Detecting Trends in Species Composition Thomas E

Iowa State University

From the SelectedWorks of Philip Dixon

1998

Detecting trends in species composition Thomas E. Philippi, University of Georgia Philip Dixon, University of Georgia Barbara E. Taylor, University of Georgia

Available at: https://works.bepress.com/philip-dixon/36/ 300 INVITED FEATURE Ecological Applications Vol. 8, No. 2

Ecological Applications, 8(2), 1998, pp. 300±308 ᭧ 1998 by the Ecological Society of America

DETECTING TRENDS IN SPECIES COMPOSITION

THOMAS E. PHILIPPI,PHILIP M. DIXON, AND BARBARA E. TAYLOR Savannah River Ecology Laboratory, Drawer E, Aiken, South Carolina 29802-0005 USA

Abstract. Species composition re¯ects a combination of environmental and historical events at a site; hence, changes in species composition can provide a sensitive measure of ecologically relevant changes in the environment. Here, we consider the analysis of species composition when multiple sites are followed through time. Analyses of temporal trends in species composition either summarize species composition into a few metrics (indices or axis scores) or analyze the similarity among sites. We develop and illustrate the similarity approach. Each pair of samples represents a pair of replicates, a pair from the same site at different times, a pair from different sites at the same time, or an unrelated pair. Differences among times can be estimated by comparing average temporal dissimilarity to average replicate dissimilarity. Temporal trends can be described by one of three statistics that measure progressive change, the correlation of temporal dissimilarity with the length of time between samples. These methods are illustrated using data on changes in a South Carolina zooplankton assemblage following disturbance, and changes in bird species composition on Skokholm Island, Wales. It is dif®cult to de®ne and interpret temporal trends. Some de®nitions of interesting trends, like increasing divergence from another set of sample plots, place additional requirements on the sampling design. Including replicate samples or clustering sample plots and including ``control'' plots for comparison with sentinel sites would contribute to an understanding of changes in species composition. Key words: community change; dissimilarity; multidimensional scaling; ordination; randomization tests; species composition; temporal differences; trends.

INTRODUCTION plankton assemblage and in the bird community of Skokholm Island, Wales. Similar sorts of questions and Most discussions of monitoring, including those in analyses are appropriate for many communities with this special feature, deal with scalar quantities: envi- multiple sources of variation, e.g., environmental stress ronmental conditions such as pH, or abundances of and spatial gradients (Vargo et al. 1982, Fausch et al. individual species. However, not all quantities that 1990, Clarke 1993). might be useful to monitor are scalars; species composition at monitored sites is a vector, or multivariate WHY MONITOR SPECIES COMPOSITION? quantity. In general, species composition may be analyzed as vectors of 0's and 1's representing absence A need to monitor species composition may arise in or presence of species, vectors of abundances of each at least three ways: species composition may provide species, or vectors of proportional abundance. Al- a strong signal of the environmental factor of interest; though most of the principles and problems applicable it may be of direct ecological interest; or it may be the to detecting change or trends in scalars also apply to only feasible measurement. Because environmental species composition, the multivariate nature of species factors differentially affect species, species composi- composition presents additional problems. Change or tion can provide information about environmental fac- differences in composition among samples may be tors (Austin and Austin 1980, ter Braak and Prentice quanti®ed, but may be dif®cult to interpret. Trends are 1988). Indirect estimation of environmental character- much more dif®cult to de®ne, especially if species com- istics from species composition can be extremely useful position is responding to changes in more than one if it is dif®cult to de®ne or directly measure relevant stressor. Here, we review the forms of questions ad- characteristics of the environment. Two examples are dressed with species composition data, propose some paleoecological reconstruction of environmental con- methods using dissimilarity metrics, and then illustrate ditions, such as climate or pH, from historical species the methods using changes in a South Carolina zoo- composition and modern species±environment relationships (Oksanen et al. 1988, Birks et al. 1990), and Manuscript received 6 January 1997; accepted 15 October using changes in the shrubby and herbaceous vegeta- 1997. For reprints of this Invited Feature, see footnote 1, p. 225. tion to monitor changes in site capability for timber

