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Statistical approaches to interpreting diversity patterns in the Norwegian mountain flora

Statistical approaches to interpreting diversity patterns in the Norwegian mountain flora Birks. H. J. B. 1996. Statistical approaches to interpreting diversity patterns in the Norwegian mountain flora. - Ecography 19: 332-340. The richness of Norwegian mountain plants in 75 .grid squares is mapped from published distributional data for 109 species. Eleven explanatory variables representing bedrock geology, geography and topography. climate. and history (relative abundance of unglaciated areas) for each square are used in multiple regression analysis with associated Monte Carlo permutation tests to find statistically significant prcdictor variables for species richness. The variance in richness explained by the four major groups of explanatory vuriables is established by (partial) multiple regression analysis in which the groups of predictors are entered in direrent orders. The variance in species richness explained by the predictor variables is partitioned into four independent components. A predictive model for species richness using partial least squm regression and all explanatory variables has a coefficientof determination (R2)of 0.79. The statistical results consistently show that species-richness patterns are well expliained by modernday factors such as climate, geology, elevation, and geography without recourse to historical variables. The nunatak hypothesis of plant survival on unglaciated areas within Noway does not explain the observed richness patterns when modern ecologicial factors are considered first. The nunatak hypothesis thus appears to be redundant, a view supported by recent palaeobotanicil. biosystematical, and evolutionary studies. H . J . B. Birks. Bor. Inst.. Uniu. of Berxen. Alliguren 41. N-5007Bergen. Norwuy und Encironnrental Cliunge Res. Centre, Depr of Geography, Uniu. College London. 26. Bedjord Wuy, London. U.K. WClH OAP. Patterns of species richness (“biodiversity”) of Norwegian mountain plants show a remarkable concentration of diversity in two areas of Norway. High diversity occurs in northern Norway and in southerncentral Norway, whereas there is a marked decrease in richness between these two areas and in southernmost Norway (Fig. 1). This bicentric concentration of species richness in two areas (“hotspots” of biodiversity) is most commonly interpreted as a result of the survival of mountain plant species during at least the last glacial stage in unglaciated areas (“refugia”) in or near the two regions where species richness is highest (e.g. Dahl 1955, 1987, 1990, Nordhagen 1963). Dahl (1990) proposed that “when a remarkable concentration of disjunct and/or locally endemic species is observed it is tempting to Accepted 21 September 1995 Copyright 0 ECOGRAPHY 1996 ISSN 0906-7590 Printed in Ireland - all rights reserved interpret this as indicating the presence of refugia during some p u t geological period”. The refugia are proposed to be mountain tops protruding above the inland ice sheet (nunatabs sensu stricto) and coastal refugia where ice calved into deep water (Dahl 1946, 1955, 1987). Implicit in the nunatak or refugial hypothesis is that the presumed refugial plant species have poor dispersal powers (Gjzrevoll 1963). The nunatak hypothesis thus predicts some spatial correspondence between plant Occurrences today and the occurrence of unglaciated areas. Dahl (1955) went as far as to consider “whether biogeography can indicate locations of the refuges where arctic-alpine biota might have survived the last glacial age. In the refuges, or in the neighbourhood, one might expect to find a concentration of rare plants.” ECOGRAPHY 193 (1996) An altcrnative historical hypothesis. the so-called squares regression (Martens and Nres 1989). to consider "tabula rasii" hypothesis. proposes that no plants sur- the question "is the hypothesis of survival on glacial vived the entire last glacial stage on unglaciated areas in nunataks necessary to explain the present-day patterns Norway and thus that they survived outside the margin of species richness of Norwegian mountain plants?'' of the ice sheet and subsequently spread into Norway iis deglaciation occurred and as climate ameliorated during the lute-glacial and post-glacial (Nordal 1987. Birks 1993).The patterns of species richness seen today Data are thus interpreted as primarily reflecting modem eco- The number of the 109 species mapped by Gjlerevoll logical conditions of altitude. climate, bedrock, and (1990) in each of 75 equally sized grid squares encomtopography. Following an extensive debate of the nuna- passing the whole of Norway (Fig. 1) was counted. All tak hypothesis, Fcgri (1963) asked "is centricity any- mapped extant records were used. Extinct, rejected, and thing more than one might expect from actual