A model-based approach to studying changes in compositional heterogeneity

Summary

1. Non-random species loss and gain in local communities change the compositional heterogeneity between communities over time, which is traditionally quantified with dissimilarity-based approaches. Yet, dissimilarities summarize the multivariate species data into a univariate index and obscure the species-level patterns of change, which are central to understand the causes and consequences of the community changes.
2. Here, we propose a model-based approach that looks for species-level effects of time period and construct a multiple-site metric as a sum across species to test the consistency of the individual species responses. Species fall into different response types, showing how they influence the changes in community heterogeneity.
3. In a comparison with other multiple-site metrics, we illustrate the properties of our method and the differences and similarities with other approaches. For instance, our metric estimates the total variation in a community data set based on species-level contributions, not the compositional dissimilarities between particular sites. Similar to some other approaches, we can distinguish between heterogeneity derived from turnover or richness differences.
4. Our approach was applied to a set of 23 forest understorey resurvey studies spread across Europe. We show the species gains and losses may as well decrease or increase levels of community heterogeneity. Although species occurrences and communities have not changed in a consistent way along continental-scale environmental gradients such as climatic conditions, several species shifted in a similar way across the different data sets.
5. Testing the significance of shifts in species prevalence over time to infer corresponding changes in the compositional heterogeneity among sites provides a very intuitive tool for community resurvey studies. The main strengths of our framework are the explicit consideration of the relative roles of species gains and losses and the straightforward generalization to different sets of hypotheses related to community changes.

Introduction

Global biodiversity is in decline at rates exceeding expectation by far (e.g. Pereira, Navarro & Martins 2012), which necessarily implies that local communities are losing species. It is, however, much less appreciated that the communities that lose species often simultaneously gain others – native and alien species that expand in response to environmental change, though possibly with a time-lag (McKinney & Lockwood 1999). As result, although global biodiversity is decreasing, species richness at local scales may either decrease or increase (Sax & Gaines 2003; Vellend et al. 2013). Predicting the impact of simultaneous species gain and loss on terrestrial ecosystems has currently become a topic of great interest in ecology that requires that we first identify the nature of the species involved (Wardle et al. 2011). Global evidence across taxonomic groups shows that the species gained and lost are often a non-random set from the regional pool (Baiser et al. 2012). Independent from the impact on the local diversity, the directional interchanges of species may reduce (community convergence) or increase (community divergence) the compositional heterogeneity between communities over time (here, we use ‘heterogeneity’ or ‘variation’, referring to the broader concept of beta diversity; Legendre & De Cáceres 2013).

Despite the establishment of an extensive ‘biotic homogenization’ conceptual framework, which focusses on the potentially large ecological and evolutionary consequences of changes in community variation (Olden et al. 2004; Clavel, Julliard & Devictor 2010), there has been surprisingly little effort in developing methods to actually quantify those changes. Studies have principally relied on multivariate distance measures, looking at shifts in the average pairwise community dissimilarities between time periods (Olden & Rooney 2006). However, a major disadvantage of distance measures is that they summarize the multivariate species data into univariate dissimilarities so that individual species responses need to be analysed separately. Understanding the potential causes and consequences of the compositional changes indeed requires knowledge on whether the species that are gained or lost share particular response and effect traits. Some past studies have compared traits between ‘winners’ and ‘losers’ (e.g. Wiegmann & Waller 2006; McCune & Vellend 2013) or changes in community-level ecological indicator values (e.g. Van Calster et al. 2007; Keith et al. 2009), but a true integration of the individual species responses into the quantification of compositional heterogeneity itself would be a valuable way forward. Furthermore, although multivariate species data have typical mean–variance relationships associated with them (as the mean abundance increases the variance also tends to increase), the distance metrics used to analyse those data often assume different mean–variance relationships (Warton, Wright & Wang 2012). This makes it often difficult to isolate the change in the multivariate dispersion between time periods, which is generally used as a measure of community heterogeneity (Anderson, Ellingsen & McArdle 2006; Anderson et al. 2011), from the compositional shifts caused by the changes in species abundances (see Warton, Wright & Wang 2012 for a schematic overview).