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May 1998 MEASURING ECOLOGICAL TRENDS 301

production, which might take decades to measure di- a spatial pair from different sites at the same time, or rectly (Korstian 1919, Leak 1992). Infrequent impacts a mixed pair from different sites at different times. (e.g., occasional discharges) may be dif®cult to detect We divide questions addressed with species com- directly without continuous monitoring, but species position into three temporal categories. Composition composition may effectively and appropriately inte- may be compared among groups of sites at a single grate such acute impacts over time, providing a means time, the amounts and directions of change in com- of detection and an estimate of severity or importance. position between two dates may be compared among Fish species composition has been used as an index of groups of sites, and trends or progressive change across pollution in rivers and streams (Fausch et al. 1990), a series of dates may be compared among sites. Each and changes in marine benthic invertebrates have been class of change corresponds to a comparison of dis- used as measures of environmental impact (Warwick similarity between types of pairs (e.g., temporal pairs and Clarke 1991). to replicate pairs). Species composition itself may be the relevant en- COMPARISON AMONG SITES AT A SINGLE TIME vironmental end point, especially in an environmental impact context where the concern is that there be no If species composition changes between impacted change in species composition due to operation of some and unimpacted sites, then the pairwise dissimilarities facility (e.g., Gray et al. 1990, Environment Canada among impacted sites and among unimpacted sites will 1995). Finally, percent species composition may be the be smaller than the pairwise dissimilarities between only feasible measurement (e.g., in palynological stud- impacted and unimpacted sites. These dissimilarities ies). Such values are not independent among species; can be summarized either by the mean or median pair- a species can have a low percent abundance in a par- wise intergroup dissimilarity, or by a test statistic such ticular sample, either because it has low absolute abun- as a Mann-Whitney U or Clarke's (1993) R that com- dance in that sample, or because another species has pares between-group to within-group dissimilarities. extraordinarily high abundance in that sample (e.g., Clarke's R is computed by ranking all n(n Ϫ 1)/2 pairwise dissimilarities between the n sites, and then com- Hellawell 1977). Therefore, it can be quite misleading puting to treat such data as re¯ecting patterns in individual species. For some taxa (e.g., soil microorganisms), it 4(r Ϫ r ) R ϭ bw is only possible to detect presence or absence; thus, an n(n Ϫ 1) individual species provides little information. Changes in species composition may be of interest where rb is the average rank of impacted±unimpacted for both retrospective and prospective monitoring. Al- (between-group) pairs, and rw is the average rank of though compositional change may be an ``effect'' rel- within-group pairs. If the smallest difference between ative to some other primary stressor, it may, at the same groups is larger than every difference within groups, time, be a ``stressor'' predictive of future changes in then R ϭ 1, but if differences between groups are similar to those among groups, R will be close to 0. ecosystem properties such as biomass and nutrient cy- Randomization tests are required to evaluate whether cling, and thus may allow earlier detection and inter- dissimilarities between groups are larger than expected vention. Underwood (1994) suggested that, although by random chance (Field et al. 1982, Smith et al. 1990, univariate chemical or indicator species measures may Clarke and Warwick 1994). Traditional signi®cance respond rapidly with strong signals to other stressors tests are invalid because dissimilarities are computed and, thus, may be preferable to assemblage data, anal- from all pairs of samples. Even if each of the n sites ysis of species or assemblage composition generally is is considered to be independent, the n(n Ϫ 1)/2 possible required if the goal is to predict community or eco- pairwise dissimilarities are not. In each randomization, system consequences of a change. labels (e.g., impacted or unimpacted) are randomly In a typical monitoring design, samples are collected reassigned (without replacement) to sites, and the mea- or measured at multiple sites monitored over time. Ide- sure is recomputed. The calculation is repeated for all ally, replicate samples are collected, but this is often permutations of labels, or for a sample of permutations not done. Although many different quantitative tech- if there are many. Note that the dissimilarity matrix niques have been used to display and summarize pat- need be computed only once. The P value for the hy- terns in species composition (e.g., Legendre and Le- pothesis test is (x ϩ 1)/(r ϩ 1), where x is the number gendre 1983, Washington 1984, Digby and Kempton of more extreme values found in r randomizations. This 1987, Magurran 1988, and ter Braak and Prentice randomization test maintains the species composition 1988), we will focus on the analysis of dissimilarity in each sample, but it randomizes labels (e.g., impact- among samples, because it most directly focuses on ed/unimpacted) among samples. For most questions, questions about temporal change. Each pair of samples this is the most appropriate randomization scheme, but is either a replicate pair from the same site and time, it is not the only possible scheme. It is also possible a temporal pair from the same site at different times, to randomly shuf¯e species among samples (Dixon Monday Sep 28 01:17 PM ecap 8 221 Mp 302 Allen Press • DTPro File # 21sc