ecologic inexactly located records were excluded. The number of conditions'? Nobody has tried to give an objective an- species in a grid varies from I to 88. swer to this, but it is a fact that very few, if any. other The "predictor" variables used for each grid square areas in Scandinavia offer the same combination of are the same as in Birks (1993) - see Table 1 and Birks favourable bed-rock. climate, and topography. If this is (1993) for further details. For convenience in analysis enough to explain the distribution without recourse to and discussion the I 1 explanatory variables are grouped other factors. centricity loses much of its argumentative into four classes (Table 1) - geography and topogravalue". He also proposed "that biologists should take phy. bedrock geology. climate, and history (see Birks up the problems for some fresh thinking". 1993). The reasons and rationale for these groupings Birks (1993) took advantage of two recent develop- are discussed by Birks (1993). ments, one botanical and one statistical. to analyse statistically the present-day distributions of eight biogeographical groups of mountain plant species in Norway in relation to modern geography. topography, geology, climate, and the occurrence of unglaciated areas, defined solely on geological criteria. These analyses were designed to answer the question "is the hypothesis of survival on glacial nunataks necessary to explain the present-day distribution of Norwegian mountain plants?". The two recent developments that made such analyses possible are I ) the publication of detailed. up-to-date. and documented distribution maps of 109 mountain plant species in Norway (Gjarevoll 1990). and 2) the development of computer-intensive Monte Carlo permutation tests in regression and constrained ordination procedures (ter Braak 1990a, b, 1992. Manly 1991). These permit the evaluation of the statistical significance of the relationship between "response" variables (e.g. species occurrences. species richness) and "predictor" variables (e.g. environmental factors) when the data do not conform to the assumptions of classical statistical theory and methodology (Manly 1991). The statistical results presented in Birks (1993) all indicate that the nunatak hyopthesis is not required to explain the distribution and relative abundance of the 109 mountain species mapped by Gjlerevoll(l990) or of plant distributional groups long considered to be "glacial survivors'' in Norway, such as the west arctic, the bicentric, and the northern and southern unicentric groups (Dahl 1955, 1990). In this paper I focus solely on the patterns of mountain species richness, or diversity. in Norway. I take advantage of the two developments discussed above Fig. I. The number of mountain plant species. as mapped by qae and of a third statistical one. namely partial least Gjaprevoll (19%) in 75 grid s u r s in Noway. ECOGRAPHY 1 9 2 11996) Table I. Explanatory “predictor” variables recorded for each grid square and used in the statistical analyses. Type of variable Geography and topography Latitude Longitude Maximum elevation Land area in grid square Bedrock geology Abundance of schist and/or Iimeston e Climate Maximum summer temperature Continuous Continuous Categorical ( 5 500 m classes) Proportional Categorical (4 abundance classes) Continuous 1°C classes Continuous Categorical (4 lo00 mm classes) Continuous IoC classes Continuous 1°C classes Accumulated respiration Total annual precipitation Mean January temperature Mean July temperature History Unglachted areas Categorical (3 abundance classes) See Birks (1993) for further details. partial regression analyses (ter Braak 1988, Legendre 1993. Sokal and Rohlf 1995) were also done with area Statistical analyses were performed in an attempt to and area + latitude + longitude entered first (as “coanswer the following four questions: variables” in the CANOCO program) as these variables I ) Are any of the eleven variables (Table 1) Statisti- are well known predictors of species richness. In the cally significant explanatory variables in explaining the context of multiple regression, as implemented by patterns of species richness (Fig. I)? A multiple regres- CANOCO, a covariable here is simply a predictor sion analysis was done using all I1 explanatory vari- variable that is entered first into the regression model. ables with forward selection of variables (Miller 1990, The EFA and HFA series were repeated with these ter Braak 1990b). At each step the variable that adds variables entered first. In such analyses, the aim is to most to the explained variance in the richness data is estimate the amount of variance in species richness that selected and the statistical significance of that variable is explained by history, elevation, geology + elevation. tested by means of a Monte Carlo permutation test (ter geology history, climate + geology + elevation, hisBriak 