Here, we developed a new method that accounts for some of the previous deficiencies. It builds on simple generalized linear models and their multivariate extensions, following the recommendations of Warton (2011) and Warton, Wright & Wang (2012). Using community composition data from multiple sites recorded in two time periods, we quantify species-level effects of time period, sum them up across species to test the consistency of the shifts in species prevalence and provide a general conclusion for the sites about community convergence or divergence. In the next sections, we (i) describe the model-based approach, with particular emphasis on different species response categories, (ii) illustrate its properties in a direct comparison with other multiple-site metrics and (iii) provide a case study with a large data set of 23 independent understorey vegetation resurveys across semi-natural deciduous forests in Europe.

A model-based approach to quantifying multiple-site compositional heterogeneity

The Binomial Deviance

The rationale of the method is that the community heterogeneity is quantified in terms of the species data that were originally observed across multiple sites and not based on distance metrics calculated from those data. Working with species presence/absence data, we are interested in whether the predicted probability of presence of each species moved towards zero or one over time, that is, indicating whether they were lost from many sites or tended to be gained, respectively. Separate GLMs of the binomial family can be fit to the presence/absence data of each species to estimate their probability of presence. The residual deviance of such models is a measure of error and expresses the heterogeneity in the species occurrence, that is, it is low if the species is principally absent or rather occurs in most communities. The deviance is exactly zero when the probability of presence of a species is zero or one (the species is completely absent or omnipresent, respectively) and rises to a maximum when this probability is 0·5 (presence and absence are equally likely). One could equivalently think of it as Shannon entropy expressing the uncertainty associated with predicting a species’ presence (and absence). The binomial deviance is:

(1)

where n is the number of sites, y_ij the presence/absence (1/0) of a species i in site j and the predicted probability of presence of the species in that site. In the case where no explanatory variables (e.g. site effect or environmental data) are included in the model, the deviance may be rewritten in relation to the relative frequency (p_i) of a species in the data set:

(2)

For a related approach using the binomial deviance, though as a pairwise dissimilarity measure, see Anderson & Millar (2004). The symmetry in D_i is very useful because both rare and omnipresent species will have similarly low D_i values, in accordance with their similar influence on community variation. The heterogeneity of occurrence of individual species underlies the overall compositional variation among communities. The sum of the species-level deviances is therefore a relevant measure of the multiple-site compositional heterogeneity D = ΣD_i. In a hypothetical example (Fig. 1), species A is omnipresent, so it does not cause differences in composition among sites and does not contribute to D (D_A = 0). Species C is present in half of the sites, which means it contributes to a difference in composition in many comparisons between sites (D_C = 5·5, the maximum value here). Legendre & De Cáceres (2013) similarly proposed to sum species-level variation terms – they used a sum of squares – to calculate the total variance of community data as a measure of the compositional heterogeneity among sites. More generally, D falls in the broader group of measures that quantify beta diversity as the total variation in a community data set (Anderson et al. 2011).

Figure 1

Hypothetical example of a data set with four sites and six species A–F (grey squares represent presences). The relative species frequencies p_i and the corresponding deviance values D_i are shown below each species. Their sum D is a measure of the multiple-site compositional heterogeneity.

Testing Temporal Changes in Compositional Heterogeneity

When the same sites are sampled in two time periods, the deviance metric can be used to test the significance of the change in compositional heterogeneity over time, at the level of the individual species as well as for the entire community data set. For each species i, the difference in deviance ΔD_i between time 2 and time 1, generally a recent and an older community survey, respectively, is a measure of its change in heterogeneity of occurrence. Based on the change in deviance, we can identify four species response types (see Fig. 2 for a schematic overview). First, species whose frequencies changed in such a way that ΔD_i < 0 decreased their heterogeneity of occurrence and are referred to as ‘community-convergence species’. They come in two distinct forms – relatively rare species (found in less than half of the sites) that became rarer between two surveys and prevalent species (found in more than half of the sites) that became more prevalent. For these species, sites will become more homogeneous in composition in the sense that nearly all of them will lack or rather contain such species, respectively. The ‘community-divergence species’ are those whose frequencies changed so that ΔD_i > 0. They also came in two forms – rare species that became less rare and prevalent species that became less prevalent. Their predicted probability of presence shifted towards 0·5, thereby increasing the chance of finding the species in only one plot in any pair of plots (i.e. increasing community heterogeneity).

