by the BTO, the Joint Nature Conservation Committee and the Royal Society for the Protection of Birds. The BBS data are available through the British Trust for Ornithology’s standard data request procedure (see http://www.bto.org/research-data-services/data-services/data-and-informationpolicy).

Before introducing families of turnover measures, we briefly review indices that have been used for, or are related to, measuring turnover. Most have been used for measuring beta diversity, i.e. assessing compositional similarity between assemblages. Jøst et al. (2010) gave a list of distance-based similarity measures, some of which can be expressed by the \(L^p\) distance-based measures proposed in Sect. 4.1. Some of the entropy-based similarity measures proposed by Jøst et al. (2010) have forms similar to the one introduced in Sect. 4.4. All of the indices that we propose can be used to measure either spatial or temporal turnover. However, spatial and temporal turnover measures have different interpretations. As pointed out by Magurran (2010), spatial heterogeneity (beta diversity) typically corresponds to different subsets of individuals, whereas in temporal studies, we follow a single community of individuals over time.

There are essentially three different methods to study turnover (Chao et al. 2006; Jøst et al. 2010). First, incidence-based and abundance-based similarity measures are widely used, and they usually share similar forms. Most studies that use them are in the context of beta diversity. When there is only one assemblage and a time series of observations on it, these indices can also be used to measure temporal change in diversity. Incidence-based indices use presence–absence data, while abundance-based indices use counts or abundances. These counts or abundances are often scaled to give species proportions.

Second, spatial turnover can also be evaluated by studying the species–area relationship, which is the relationship between species richness (i.e. the number of species in an assemblage) and the size of the area that the assemblage occupies. Power and logarithmic functions have been used to estimate how the number of species increases as the size of the sampled area increases (Conner and McCoy 1979; Lennon et al. 2001; Rosenzweig 1995). The species–time relationship, a temporal analogue of the species–area relationship, is used to evaluate the dependence of species richness on temporal scale (Grinnell 1922; Preston 1960; Rosenzweig 1995). Power functions (Adler and Lauenroth 2003; Hadly and Maurer 2001) and logarithmic functions (Rosenzweig 1995; White 2004) have been used to estimate the species–time relationship and hence the temporal turnover of species.

Third, the species range shifts, i.e. changes in species’ ranges over time, are estimated to quantify species turnover. As for incidence-based indices, presence–absence data are typically used, and turnover is measured by modelling species ranges, thus allowing the species extinctions and colonizations in the survey area to be estimated (Nenzén and Araújo 2011; Thuiller et al. 2005; Lawler et al. 2009). In the study of Island Biogeography theory, MacArthur and Wilson (1967) defined species turnover as the number of species eliminated and replaced per unit time, and focus on equilibrium state in terms of immigration and extinction in an island population. In applications, we often take the predicted future range of each species based on modelling climate or land use changes, and the consequent impact on the species.

Both incidence-based and species–area relationship methods use presence–absence data. However, ‘absence’ typically equates to ‘not recorded’, which may be a consequence of failure to detect the species when it is present, rather than genuine absence. In addition, rare species are more difficult to detect and may be under-represented relative to more abundant species. For the method based on species range shifts, change in species’ ranges tends to be slow and difficult to detect, as species are typically sparsely distributed at the edge of their range, so that the problem of undetected presence is greater. However, species proportions change almost continuously. Methods based on species proportions are more sensitive to changes in the community than those based on changing ranges. We therefore concentrate on turnover measures that use the species proportion vector, derived from the estimated species abundance distributions over time or space. We introduce notation in Sect. 3.1 and some key transformations in Sect. 3.2. We give a list of criteria and discuss their importance in measuring turnover in Sects. 3.3 and 3.4. We then introduce four families of turnover measure (Sect. 4). We summarize the proposed turnover measures in tables (Web Appendix A) and compare them through a simulation study (Web Appendix B). In Sect. 5, we apply our measures to quantify turnover in the farmland breeding bird community of the British mainland for the period 1994 to 2011. Finally, we summarize our findings from the simulation study (Sect. 6) and discuss the choice of different turnover measures (Sect. 7).

The BBS is conducted annually on a stratified random sample of 1 km squares (see Web Appendix C for data accessibility). Line transect surveys are carried out along two parallel 1 km lines, and detected birds are assigned to one of four categories: 0–25m from the line, 25–100m, \(>\)100m, or flying over. We use a preference index to determine which species form the farmland community (Newson et al. 2008; Renwick et al. 2012; Johnston et al. 2014).

For each species, Harrison et al. (2014) analysed the abundance data using a generalized additive model with time point, easting, northing, elevation and habitat of each 1 km square as covariates. The models incorporate a space-time smoother using eastings, northings and time point, along with a separate smooth term for altitude and each habitat covariate (Harrison et al. 2014). We use abundance estimates of each species in each 1 km square within its assumed range (see Harrison et al. (2014)) for each time point to evaluate the measures proposed in Sects. 4.1, 4.2, 4.3 and 4.4. The results are plotted in Fig. 1. For a more direct comparison of the measures shown in Fig. 1, each of the nine estimated measures is represented by a different colour in each 100 km square in Fig. 2.

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All measures indicate relatively high turnover in the west of Scotland and in the south-east of England. Harrison et al. (2015) analyse BBS data in greater depth, using three measures (\(L^1\)-distance, \(d_\mathrm{cos}\) and \(d_2^{clr\varvec{S}}\)), and include 94 species in their analyses.

We provide details of a simulation study to assess the power of each measure for detecting turnover in Web Appendix B. Our study shows that all measures but the \(L^q\)-distance measures with \(q<1\) perform well in detecting turnover when there are large changes in the community. Over-dispersion has little effect on the conclusions. The mathematical form of the measures means that \(d_2^{clr\varvec{S}}\), \(d_\mathrm{sin}\) and \(d_\mathrm{cos}^*\) should be more sensitive to changes among the scarce species than are \(d_1\), \(d_2\) and \(d_\mathrm{cos}\). Close inspection of the simulation results confirms this, although the differences are small. This greater sensitivity is likely to be offset at least to some degree by lower precision for these measures (as greater weight is given to scarce species with smaller sample sizes), and their inability to accommodate zero species proportions.

If a measure sensitive to changes in the scarce species is required, we recommend \(d_2^{clr\varvec{S}}\), which is the only measure that satisfies all five of the desirable properties of Sects. 3.3 and 3.4. If a measure that has good precision is required, and sensitivity to changes in scarce species is not of primary interest, then we recommend \(d_1\), which satisfies four of the properties, and is simple, being half the sum of absolute differences in species proportions. If greater discrimination is needed between communities showing high turnover from those showing rather lower turnover, then measure \(d_2\) or \(d_\mathrm{cos}\) might be preferred. In practice, given the multivariate nature of biodiversity data, we recommend applying several turnover measures, to gain a better understanding of changes in the scarce and dominant species of the community. When the measures are applied to the BBS data, they identify high turnover in the west of Scotland and in the south-east of England. The measure \(d_2^{clr\varvec{S}}\) differs from the rest by also indicating high turnover in Wales.

Figure 1 shows that precision of our turnover measures is relatively poor in the west of Scotland, reflecting poor survey coverage. Nevertheless, the lower confidence limits for some of our measures in this area exceed the upper confidence limits for most of Britain, supporting our conclusion that turnover is high here. Harrison et al. (2015), in a more extensive analysis of 94 species, also reached this conclusion, and speculated that this reflects an increase in species that benefit from climate change. They attributed the high turnover in the south-east of England at least in part to a decline in scarcer specialist species.