1990b, 1992) using 999 unrestricted permuta- tory + climate + geology + elevation, etc. after the tions. The forward selection procedure is stopped when effects of land area within the grid squares, latitude. the additional effect of the chosen variable is not signifi- and longitude are considered first statistically. The cant at the a“ = a/v level (where a = 0.05, v = number statistical significance of each model was assessed by of multiple tests performed at each step in the forward Monte Carlo permutation tests (999 unrestricted perselection, namely 1,2,3, .... v), according to the Bonfer- mutations). roni method of correcting for multiple tests (Cooper 3) D e history (relative abundance of unglaciated os 1968, Legendre and Fortin 1989). areas) make a unique and statistically significant contri2) How much of the variance in the richness data is bution to the variance of the species-richness patterns explained by the four groups of predictor variables when the effects of variables operative today (bedrock, (Table l)? A series of multiple regressions was done. In geology, climate, etc.) are considered first and allowed the “Ecology First Analysis” (EFA series), the groups for statistically? The variance in the richness data was of explanatory variables were used in the order 1) decomposed into different components using partial geography topography, 2) geology geography regression analysis (Whittaker 1984, Borcard et al. topography, 3) climate + geology + geography + topo- 1992, Legendre 1993, ter Braak and Wiertz 1994). graphy, and 4) history + climate + geology + geo- Initially the variance was partitioned into three nongraphy topography, thereby defining four different independent components: 1) the variance explained by multiple regression model specifications (see Table 3). all 11 predictor variables, 2) the variance explained by In a second series, (“History First Analysis” - HFA), history alone, and 3) the unexplained variance. As the the order of groups of variables was 1) history, 2) Occurrence of unglaciated areas may, to some degree, geology history, 3) climate + geology history, 4) be related to bedrock geology, elevation, latitude, and geography + topography + climate + geology + history longitude, a more realistic variance decomposition is (see Birks (1993) for a discussion of the rationale for into four independent components: 1) the variance exadding these groups of explanatory variables in differ- plained by geography, topography, climate, and geolent orders into the regression models). Several series of ogy after taking account of unglaciated areas (history). Methods ECOGRAPHY 193 (1996) Table 2. Results of forward selection in multiple regression analysis to find a minimal set of statistically significant explanatory predictor variables among the eleven variables (Table I ) for the observed patterns of species richness. Only significant variables are shown ( p 5 0.05 with Bonferroni corrections for multiple tests) in order of selection. Explanatory variable Mean July temperature Mean January tcmperature Abundance of schist and/or limestone Maximum summer temperature Total model Percentage variance explained (R’x loo)+ 61 4 5 4 75 -0.78 -0.49 0.52 Regression coeficieritt -0.26 -0.36 + 0.27 -0.65 - 0.35 - P = Exact Monte Carlo significance level (ter Braak 1990a) r = Correlation coefficient = Regression coefficients of the regression of the response variable on standardised explanatory variables * = Additional explained variance at each step in the regression 2) the variance explained by history after taking account of geography, topography, climate, and geology, 3) the variance explained by history that covaries, to some extent, with geography, topography, climate, and geology, and 4) the unexplained variance. As area is often an important predictor of species richness, the variance partitionings were repeated with the effects of area allowed for statistically by entering area first into the podels. In all these analyses, a cubic trend-surface of latitude and longitude was used (Legendre 1990, Borcard et al. 1992) to ensure that complex spatial patterns requiring quadratic or cubic terms and interaction terms of their spatial coordinates were adequately modelled (Birks 1993). To avoid overfitting of explanatory variables, the nine terms of the cubic surface were screened by forward selection to retain only statistically significant variables, as identified by Monte Carlo permutation tests (999 unrestricted permutations; ter Braak 1990b). Only two terms had p s 0.05 (with Bonferroni correction) (latitude, longitude2) and. were included as spatial variables in the variance decompositions. 