302 INVITED FEATURE Ecological Applications Vol. 8, No. 2

1994) or to randomly shuf¯e individuals among species dissimilarity via Clarke's R). With fewer temporal sam- and samples (Solow 1993). ples, there is no generally applicable test, although sit- uation-speci®c randomization tests may be possible. EVALUATION OF TEMPORAL CHANGE Temporal trend in a scalar quantity is relatively easy Three major classes of questions about temporal to de®ne: a tendency to increase or decrease over a change are as follows. Is temporal dissimilarity greater speci®c time period. Although it is easy to test for than sampling variation between replicates? Does one change in species composition, it is more dif®cult to group of sites change more than another group, and de®ne trend in species composition. If species com- does between-group dissimilarity increase or decrease position can be used to estimate some environmental over time? Is there a temporal trend in dissimilarity at scalar (e.g., by calibration), then the problem is reduced a given site? Answering these questions is more dif- to evaluating a trend in the calibrated scalar. However, ®cult than answering similar questions about scalar a more general de®nition of trend in species compo- quantities. If there is no change in a scalar environ- sition is not clear. Requiring a trend in the abundance mental variable, the expected difference between two of every species is overly restrictive. We suggest a less samples is zero, because sampling errors are both pos- restrictive de®nition, which we call progressive itive and negative. With a sample of compositional change, that the dissimilarity in species composition data, all dissimilarities are positive, so the expected between two samples tends to increase with their tem- dissimilarity is nonzero, even if there is no true dif- poral separation. ference between two samples. The expected dissimi- Progressive change can be tested using at least three larity can be estimated with monitoring designs that different test statistics. Each is sensitive to subtly dif- include replicate samples at each site and time. ferent types of change. In all cases, the concern is with For the ®rst class of questions, if temporal change trend over time, not simply variation among times, so is larger than sampling variation, then the temporal the hypothesis of no trend should be tested by random- dissimilarities within replicates are larger than the rep- izing each set of replicates together. Alternatively, one licate dissimilarities computed among replicates within can randomize labels (times) to the average dissimi- each time. This is a comparison between temporal sim- larities. The simplest test for progressive change fo- ilarity and replicate similarity, and it can be tested using cuses on change from a speci®ed baseline condition, Clarke's R and randomization tests (Clarke 1993). If and considers the correlation or rank correlation be- multiple sites are sampled, the test can be performed tween time and dissimilarity with the baseline. Suitable separately for each site, or results from all sites can be nonparametric test statistics include Spearman's rank pooled (Clarke and Warwick 1994). correlation and Kendall's tau correlation (Kendall and Questions about differences in the magnitude of tem- Gibbons 1990). These statistics test the hypothesis that poral dissimilarity between groups of sites are appro- D11 ϭ D12 ϭ D13 ϭ D14 ϭ D15 against the alternative priate when the monitoring follows a Before±After, that D11 Ͻ D12 Ͻ D13 Ͻ D14 Ͻ D15, where Dij is the Control±Impact (BACI) design with replicate sites dissimilarity between dates i and j, and date 1 is the (Underwood 1992), where impacted sites may be ex- chosen baseline condition. The second test generalizes pected to change more than control sites. The appro- the possibly arbitrary choice of a single baseline by priate comparisons and tests depend on the details of computing the correlation between date and dissimi- the sampling design. One common design is to sample larity using each date as the baseline to which subse- multiple, permanently marked sites once before and quent or previous dates are compared. This test is sen- once after the impact. A single dissimilarity measure, sitive to alternatives of the form: D11 Ͻ D12 Ͻ D13 Ͻ comparing before and after samples, can be computed D14 Ͻ D15, D22 Ͻ D23 Ͻ D24 Ͻ D25, D33 Ͻ D34 Ͻ D35, from each site. These dissimilarity measures are in- D44 Ͻ D45, D55 Ͻ D45 Ͻ D35 Ͻ D25 Ͻ D15, D44 Ͻ D34 dependent, if sites are independent; thus, the difference Ͻ D24 Ͻ D14, D33 Ͻ D23 Ͻ D13, and D22 Ͻ D12. This between control and impacted sites can be tested by method uses all dates as baselines, but only compares traditional statistical tests, e.g., the Mann-Whitney U species composition in overlapping time periods (e.g., test. between dates 1 and 2 and between dates 1 and 3). The Questions about divergence or convergence among third test calculates the correlation between dissimi- groups of sites over time arise if the monitoring design larity in species composition and difference in times, has repeated sampling during the potential response to using all pairs of samples. This is a Mantel test of the impact (divergence) or recovery (convergence), or if association between two distance matrices (Manly