Figure 2

(a) Schematic overview of the relation between the deviance metric D_i and the relative frequency of a species in a survey. The arrows show the changes in deviance for different scenarios in which a species i with initial relative frequency p_i = 0·2 increases or decreases its prevalence between time periods. (b) Changes in the relative frequency of a species between time period one (t1) and time period two (t2). Each point represents a change in frequency corresponding to the scenarios in (a), indicated with numbers. A species falling in a blue area is a community-convergence species – its relative frequency shifted to 0 or 1 so that its heterogeneity of occurrence decreased; such species follows a trajectory of decreasing deviance. A species in a green area is a community-divergence species, its relative frequency shifted towards 0·5, and its deviance increased.

The significance of the change in deviance can be tested with a permutation test, where sampling period labels are permuted within sites before calculating a ΔD_{i, random}. Under the null hypothesis of no change in deviance, the species presence data are equally heterogeneous in each time period, and, hence, we can choose the time ordering of the two surveys of each site at random. The significance (P-value) of ΔD_i was calculated as the proportion of the permutations with an absolute change in deviance equal or larger than the observed absolute change (absolute values to test two-sided), hence comparing |ΔD_{i, random}| ≥ |ΔD_i|. This test results in a list of significant community-convergence and community-divergence species. An R script is provided in the Supporting Information (Appendix S5). All analyses in this paper were done in R 3.0.1 (R Core Team 2013).

We can also test whether there is a consistent trend of change in prevalence across all the species. Such test summarizes the species-level effects to determine the change in overall community heterogeneity between time periods. The species-level test statistics ΔD_i are either positive or negative, so their sum indicates a consistent change if it strongly deviates from zero (ΔD = ΣΔD_i). A similar permutation test can be used to test its significance (cf. the ‘sum-of-likelihood ratio’ test approach; Warton 2011; Warton, Wright & Wang 2012). Hence, the test statistic is a multiple-site measure of community convergence (ΔD < 0) or divergence (ΔD > 0) in a typical resurvey study. The summed change in deviance quantifies the balance between the number (and the strength of their change) of community-convergence vs. community-divergence species that are present across the sites. Referring back to Fig. 2, if the species show a consistent departure from the x = y line, with most species falling in the blue areas, the compositional heterogeneity decreased because rare species were lost or locally extinct between two surveys, and frequent species became omnipresent.

Richness Differences or Turnover

The compositional variation between communities is usually not only derived from true spatial turnover (the replacement of some species by others), but also from richness differences between sites, that is, due to nestedness (poorer sites are subsets of richer sites) or other richness differences (Baselga 2010). So, part of the variation in species occurrences across sites may be easily explained by richness differences, for example some species are consistently present in the richer sites and absent in the poorer. We can account for the effect of richness differences when using one model for the entire community data set, that is, considering the presence/absence data of all species across all plots as one response variable. The sum of the deviances of the species-level models (i.e. our deviance metric D = ΣD_i) equals the residual deviance of the single binomial model y_ij ~ Species_i. The difference in the residual deviance of separate models for each time period matches the ΔD metric. Adding a Site effect term to the model, that is, y_ij ~ Site_j + Species_i, controls for the richness differences. The residual deviance of this model, which we will call D_T, then quantifies the compositional heterogeneity due to turnover only. For instance, in the case of complete nestedness, the presence of each species in a plot is perfectly predictable from the model and, hence, the total heterogeneity is zero (D_T = 0).

Properties: comparison with other multiple-site measures

Different methods to quantify compositional heterogeneity are not in opposite, but are complementary, and each expresses the variation among assemblages in a way that is useful to alternative ecological questions (Legendre & De Cáceres 2013). Our approach is particularly relevant to address the influence of non-random species gains and losses on the multiple-site community heterogeneity. Some of the basic properties of the deviance metric D and its turnover component D_T will be illustrated here in two hypothetical examples where we make a direct comparison with two other multiple-site approaches. First, Whittaker's beta β_W is the ratio of gamma and mean alpha richness and is often considered as strict-sense beta diversity (Whittaker 1960). Secondly, we compare with a dissimilarly approach, since community dissimilarities are widely used to quantify taxonomic homogenization – note, however, that homogenization is not exclusively defined in terms of dissimilarities (Olden & Rooney 2006). Here, we used the multiple-site analogue of Sørensen pairwise dissimilarity β_SOR and its turnover component β_SIM (Baselga 2010, 2013). The Jaccard index is also generally used in homogenization studies (e.g. Olden & Rooney 2006), but the index is intimately related to the Sørensen index and is therefore not further discussed here.