4) How well can the eleven explanatory variables (Table 1) and all the variables except history predict total species richness in the grid squares? In other words, what is the predictive value of the explanatory variables with and without history included? Partial least squares (PLS) regression (Martens and Nzes 1989) was used to answer this question. In PLS a large number of correlated explanatory variables are replaced by a few latent variables or orthogonal components chosen to have maximum covariance with the response variable and hence to maximise predictive power. These components are used in a regression of the response variable and the significance of each component is assessed by cross-validation on the basis of empirical predictive power (prediction error sum-of-squares, PRESS). PLS is related to ordinary least squares regression, principal components regression (PCR), and ridge regression (RR) (Stone and Brooks 1990, Sundberg 1993, de Jong and Farebrother 1994). However, PLS usually gives the lowest prediction error, as estimated ECOGRAPHY 1 9 3 (IY96) by the root mean square error of prediction (RMSEP) derived by the cross-validation procedure of “leaveone-out’’ jack-knifing (Martens and Nres 1989). With a data-set of 75 grid squares, PLS was done 75 times using a set of 74 squares, leaving out each square in turn. The regression model based on the 74 squares was applied to the one excluded grid to give a predicted species richness and, by subtraction from the observed value, a prediction error. The prediction errors are accumulated to give a leave-one-out root mean square error which is a consistent estimate of the true RMSEP (Marten and Nres 1993). PLS, like PCR and RR, are biased regression methods that guard against multicollinearity among explanatory vdriubles. Such techniques have, rather surprisingly, hardly been used in biogeography. Examples include McCoy and Connor (1976) (RR), Mauriello and Roskowski (1974) (RR), and Nilsson et al. (1994) (PLS). All computations were done with CANOCO version 3.12 (ter Braak 1990a. b) except for PLS that was done using CALI version 0.54 (Juggins and ter Braak unpubl.). It should be noted that, although CANOCO is primarily a program for multivariate data analysis, simple multiple regression with Monte Carlo permutation tests can be implemented in CANOCO as a redundancy analysis (RDA) with only one response variable and with appropriate scaling of fitted values (ter Braak 1990a). Ter Braak (1990a) shows how the multivariate methodology of RDA with one response variable reduces to standard multiple regression analysis (cf. Borcard et al. 1992). Results Forward selection of statistically significant predictor variables for a multiple regression model for species richness (Table 2) identifies mean July temperature as the major explanatory variable (61% variance explained), and with mean January temperature, the abundance of schist and/or limestone, and maximum 335 summer temperature (Dahl 1955) as minor explanatory variables. each explaining 4-5% variance only. The regression equation suggests, not surprisingly, that species richness of mountain plants in Norway decreases with high maximum summer, mean January, and mean July temperatures and increases with high amounts of schist and/or limestone. The model predicts that highest species richness will occur in areas of low mean and maximum summer and low mean winter temperatures and with an abundance of calcareous bedrock. Other variables, including history, make no statistically significant contribution (p > 0.05). The results of the “ecology first analysis” (EFA) and the “history first analysis” (HFA) series of regressions are given in Table 3. In the EFA series, geography and topography explain a large amount of the variance in species richness (73.5%). increasing to 85% when geology (6.3‘X), climate (5.1%1), and history (0.1%) are added. If the order of variable addition is changed, as in the HFA series, history by itself explains 7.6?4 of the variance but this is not statistically significant (p = 0.072). When geology is added, the variance in species richness explained increases to 3 I .6‘%1,and when climate is added 77.8% variance is explained. Addition of topography and latitude and longitude results in a small increase in variance (7.7%). When the effects of the amount of land area in each grid square are allowed for statistically (Table 3). the results for the EFA and HFA series of regressions are virtually unchanged. When the effects of area, latitude, and longitude are allowed for statistically (Table 3), variables such as elevation. geology, and climate still remain as the most important variables in explaining the observed patterns of species richness. The results of the EFA and HFA series of regressions and their partial counterparts (Table 3) consistently show that for the explanatory variables considered (Table 1). history (relative abundance of unglaciated areas) explains the smallest amount of variance (0.I 7.6%) in the species richness data. The amount explained is not, however, significant statistically (p = 0.072-0.083). Modem ecological