restoration and remediation efforts are monitored. The 1991). This tests alternatives of the form (D11, D22, D33,

form of possible tests depends on the number of sam- D44, D55) Ͻ (D12, D23, D34, D45) Ͻ (D13, D24, D35) Ͻ

pling times and pattern of within-group dissimilarities (D14, D24) Ͻ (D15). Unlike the second test, the Mantel over time. With many temporal samples, a simple rank approach presumes that change in species composition correlation between date and between-group dissimi- can be compared between non-overlapping time peri- larity may be used (possibly corrected for within-group ods. Monday Sep 28 01:17 PM ecap 8 221 Mp 303 Allen Press • DTPro File # 21sc

May 1998 MEASURING ECOLOGICAL TRENDS 303

DISSIMILARITY METRICS enough temporal data are collected, the space-for-time The preceding tests were presented in terms of un- substitution must remain an untested assumption of all speci®ed dissimilarities. Although the general princi- such analyses. A second caveat is that correlation is ples of similarity and dissimilarity in species compo- not causation, and the calibration data will rarely be sition are simple and clear, the de®nition of dissimi- from matched, experimentally manipulated sites, so the larity can be troublesome, because of the in®nite num- assumption of all else being equal may be crucial. The ber of ways to collapse the difference between two calibration approach may be used both for inferring the vectors into a single number and the great variety of cause of the compositional change and for inferring the named similarity and dissimilarity metrics (Goodall effects of the compositional change on subsequent eco- 1982, Boyle et al. 1990). There is no universally best system properties. dissimilarity metric. Choice of a metric should be based EXAMPLE:TRENDS IN ZOOPLANKTON SPECIES on biological knowledge: what forms of compositional COMPOSITION AFTER DISTURBANCE differences are expected or considered to be important. In some cases, simulation studies suggest metrics with We will illustrate the dissimilarity-based analysis of desirable properties for speci®c questions (Faith et al. trends and differences in species composition with data 1987). Metrics vary in the relative weightings they give on recovery from episodic disturbance of zooplankton to many small differences in abundances vs a few large in a cooling water reservoir on the Savannah River Site, differences in abundances of common species. Asym- South Carolina, USA (Leeper and Taylor 1995). Pairs metric metrics only treat shared presences as infor- of replicate estimates of zooplankton density were mative of similarity, which often is appropriate because made at six times and at three sites in a nuclear reactor there are many different reasons why a species might cooling-water reservoir. One site (MC-10) was in the be absent from a sample. Finally, dissimilarity mea- middle of the main channel of the reservoir. The other sures are usually computed from a sample of individ- two sites (SC-30 and BD-30) were in protected coves. uals, not from the entire community, and are sensitive The ®rst sample (23 May 1986) was taken when the to sample sizes; those that are independent of sample reactor was operating and the reservoir was receiving size are so only for a speci®c species abundance dis- heated water. Water temperatures in the main channel tribution (e.g., Morisita for log-series abundances, were hotter (up to 58ЊC) than those in the coves (38Њ± Wolda 1981). 49ЊC). No zooplankton were present in the main channel on 23 May 1986. The next four samples (June±late CALIBRATION August 1986) were taken during an extended reactor If the goal of a monitoring program is to detect re- outage that began on 1 June 1986. Water temperatures sponse to environmental change, then detection of at the three sites were equivalent (25Њ±35ЊC) when the change or even trend in species composition is not reactor was not operating. The data used here are a enough. Temporal change in species composition oc- subset from a much larger data set; details of sample curs for many reasons, only one of which is a response collection, processing, and zooplankton counting and to a change in the underlying environment. An obvious analysis of trends in individual species are given in example is secondary succession following an acute Leeper and Taylor (1995). disturbance such as clearing or a hurricane. However, We ask four questions. What are the relative mag- plant species composition naturally changes at tem- nitudes of dissimilarity between replicate, temporal, poral scales from seasonal phenology and year-to-year spatial, and unrelated pairs? Does the species compo- ¯uctuations (Philippi et al. 1990) through several mil- sition differ between the three sites? Does the species lennia, e.g., the 6000-yr chronosequence in McAuliffe composition change over time? Is there a trend in spe- (1991) and migration since the last ice age in Davis cies composition over time? All four questions can be (1986). Therefore, an additional step is required to al- addressed by comparing dissimilarity in species com- low interpretation of the change in species composi- position among sets of samples. Because the sampling tion. program included multiple sites and multiple dates, If control and impacted plots are monitored, then the there are four different types of pairs of samples. Rep- divergence between the two sets of sample plots re¯ects licate pairs are those collected at the same site on the different temporal trajectories, and is thus directly in- same date. Temporal pairs are collected at the same site terpretable as a difference caused by the impact. Oth- on different dates. Spatial pairs are collected from dif- erwise, a transfer function may be generated via a cal- ferent sites on the same date, and unrelated pairs are ibration data set and may be used to translate the ob- collected from different sites on different dates. Pair- served changes in composition into differences in en- wise dissimilarities were calculated using the Bray- vironmental factors. The calibration data set is usually Curtis metric on fourth-root transformed data, using a set of species compositions sampled at sites differing the DISTANCE macro in SAS version 6.12 (METH- in environmental factors. Therefore, one caveat is that ODϭNONMETRI; Kuo 1995). the space-for-time substitution may not be valid. Until A visualization of the matrix of pairwise distances Monday Sep 28 01:17 PM ecap 8 221 Mp 304 Allen Press • DTPro File # 21sc