In the first example, some rare species are lost and the three types of measures decrease, showing the reduction in compositional heterogeneity with time (Fig. 3a). The species loss caused the compositional differences between sites to become completely due to nestedness in the second time period. The dissimilarities as well as the deviance metric permit quantifying this complete loss of spatial turnover (β_SIM and D_T = 0), while β_W does not distinguish between nestedness and turnover patterns. Note that D_T controls for nestedness and other richness differences (in this case, there is only nestedness), while β_SIM quantifies turnover without the influence of nestedness only. For instance, when communities share no species and have a different number of species, that is, there are richness differences without nestedness, then D_T < D and β_SOR = β_SIM. Another evident difference between the approaches is that we can test the significance of the change in prevalence of each species based on the species-level deviances (i.e. ΔD_A, ΔD_B…). In this case, species C, E and F represent community-convergence species. Note that if most species that were lost were prevalent species (p_i > 0·5), the heterogeneity would increase rather than decrease. The second example shows how simultaneous species loss and gain may reduce the compositional heterogeneity (Fig. 3b). Whittaker's beta β_W does not capture this change in species patterns since both the mean species richness and the total number of species did not change. The species loss and gain removed the richness differences between sites so that the compositional differences are completely caused by turnover in time period 2 (β_SOR = β_SIM and D = D_T). Even though the overall heterogeneity (β_SOR) decreased, β_SIM increased with time, which means the decrease in overall heterogeneity is completely due to the loss of nestedness. Similarly, the difference between D and D_T diminished with time (the difference even became zero), showing that richness differences became smaller. The change in frequency graph (right panel Fig. 3b) shows which species caused the change in compositional variation: species B and C reduced their heterogeneity of occurrence because they became omnipresent and rarer, respectively.

Figure 3

Hypothetical examples of a change in community composition between two time periods – the initial (time period 1) community composition in sites 1–4 is the same (and equal to Fig. 1). Several multiple-site metrics are provided: mean species richness (), Whittaker's beta (β_W), multiple-site dissimilarities (β_SOR, β_SIM) and the binomial deviance (D, D_T). The graphs on the right represent changes in relative frequencies of species A–F between time period 1 and 2.

While Whittaker's beta, the dissimilarity metrics and our deviance metric appear to be very distinct ways to quantify compositional variation, they exhibit some clear similarities. The deviance metric does not estimate the compositional differences between sites, but folds the variation between sites into marginal species frequencies (but we can add a ‘site effect’ to calculate D_T). The same applies, however, to Whittaker's beta, which reflects the inverse of the average frequency of species (Vellend 2001). Most dissimilarities can be understood as a sum across species as well. For instance, the numerator of a pairwise Sørensen (and Jaccard) is the total number of species that only occur in one of the two sites. This is equivalent to summing an indicator I_i across species, which takes the value one if a species i is only present in one of the two sites and zero otherwise. Since the indicator depends on the species’ relative frequency in the plot pair (I_i = 4p_i [1 – p_i], with p_i = 0, 0·5 or 1), Sørensen is also a sum of marginal species frequencies (rescaled by species richness in the denominator) (See Appendix S1 for the multiple-site analogue). Furthermore, many dissimilarity measures exclude joint-absence information: joint presences decrease the differentiation among communities, joint absences not. Ignoring double zeros is indeed relevant for pairwise metrics because the similarity of two sites should not increase because of the joint absence of some arbitrary species that would never occur in the studied habitat type. An analogue multiple-site criterion is to ignore ‘complete absences’, that is, under the assumption that a species that is not observed is not present. This means we analyse all species that occur at least once in a data set, so even if a species i is not present in one of the time periods, its heterogeneity of occurrence (D_i value) is calculated for that period. Species that are absent from all sites at both sampling periods have no effect on D or D_T, and thus, these measures have the desired property of ignoring complete absences.