variables such as bedrock geology, climate, topography, and geography are considerably more effective explanatory variables of species richness than history is. Results of the variance decomposition are given in Tables 4 and 5. In none of the analyses (history by itself (Table 41, history after taking account of modem ecological factors (Table 5), or history after taking account of modem ecological factors when the effects of land area are allowed for statistically (Table 5) does the ) history variable contribute a statistically significant component of variance (p = 0.072.0.532, 0.381, respectively) in the species-richness patterns. Modem ecological variables account for over 75% of the variance in species richness. There is a small component (7.5%) of variance explained by ecological variables that covary 336 with the history variable. As discussed by Birks (1993). this common variation could possibly result from areas of deeply weathered bedrock having a higher species richness than other areas. More likely, it could be noncausal and may simply result from the spatial coincidence of unglaciated areas with high elevations, western coastal areas, and certain types of bedrock. hence the description “ecology” covarying with history ( = unglaciated areas). The unexplained variance is low (15%). Additional factors that might help explain further the patterns in species richness include local soil factors, maximum forest extent during the postglacial, topographical diversity, biotic factors, and recording effort. The overall conclusion from the variance partitionings is that present-day patterns of species richness are largely explained by modem ecological variables and that there is no statistically significant explanatory contribution from the history variable. Partial least squares regression results (Table 6) show that the lowest RMSEP, as assessed by leave-one-out cross-validation occurs with 4 PLS components irrespective of whether the history variable is included or excluded. The predictive models (Fig. 2) are good, with a R’ between observed species richness and predicted species richness in leave-one-out jack-knifing of 0.79 (r = 0.89). There is no significant difference in the predictive abilities of the models with or without the history variable included (RMSEP = 10.99 and 10.90, respectively). The PLS models (Fig. 2) show that species richness is well modelled and predicted by the l l predictor variables (Table I ) but that the history variable does not improve the predictions. In fact its inclusion results in a very small decrease in the predictive power of the PLS model, raising the RMSEP by 0.09! Discussion The results of the statistical analyses presented here provide no reason for suggesting that the hypothesis of plant survival on glacial nunataks is necessary to explain the present-day patterns of species richness of Norwegian mountain plants. All the analyses are consistent in suggesting that there is no statistically significant contribution from the history variable irrespective of whether the effects of modem topography, geology, geography, and climate are considered first (cf. Birks 1993). The observed patterns of species richness (Fig. 1) are well explained by modern geology, climate, and topography, a view first presented by Blytt (1876) and repeated by Fsgri (1963) and Berg (1963) but frequently disregarded in favour of the nunatak hypothesis (e.g. Gjarevoll 1990, Dahl 1990). The results presented here and in Birks (1993) provide an answer to Fzgri’s (1963) question “is centricity anything more ECOGRAPHY 193 (1996) Table 3. Percentages of variance in species richness explained by groups of predictor variables in (partial) multiple regression analysis in the “Ecology First Analysis”(EFA) and the ”History First Analysis” (HFA) series of regression models. The change in R’ as groups of explanatory variables are added into the regression is also listed, along with the statistical significance (p) of each overall regression model. Analysis Explanatory variables included in model Explanatory variables included initially (covariables) in model Percentage variance explained Change in R- (R’) EFA EFA 84.9 E FA 85.0 .................................................. E FA H FA H FA H FA H FA H FA , . Geography topography As above + geology As above + climate As above+ history 6.3 5. I 0.1 0.00I ... ...... ........................................... EFA E FA Elevation + latitude+ longitude As above+ geology As above+ climate As above+ History Area Area Area Area Area Area Area Area History As above+ geology As above+ climate As above+ topography As above+ fAeograPhY ....... 24.0 445.2 3.7 4.0 ..... 0.00I .............. ......... E FA EFA ...... H FA H FA H FA H FA ........................................... History As above+ !J~h3Y As above+ climate As above+ elevation + latitude+ longitude Elevation As above+ geology As above+ climate As above+ history History As above+ geology As above+ climate As above+ elevation ......... ........ 