304 INVITED FEATURE Ecological Applications Vol. 8, No. 2

TABLE 1. Dissimilarity in zooplankton species composition among samples on the Savannah River site, South Carolina, USA. Mean spatial, mean replicate dissimilarity, Clarke's R, and the probability of observing an equal or larger Clarke's R under randomization are given for each date and for all dates, stratifying by date.

Mean Mean Date spatial replicate Clarke's RP 23 May 1986 0.732 0.091 1.0 0.33 6 June 1986 0.311 0.105 1.0 0.067 20 June 1986 0.368 0.218 0.89 0.20 8 July 1986 0.286 0.152 1.00 0.067 25 July 1986 0.269 0.157 1.00 0.067 All dates 0.344 0.122 0.973

ϭ 0.62) was similar to temporal dissimilarity. The same pattern of replicate dissimilarity (median ϭ 0.12) Ͻ spatial dissimilarity (median ϭ 0.33) Ͻ temporal dissimilarity (median ϭ 0.65) was found among the subset of samples taken when the reactor was not operating. The MDS plot suggests that spatial variability among FIG. 1. Con®guration of zooplankton samples in a two- sites is highest on 23 May 1986 and smaller on sub- dimensional nonmetric multidimensional scaling (NMMDS) representation of the Bray-Curtis distances. Symbols identify sequent dates, and that dissimilarities among sites are the site: Ⅺ, BD30; ᭝ SC30; ϫ, MC10. Solid symbols indicate larger than those between replicates. Both of these pat- when the reactor was operating (23 May 1986). Convex hulls terns can be con®rmed using the observed dissimilar- enclose all samples taken on the same date. Dates are coded ities for spatial and replicate pairs of samples (Table as: 1, 23 May 1986; 2, 6 Jun 1986; 3, 20 June 1986; 4, 8 July 1986; 5, 25 July 1986. 1). The mean dissimilarities among the spatial pairs are considerably larger on 23 May 1986 than on any subsequent date. On all dates, the mean spatial dissimi- was obtained using nonmetric multidimensional scal- larity is larger than the mean replicate dissimilarity. On ing (SAS PROC MDS LEVELϭORDINAL, SAS ver- most dates, the smallest pairwise dissimilarities are as- sion 6.12). NMMDS arranges points in 1, 2, 3, or per- sociated with replicate pairs of samples, not spatial haps more dimensions, so that the ranking of Euclidean pairs of samples; thus, Clarke's R is 1. Because of the distance between points is maximally correlated with small number of samples on any single date, the number the ranking of pairwise dissimilarity in species com- of possible permutations in the randomization test is position (Kenkel and Orloci 1986, Clarke 1993). A small. When two replicates are taken at three sites, two-dimensional plot provides a reasonable summary there are 6!/(3! ϫ 2! ϫ 2! ϫ 2!) ϭ 15 possible per- of the pairwise distances (Fig. 1). Each pair of repli- mutations of labels. None of the tests has P values cates lies close together, and points for samples taken Ͻ0.05, even though the observed results for these data at the same time tend to form clusters. Samples taken are generally the most extreme possible. If results from at different times (temporal clusters) tend to be well all dates are combined, either by Fisher's method of separated from each other. Although such plots are very combining P values (Sokal and Rohlf 1981), or by useful for portraying relationships among samples, dis- stratifying by date, the spatial dissimilarity is signi®- tances between points on the plots should not be used cantly larger than the replicate dissimilarity (␹2 ϭ as a measure of the dissimilarity in species composition 21.664, df ϭ 10, P ϭ 0.016 for combining approach). (Clarke 1993). MDS, like all other ordination tech- Although there are differences in species composition niques, distorts the actual pairwise distance between among the sites, these spatial differences are smaller samples into an arti®cial distance in a small number of when the reactor is not operating. dimensions. Hence, comparisons and tests should use Temporal differences in composition can be assessed the observed dissimilarities. by comparing the temporal dissimilarities to the rep- We found that species compositions in replicate pairs licate dissimilarities (Table 2). Because there are data collected at the same time and place were quite similar. from ®ve dates at two sites (BD and SC) and from four Between-replicate dissimilarities were small (median dates at the other (MC), there are many possible per- ϭ 0.14). The spatial dissimilarities, among sites at the mutations of temporal and replicate dissimilarities. For same time, were larger (median ϭ 0.30), but temporal example, at the BD10 site, there are 10!/(5! ϫ 2! ϫ 2! dissimilarity, among times at the same site, was larger ϫ 2! ϫ 2! ϫ 2!) ϭ 945 arrangements of the pairwise still (median ϭ 0.60). Dissimilarity between samples dissimilarities into temporal and replicate groups. At collected in different times and different sites (median each of the three stations, the observed between-rep- Monday Sep 28 01:17 PM ecap 8 221 Mp 305 Allen Press • DTPro File # 21sc