Changes in the mean species richness of sites between time periods generally influence the metrics quantifying compositional heterogeneity as well. We can use metrics that only measure the turnover component of the compositional heterogeneity to account for the effect of richness differences between sites within a time period, but they do not control for changes in mean richness between time periods. The denominator of β_W and many dissimilarities (including β_SOR, β_SIM) contains a measure of species richness in one way or another. This means that when the mean richness decreases between time periods, communities will appear more differentiated when the numerator (e.g. gamma diversity for β_W) is not changing in the same proportion (which is generally not expected). Changes in β_W, β_SOR and β_SIM between time periods may thus partly express changes in mean plot-level richness. The deviance metric is not a priori related to a change in richness: it can decrease because either rare species become rarer or prevalent species become more prevalent; in these cases, the species richness would decrease or increase, respectively. There are other examples illustrating the metrics have different interpretations. When initially rare species become prevalent (or prevalent become rare) so that their species-level deviance does not change (see scenario 4 in Fig. 2a), this would be a case for reduced community heterogeneity (and increased mean species richness) when using dissimilarity metrics, but D would indicate no change – the interpretation is that communities are equally homogeneous in the sense that nearly all of them initially lack those species, while in a second time period, nearly all of them share those species. In sum, differences in the way changes in richness influences the metrics, variation in interpretation, but also other differences such as the confounding of shifts in composition and multivariate dispersion in many dissimilarities (Warton, Wright & Wang 2012), may lead to unintuitive results when directly comparing the metrics (e.g. a decrease in D vs. an increase in β_W or β_SOR) (see simulations in Appendix S2).

Meta-analysis of changes in forest understorey community heterogeneity across Europe

Selected Data Sets

To illustrate our approach with empirical data, we used 23 independent forest understorey resurvey studies collected in semi-natural deciduous temperate forests across Europe: from Switzerland to mid-Sweden (south–north) and from the United Kingdom to the Czech Republic (west–east) (Table S1; Verheyen et al. 2012). All vascular plant species in the understorey layer (<1 m plant height, incl. woody saplings) were recorded using permanent and semipermanent plots in two time periods. The intercensus interval was at least ca. two decades (median 31 years, range 17–67 years). The initial surveys were carried out between 1935 and 1989 and the final surveys between 1987 and 2009. The mean number of plots per study was 52 (range 17–139; total 1197 plots), and plot sizes ranged between 1 m² and 1000 m². A total of 656 different herb layer species were recorded (mean number of species per study = 112 ± 11 SE), and species occurred on average in 3·9 ± 0·17 SE different studies. All plots were in ancient forest sites (sensu Peterken 1996), that is, sites that had been continuously forested at least since the oldest available land-use maps (usually minimum 200 years). No forest stand replacement had taken place between the surveys (e.g. no clear cutting and replanting). Generally, forest management had become less intensive over the past decades: all sites were either unmanaged or experienced only low intensity thinning at low frequency in the most recent survey period.

Results

We calculated and tested the significance of changes in compositional heterogeneity (ΔD) for each individual study, summarizing the species-level effects for that study. A correction for multiple comparisons was required since the same hypothesis of no change is tested repeatedly: the classical one-stage method to calculate false discovery rate (FDR) adjusted P-values was used based on a threshold value q = 0·05, that is, the error rate in the set of comparisons that are called significant (Pike 2011). The summed deviance decreased significantly for seven studies (FDR-adjusted P < 0·01; Fig. 4), indicating loss of community heterogeneity between sites, that is, the number of community-convergence species strongly exceeded the number of community-divergence species. The community-convergence species were mainly the rare species that became more rare (or went locally extinct), not prevalent species that became more prevalent (Appendix S3). In six studies, community heterogeneity increased because many initially rare species increased between surveys. For the remaining 10 studies, the number of community-convergence and community-divergence species was similar, and many species did not change their frequency much. This result challenges the general notion in the literature that decreases in community heterogeneity would be the default outcome of contemporary species gains and losses (Olden 2006; Baiser et al. 2012). Some of the forest understorey resurvey studies have explicitly determined within-study variation of the changes in heterogeneity, and, also at that scale, variable outcomes are being reported depending on the nature of the local environmental changes such as different alterations of the forest management (Rogers et al. 2008; Van Calster et al. 2008).

Figure 4

Changes in community heterogeneity among 23 independent forest understorey resurvey studies in Europe between two surveys. (a) Spatial distribution of the 23 studies, with symbols indicating community convergence (white circles), divergence (black circles) or no change (grey circles). (b) Relationship between the mean change in species richness (SR) – expressed as a log ratio ln(SR_t2/SR_t1) ± 2SE – and the mean change in deviance (ΔD/number of species in study). Toponyms and country codes: 1: Gaume (BE); 2: Binnen-Vlaanderen (BE); 3: Zoerselbos (BE); 4: Herenbossen (BE); 5: Vorte Bossen (BE); 6: Meerdaalwoud (BE); 7: Florenne (BE); 8: Tournibus (BE); 9: Dalby (SE); 10: Tullgarn (SE); 11: Elbe-Weser (DE); 12: Děvín (CZ); 13: Milovice Wood (CZ); 14: Rychlebské hory Mts. (CZ); 15: Wytham Woods (GB); 16: Göttingen (DE); 17: Milíčovský les (CZ); 18: Switzerland (CH); 19: Hirson/Saint-Michel (FR); 20: Andigny (FR); 21: Speulderbos (NL); 22: Lady Park (GB); 23: Münich (DE).