0.00I 0.00I ...... ............. EFA EFA EFA EFA ..................... Area, latitude, longitude A5 above .... ... ..... As above As above Area, latitude, longitude As above As above As above ...... H FA H FA ................... ............................... ...... H FA H FA p = Exact Monte Carlo significance level for each overall model as assessed by Monte Carlo mutation tests (999 unrestricted permutations) (ter Braak 1990a. b). It is the significance level of R’ for each overarregression model. It is not the significance level for the change in R’ as groups of explanatory variables are added into the regression models. ECOGRAPHY 1 9 3 (1996) Table 4. Variance decomposition into I ) total variance explained by all explanatory variables including statistically significant terms of a cubic trend-surface of latitude and longitude 2) variance explained by history alone, and 3) the total unexplained variance in species richness. The statistical significance (p) of the explained components was assessed by Monte Carlo permutation tests (999 unrestricted permutations). Note that as History is included in the Total explained component of variance, the column sum exceeds 100?!1. ‘% Table 6. Predictive abilities of the explanatory variables listed in Table I in estimating species richness in relation to the number of PLS components. The abilities are assessed by apparent RMSE. apparent R2, leave-one-out RMSEP, and leave-one-out R2 (see ter Braak and Juggins (1993) for details). All 1 1 variables PLS components RMSE R2 RMSEP R2 (leavesne-out) Total explained variance Unexplained variance History I5 All variables excluding history PLS components RMSE R2 RMSEP R2 (leavesne-out) than one might expect from actual ecological condi0.12 12.01 0.75 12.62 tions?’ The statistical results suggest that the centric 1 0.77 10.50 0.81 11.33 patterns in species richness are indeed nothing more 2 0.19 3 9.90 0.83 11.05 than one might predict from the modem topography, 4 0.19 9.51 0.84 10.90* climate, and geology of Norway. The nunatak hypothe- 5 0.19 9.43 0.84 10.92 0.79 9.32 0.85 10.89 sis as an explanation for the observed present-day 6 patterns of species richness and distributions of moun=model with lowest RMSEP tain plants is an example of not maintaining the critical distinction in biogeography between observed patterns and inferred processes, and of an apparent disregard conditions result in a range of natural disturbances and for alternative, simpler explanatory hypotheses. The open habitats resulting from solifluction processes, a patterns of modem plant distributions were described variety of open spring and flush habitats, an abundance in terms of the assumed causal processes and were used of open screes, wind-blasted plateaux, and late snowto suggest the existence of unglaciated areas (e.g. Dahl beds, and thus a high habitat diversity. High habitat 1955). These areas were then used to “explain” the diversity commonly results in a high species richness observed distribution patterns (e.g. Gjzrevoll 1963, (Williamson 1988, Hart and Horwitz 1991). Nordhagen 1963). An increasing body of palaeobotanical evidence It is clear from Fig. 1 that certain areas of Norway (Birks 1994) independently indicates it is not necessary are richer in mountain plant species than others. Multi- to invoke refugial survival to explain the present-day ple regression analysis (Table 2) identifies those vari- distribution of Norwegian mountain plants. Many ables that best explain, in a statistical sense, the mountain species grew beyond the ice-sheet margins in species-richness patterns. Besides low mean January, the last glaciation and were clearly capable of rapid mean July, and maximum summer temperatures and an migration as new habitats became available soon after abundance of calcareous schist or limestone, the spe- the ice melted. They were able to colonise their present cies-rich mountain areas are also extensive and high mountain habitats, but their widespread lowland lateand often have gentle, rather subdued slopes. These glacial distributions were subsequently restricted by Table 5. Variance decomposition into 1) total variance explained by the climate, geology, geography, and topography variables after taking account of the history variable, 2) variance explained by the history variable after taking account of geography, topography, climate, and geology (“ecology”), 3) variance explained by the history variable that is itself influenced by and covanes with climate, geology, geography, and topography (“ecology”), and 4) total unexplained variance in species richness. Statistically significant terms of a cubic trend-surface of latitude and longitude were included in the geography variables. In a second analysis the effects of land area within each grid square were partialled out by entering area into the regression model first. The statistical significance (p) of component 2 (history after taking account of other explanatory variables) was assessed by Monte Carlo permutation tests (999 unrestricted permutations). Component “Ecology” aRer taking account of history History after taking account of “ecology” “Ecology” covarying with history Unexplained 338 Percentage variance Effects of area allowed for statistically ECOGRAPHY I93 (1996) . . .