May 1998 MEASURING ECOLOGICAL TRENDS 305

TABLE 2. Replicate and temporal dissimilarity at SC30, ple size is too small to get P values Ͻ0.05, even though BD30, and MC10 stations in 1986, from the dates in column 1 to the dates in the column heads. Values on the diagonal there is a perfect correlation between dissimilarity and are between-replicate dissimilarities. Values above the di- time (Table 3). If it is reasonable to compare dissim- agonal are average pairwise dissimilarities between two ilarities among non-overlapping time periods, the Man- dates. Only one sample was counted at SC30 on 6 June tel test is appropriate. It indicates a large and statisti- 1986, so there is no between-replicate dissimilarity for that date. No species were present at MC10 on 23 May 1986. cally signi®cant correlation of dissimilarity and time (Table 3). What is probably happening to the zooplank- From: 23 May 6 June 20 June 8 July 25 July ton species composition is simultaneous repopulation SC30 of the entire reservoir, followed by seasonal succession 23 May 0.114 0.727 0.896 0.952 0.874 during July. 6 June ´´´ 0.588 0.701 0.724 20 June 0.278 0.424 0.525 EXAMPLE:PROGRESSIVE CHANGE IN THE LAND-BIRD 8 July 0.174 0.387 COMMUNITY OF SKOKHOLM ISLAND 25 July 0.206 BD30 As a second example of testing progressive change, 23 May 0.067 0.672 0.746 0.779 0.750 we examine changes in the species composition of the 6 June 0.141 0.699 0.805 0.616 land-bird community of Skokholm Island (off the 20 June 0.144 0.285 0.527 8 July 0.125 0.504 southwest coast of Wales) from 1928 until 1979, using 25 July 0.101 the data given by Williamson (1983). There are no MC 10 replicate samples, because the data are a complete cen- 23 May ´´´ ´´´ ´´´ ´´´ ´´´ sus of all birds on the entire island, with the exception 6 June 0.069 0.587 0.668 0.559 of some interpolated missing values. NMDS of the 20 June 0.232 0.391 0.598 Bray-Curtis distance in species composition shows 8 July 0.158 0.448 25 July 0.165 three periods of relative small and erratic changes in species composition from 1928 until 1944, from 1951 until 1960, and from 1975 until 1979 (Fig. 2). In be- licate dissimilarities are smaller than any of the tem- tween, there are repeated and consistent trends in spe- poral dissimilarities; hence Clarke's R is 1.0 for each cies composition, especially from 1963 until 1975. site. The observed pattern of rank dissimilarity rep- These patterns are similar, but not identical, to the pat- resents the most extreme temporal difference that can terns seen by Williamson using a different dissimilarity be found by randomizing samples, so P values for tests measure and ordination technique. The progressive of no temporal differences are small (P ϭ 0.0011 for trend statistics (Table 4) indicate that there is a highly BD and SC sites; P ϭ 0.0095 for MC site). However, signi®cant trend in species composition across the en- temporal differences between samples do not imply a tire period. If individual decades are considered, there trend in species composition. is strong evidence of progressive change in all decades With these data, there is weak evidence of progres- except 1950±1959, where the evidence is slightly sive change. Between 6 June 1986 and 8 July 1986, weaker. Although all of these tests indicate that there the species composition is increasingly dissimilar to is progressive change, the test statistics and P values the species composition on 23 May 1986 (Fig. 1, Table do not indicate the amount or importance of that 2). However, this trend does not continue on 25 July change. One measure of the magnitude of change is 1986. The tests of progressive trend provide equivocal the Bray-Curtis distance between the beginning and end answers (Table 3). The ®rst and second tests suggest of the period (Table 4). By that measure, the change that the correlations of dissimilarity and time are mod- during the 1930s and 1950s is smaller than that during erately large, but not statistically signi®cant. If only the 1960s and 1970s, matching Williamson's (1983) data from the ®rst four time periods are used, the sam- interpretation.