The changes in community heterogeneity were clearly paralleled by changes in local species richness (Fig. 4b): studies for which local species richness decreased were also the studies experiencing a reduction in community heterogeneity. This relation reflects the nature of the species gains and losses in the studied vegetation: the predominant loss of many relatively rare species caused local species richness to decrease and forest understorey communities to become more similar. If these losses would have been counterbalanced by several prevalent species that expanded further, the heterogeneity would still decrease but local species richness would not change much. No obvious spatial patterns of community convergence or divergence emerged, illustrating that the species occurrences and communities have not changed in a consistent way along gradients in climatic conditions (temperature, precipitation) and nitrogen deposition rates over the past decades (non-significant correlations with those environmental variables; Appendix S3). Local factors such as changes in forest management, susceptibility of the soil to acidification or desiccation, altered grazing pressure or pest and pathogen outbreaks are predicted to be much more important (Lameire, Hermy & Honnay 2000; Rooney et al. 2004; von Oheimb & Brunet 2007; Rogers et al. 2008; Van Calster et al. 2008; Dierschke 2009; Baeten et al. 2012), or at least they obscure the large-scale patterns of change (Verheyen et al. 2012; De Frenne et al. 2013). This would explain why studies that are only one hundred kilometres apart showed contrasting patterns of change.

A Test of Species-Level Shifts Across Studies

Just as we searched for species-level effects and summed them across species to come to a study-level conclusion, we also looked at study-level effects and summed them up to test the consistency of the individual species responses across the studies (a generalization of the approach). A binomial model was fitted again for each species, but now using the species occurrence data pooled across the studies (in which the species occurred at least in one plot, so excluding all studies in which it never occurred) and with a study indicator as explanatory variable: y_ijk ~ study_k, with y_ijk the presence/absence of species i in plot j of study k. Again, the difference in deviance was the test statistic (here ΔD_species), the significance was assessed by permuting sampling period labels within sites (2000 permutations), and the P-values were FDR-adjusted because multiple species were tested. Here, we choose to model all species occurring in at least three studies, but note that conclusions about the consistency of species change are most reliable for species that occur across many studies. The interpretation is analogous to the study-level analysis with negative and positive changes in deviance for community-convergence and community-divergence species, respectively. For example, a species that occurred in several studies with a low frequency, but became consistently rarer over time in most of those studies is an overall community-convergence species. The results for four species that were selected to illustrate contrasting patterns of change are provided in Fig. 5; a full list of significant species is in Appendix S4. For example, the estimated change in deviance for Ajuga reptans across the 19 studies in which the species occurred was very negative, hence it is an overall community-convergence species across data sets. The species decreased its frequency in 13 studies, while it increased in only three, so A. reptans is a typical rare species that became rarer between surveys (consistent departure from the x = y line; Fig. 5).

Figure 5

Relative frequency changes of four understorey species between the initial (t1) and final (t2) vegetation surveys of the studies in which they occurred. The species were selected to illustrate contrasting patterns of change. Ajuga reptans: a typical community-convergence species that generally decreased in frequency (ΔD_species = −216, FDR-adjusted P < 0·01, N studies = 19). Dryopteris carthusiana: community-divergence species that generally increased where it was initially not very frequent (ΔD_species = 220, adj. P < 0·01, N studies = 17). Mercurialis perennis: community-divergence species through a decrease in some studies where it was initially quite frequent (ΔD_species = 116, adj. P < 0·01, N studies = 14). Pteridium aquilinum: species frequency did not change much, it is scattered around the diagonal indicating no change (ΔD_species = 0·3, adj. P = 1, N studies = 14).