=. . . . r A rA -i -w . . .. * . a2 .rA rA ._ L . I B 0 0-b -1 2 a Observed species richness Observed species richness Fig. 2. Plot of predicted species richness, as estimated by leave-one-out jack-knifing and a 4component PLS model. against observed species richness when (a) all eleven predictor variables are included in the PLS regression and (b) all predictor variables with the exception of the history variable (unglaciated areas) are included in the PLS regression. post-glacial climatic warming, by the resulting competition from forest development, and by soil stabilisation and deterioration through leaching and podsolisation (Pigott and Walters 1954, Fsgri 1963). Although biogeographers have rarely been able to resist the temptation of interpreting hotspots of species richness as resulting from survival in glacial refugia (e.g. Dahl 1990), all such refugial hypotheses have turned out to be unproven or unnecessary when examined statistically, palaeobotanically, or biosystematically (see Birks 1993). Examples of such statistical analyses include Endler (1982a, b), and Beven et al. (l984), and Birks (1993). With detailed biogeographical data and statistical techniques of (partial) regression and constrained ordination and Monte Carlo permutation tests to evaluate the statistical significance of the statistical results, biogeographers have powerful means of exploring patterns in biodiversity data and of considering and testing alternative hypotheses to explain patterns in species richness. I am indebted to Y. Haila for the invitation to participate in the 1994 Pori Workshop on Quantitative surveys in biodiversity evaluation, to M. P. Austin, H. H. Birks. A. 0. Nicholls, and Y. Haila for helpful discussions, to P. Legendre and C. J. F. ter Braak for valuable comments as journal reviewers, to S. M. Peglar for drafting Fig. I. and to A. B. Ruud Hage for word-processing the manuscript. Acknoidedgemenrs ECOGRAPHY I93 (19961 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Ecography Wiley

Statistical approaches to interpreting diversity patterns in the Norwegian mountain flora

Ecography , Volume 19 (3) – Jan 1, 1996

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Copyright © 1996 Wiley Subscription Services, Inc., A Wiley Company
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1600-0587
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Abstract

Birks. H. J. B. 1996. Statistical approaches to interpreting diversity patterns in the Norwegian mountain flora. - Ecography 19: 332-340. The richness of Norwegian mountain plants in 75 .grid squares is mapped from published distributional data for 109 species. Eleven explanatory variables representing bedrock geology, geography and topography. climate. and history (relative abundance of unglaciated areas) for each square are used in multiple regression analysis with associated Monte Carlo permutation tests to find statistically significant prcdictor variables for species richness. The variance in richness explained by the four major groups of explanatory vuriables is established by (partial) multiple regression analysis in which the groups of predictors are entered in direrent orders. The variance in species richness explained by the predictor variables is partitioned into four independent components. A predictive model for species richness using partial least squm regression and all explanatory variables has a coefficientof determination (R2)of 0.79. The statistical results consistently show that species-richness patterns are well expliained by modernday factors such as climate, geology, elevation, and geography without recourse to historical variables. The nunatak hypothesis of plant survival on unglaciated areas within Noway does not explain the observed richness patterns when modern ecologicial factors are considered first. The nunatak hypothesis thus appears to be redundant, a view supported by recent palaeobotanicil. biosystematical, and evolutionary studies. H . J . B. Birks. Bor. Inst.. Uniu. of Berxen. Alliguren 41. N-5007Bergen. Norwuy und Encironnrental Cliunge Res. Centre, Depr of Geography, Uniu. College London. 