TABLE 3. Spearman rank correlations and randomization P values (in parentheses) for tests of progressive change. Details of each test are given in the text. P values are computed by permuting date labels to the matrices of average dissimilarity in Table 2.

Test SC site BD site MC site A) From 23 May 1986 through 25 July 1986 Change from baseline 0.60 (0.33) 0.80 (0.17) 0.33 (0.83) All changes 0.88 (0.017) 0.79 (0.067) 0.78 (0.25) Matrix correlation 0.86 (0.017) 0.86 (0.033) 0.85 (0.25) B) From 23 May 1986 through 8 July 1986 Change from baseline 1.00 (0.17) 1.00 (0.17) ´´´ All changes 1.00 (0.083) 1.00 (0.083) ´´´ Matrix correlation 0.92 (0.083) 0.92 (0.083) Monday Sep 28 01:17 PM ecap 8 221 Mp 306 Allen Press • DTPro File # 21sc

306 INVITED FEATURE Ecological Applications Vol. 8, No. 2

may be adjacent in a two-dimensional ordination plot if their differences were loaded onto the third and higher ordination axes (Digby and Kempton 1987). This problem can be quite serious, because the ®rst two axes might be determined by random changes in a few rare species (Gauch 1982), in which case the biologically important variation is completely missed, or by two strong spatial environmental gradients, in which case most temporal change might fall along higher axes. The detrending and corresponding rescaling of the ®rst axis in detrended correspondence analysis, the most com- monly used variant, exacerbate the problem of treating arrow lengths as dissimilarities. Aitchison (1986) popularized an approach to composition data analysis that may be appropriate when all or most species are present in every sample. In this approach, the observed species compositions are log-

ratio transformed: Yi ϭ log(Xi/X1), where Xi is the proportion of species i in the sample. The proportion of the ®rst species is arbitrarily chosen as a reference FIG. 2. Con®guration of Skokholm land-bird communi- proportion. Principal components analysis or multi- ties in a two-dimensional nonmetric multidimensional scaling variate regression modeling of the transformed pro- representation of the Bray-Curtis distances. Selected dates are marked at the side of the points. portions is used to summarize the multidimensional structure or to model temporal trends (Grunwald et al. 1993). This approach is consistent with the general OTHER APPROACHES dissimilarity approach suggested here when Euclidean Austin (1977) proposed that indirect ordination distance between transformed proportions is used as could be performed on the entire set of spatial and the dissimilarity measure (Aitchison 1986:193). temporal samples to reduce variation to two dimen- The dissimilarity approach described here evaluates sions, and then trajectories of individual plots over time change in composition. If the species±environment re- in this ordination space could be interpreted to inves- lationship were known, then calibration could be used tigate succession. The trajectories over time are pre- to infer environmental change from the species com- sented as arrows tracking the change in a plot's ordi- position change. Another family of approaches reverses nation scores over consecutive time periods. The mag- the order of those steps, ®rst inferring environmental nitudes and directions of such arrows are interpreted measures from the species compositions, and then es- and perhaps tested, in effect treating Euclidean dis- timating change or trend in those measures. Such pro- tances in the two-dimensional ordination space as dis- cedures go by many names: direct ordination (Gauch similarities. This approach has also been widely rec- 1982), weighted-average calibration (Oksanen et al. ommended for other groups of species (e.g., Environ- 1988, Birks et al. 1990), or an analysis of indices of ment Canada 1995), but has several drawbacks if the biotic integrity (Karr 1981, 1991). Although the details ordination is done by a projection method (e.g., PCA, of each procedure differ, all require information about RDA, CA, DCA, CCA). Samples that are very different the relationship between each species and an environ-