Discussion

A solid theoretical framework describing the causes and consequences of temporal changes in community heterogeneity has rapidly emerged during the past two decades (McKinney & Lockwood 1999; Olden et al. 2004; Clavel, Julliard & Devictor 2010), but methods that actually quantify the underlying non-random species interchanges have been scarcely developed. Biotic homogenization is the process of local species colonization and extinction that reduces the compositional variation among communities. A large number of studies have quantified the patterns resulting from this process, generally using community dissimilarities and the temporal changes therein (Olden & Rooney 2006). We developed a novel approach that determines the relative roles of the species gains and losses more directly and enables us to answer different, but complementary ecological questions related to homogenization. Our approach estimates the total variation in the community data set based on species-level contributions, so it does not quantify the compositional dissimilarities between particular sites. Other properties include the option to control for richness differences (including nestedness) between sites within a time period and the possibility to explore the relation with changes in mean richness between time periods, by looking directly at the importance of the four species response types.

A major advantage of the developed approach is the possibility to generalize it to various other hypotheses. One such generalization involves modelling the data from K different time periods (usually two) in one model. We already showed that we can model the entire community data set of one time period in one binomial model with species effects y_ij ~ Species_i. For a data set collected over K time periods, a test of y_ijk ~ Species_i + Species_i:Time_k against y_ijk ~ Species_i shows a shift in species composition with time when the deviance changes significantly across models. Then, we can verify whether the compositional shift caused the heterogeneity among sites to change as well. The model y_ijk ~ Site_j:Time_k + Species_i against y_ijk ~ Site_j + Species_i looks for alterations in heterogeneity caused by changed richness differences among plots, for example species loss strengthening a nestedness pattern between surveys. The model y_ijk ~ Site_j:Time_k + Species_i + Species_i:Time_k controls for richness differences and can be tested against y_ijk ~ Site_j:Time_k + Species_i to test specifically for turnover over time. Finally, it is also possible to assess the consistency of individual species responses across different data sets, which was illustrated here with the empirical forest understorey community data. A complete model approach with species effects mainly differs from the species-level modelling approach because the underlying species patterns remain unknown, and the complete model does not account for the direction of the changes (deviances at different times need to be calculated separately). Yet, these generalizations may be useful for particular ecological questions or for first data explorations.

We discriminated between four species response types, depending on whether they were lost (losers) or gained (winners) over time and whether they were initially rare or prevalent, and their contribution is easily explored in frequency graphs (e.g. Fig. 3). These types cause either community convergence (rare losers, prevalent winners) or divergence (rare winners, prevalent losers), that is, community-convergence and community-divergence species do not necessarily correspond to the more commonly studied winners and losers categories, respectively (e.g. Wiegmann & Waller 2006; McCune & Vellend 2013). Yet, the groups may largely overlap in practice. Indeed, species usually have a low relative frequency of occurrence in nature, only few are omnipresent, and the losses and gains of such locally rare species correspond to convergence and divergence. If losses predominate, the potential ecological consequences strongly depend on whether the species that are lost represent unique trait states for particular traits compared to the complete collection of traits in the community (Olden et al. 2004; Clavel, Julliard & Devictor 2010). Likewise, increases in heterogeneity and local richness would only have ecosystem effects if the expanding species also add complementary traits to the extant community. Such predictions can be easily explored within our framework, for example, by comparing trait values across the four species response groups or the species-level test statistic ΔD_i within those groups, with or without accounting for phylogenetic relatedness. Adding species traits directly as explanatory variables in the binomial model forms an important direction for future research. More generally, predicting the ecosystem consequences of simultaneous species gains and losses requires that we understand which traits predispose species to a higher chance of local extinction or establishment (response traits) and how those traits covary with traits that influence ecosystem functioning (effect traits) (Suding et al. 2008; Wardle et al. 2011). Such analyses rely, however, on the development of techniques that first analyse the species-level data and identify the winners and loser species involved (Gosselin 2012), which is exactly what our approach is doing.

Acknowledgements

The research leading to these results has received funding from the Research Foundation Flanders (FWO), through a postdoctoral fellowship held by L.B. and P.D.F and supporting the scientific research FLEUR network (www.fleur.ugent.be). L.B. also held a postdoctoral fellowship from the Special Research Fund of Ghent University (BOF). R.H. and P.P. were supported by the long-term research development project RVO 67985939. Thanks to Jörg Brunet, George Peterken, Hartmut Dierschke and Jörg Pfadenhauer for sharing their data sets. The comments of three reviewers were very useful to improve a previous version of the paper.