TABLE 4. Tests and measures of change in the Skokholm land-bird community. Values are given for the entire data set and then for each decade. The 1940s decade was not analyzed because no data were collected during 1941±1945.

Dissimilarity Dissimilarity Dissimi- to initial in nested sets Mantel larity sample of years test (®rst to Period correl. (P) correl. (P) correl. (P) last) Entire sequence 1928±1979 0.81 (Ͻ0.0001) 0.75 (Ͻ0.0001) 0.82 (Ͻ0.0001) 0.60 Individual decades 1930±1939 0.56 (0.027) 0.70 (Ͻ0.0001) 0.80 (0.0015) 0.13 1950±1959 0.44 (0.067) 0.68 (Ͻ0.0001) 0.66 (Ͻ0.0001) 0.25 1960±1969 0.83 (Ͻ0.0001) 0.84 (Ͻ0.0001) 0.89 (Ͻ0.0001) 0.33 1970±1979 0.89 (Ͻ0.0001) 0.86 (Ͻ0.0001) 0.81 (Ͻ0.0001) 0.31 Monday Sep 28 01:17 PM ecap 8 221 Mp 307 Allen Press • DTPro File # 21sc

May 1998 MEASURING ECOLOGICAL TRENDS 307

mental variable. For example, if the optimum and tol- Finally, very little-to-nothing is known about appro- erance for an important environmental factor are avail- priate sample sizes and the trade-off among number of able for each taxa, weighted-averaging calibration will replicates, number of sites, and number of times to estimate environmental scores for each site. The anal- sample. The power to detect a trend in species com- ysis of trends is then an analysis of the estimated en- position depends on the sample size, the magnitude of vironmental scores. the trend, and the magnitude of random variation, just as it does when sampling scalar quantities (Urquhart IMPLICATIONS FOR THE DESIGN OF MONITORING 1998). A detailed study of sample size and the power PROGRAMS of tests of change in species composition has not yet The design of a monitoring program for detecting been done, but it is possible to suggest some minimum change in species composition suffers from the same sample sizes. These are determined by the number of con¯icting goals as any other ecological monitoring possible permutations in the randomization tests, as program. We simultaneously want to have widespread, illustrated by the zooplankton data analysis. Two rep- ®ne-grained spatial coverage and long-term, detailed, licates at three sites were not enough to identify sig- temporal sampling at individual sites. Unfortunately, ni®cant differences among sites, but two replicates at such detailed monitoring of so many sites will be too four times were suf®cient to identify signi®cant dif- costly to implement for most ecological questions. ferences between times. Five sampling dates were bare- One component of a monitoring design for species ly suf®cient to test for progressive change, but 10 sam- composition that should not be sacri®ced is the esti- pling dates were suf®cient to detect relatively small mation of among-replicate similarity. Ideally, this changes in the Skokholm data. comes from replicate samples. Two replicates are the ACKNOWLEDGMENTS minimum, but power of tests that compare among-rep- This research was supported by Financial Assistance licate similarity to among-time or among-site similarity Award DE-FC09-96SR18546 from the U.S. Department of is greatly enhanced if more than two replicates are Energy to the University of Georgia Research Foundation. available. With R replicates, the number of pairs of The very helpful comments of Tony Olsen and two anony- among-replicate similarities is (R2 Ϫ R)/2, i.e., 3 for mous reviewers were much appreciated. three replicates and 6 for four replicates. If true rep- LITERATURE CITED licate plots are not possible, spatially clustered or Aitchison, J. 1986. The statistical analysis of compositional neighboring plots might be usable to estimate within- data. Chapman and Hall, London, UK. site dissimilarity; the tighter the clustering, the smaller Austin, M. P. 1977. 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