26. Bedjord Wuy, London. U.K. WClH OAP. Patterns of species richness (“biodiversity”) of Norwegian mountain plants show a remarkable concentration of diversity in two areas of Norway. High diversity occurs in northern Norway and in southerncentral Norway, whereas there is a marked decrease in richness between these two areas and in southernmost Norway (Fig. 1). This bicentric concentration of species richness in two areas (“hotspots” of biodiversity) is most commonly interpreted as a result of the survival of mountain plant species during at least the last glacial stage in unglaciated areas (“refugia”) in or near the two regions where species richness is highest (e.g. Dahl 1955, 1987, 1990, Nordhagen 1963). Dahl (1990) proposed that “when a remarkable concentration of disjunct and/or locally endemic species is observed it is tempting to Accepted 21 September 1995 Copyright 0 ECOGRAPHY 1996 ISSN 0906-7590 Printed in Ireland - all rights reserved interpret this as indicating the presence of refugia during some p u t geological period”. The refugia are proposed to be mountain tops protruding above the inland ice sheet (nunatabs sensu stricto) and coastal refugia where ice calved into deep water (Dahl 1946, 1955, 1987). Implicit in the nunatak or refugial hypothesis is that the presumed refugial plant species have poor dispersal powers (Gjzrevoll 1963). The nunatak hypothesis thus predicts some spatial correspondence between plant Occurrences today and the occurrence of unglaciated areas. Dahl (1955) went as far as to consider “whether biogeography can indicate locations of the refuges where arctic-alpine biota might have survived the last glacial age. In the refuges, or in the neighbourhood, one might expect to find a concentration of rare plants.” ECOGRAPHY 193 (1996) An altcrnative historical hypothesis. the so-called squares regression (Martens and Nres 1989). to consider "tabula rasii" hypothesis. proposes that no plants sur- the question "is the hypothesis of survival on glacial vived the entire last glacial stage on unglaciated areas in nunataks necessary to explain the present-day patterns Norway and thus that they survived outside the margin of species richness of Norwegian mountain plants?'' of the ice sheet and subsequently spread into Norway iis deglaciation occurred and as climate ameliorated during the lute-glacial and post-glacial (Nordal 1987. Birks 1993).The patterns of species richness seen today Data are thus interpreted as primarily reflecting modem eco- The number of the 109 species mapped by Gjlerevoll logical conditions of altitude. climate, bedrock, and (1990) in each of 75 equally sized grid squares encomtopography. Following an extensive debate of the nuna- passing the whole of Norway (Fig. 1) was counted. All tak hypothesis, Fcgri (1963) asked "is centricity any- mapped extant records were used. Extinct, rejected, and thing more than one might expect from actual ecologic inexactly located records were excluded. The number of conditions'? Nobody has tried to give an objective an- species in a grid varies from I to 88. swer to this, but it is a fact that very few, if any. other The "predictor" variables used for each grid square areas in Scandinavia offer the same combination of are the same as in Birks (1993) - see Table 1 and Birks favourable bed-rock. climate, and topography. If this is (1993) for further details. For convenience in analysis enough to explain the distribution without recourse to and discussion the I 1 explanatory variables are grouped other factors. centricity loses much of its argumentative into four classes (Table 1) - geography and topogravalue". He also proposed "that biologists should take phy. bedrock geology. climate, and history (see Birks up the problems for some fresh thinking". 1993). The reasons and rationale for these groupings Birks (1993) took advantage of two recent develop- are discussed by Birks (1993). ments, one botanical and one statistical. to analyse statistically the present-day distributions of eight biogeographical groups of mountain plant species in Norway in relation to modern geography. topography, geology, climate, and the occurrence of unglaciated areas, defined solely on geological criteria. These analyses were designed to answer the question "is the hypothesis of survival on glacial nunataks necessary to explain the present-day distribution of Norwegian mountain plants?". The two recent developments that made such analyses possible are I ) the publication of detailed. up-to-date. and documented distribution maps of 109 mountain plant species in Norway (Gjarevoll 1990). and 2) the development of computer-intensive Monte Carlo permutation tests in regression and constrained ordination procedures (ter Braak 1990a, b, 1992. Manly 1991). These permit the evaluation of the statistical significance of the relationship between "response" variables (e.g. species occurrences. species richness) and "predictor" variables (e.g. environmental factors) when the data do not conform to the assumptions of classical statistical theory and methodology (Manly 1991). The statistical results presented in Birks (1993) all indicate that the nunatak hyopthesis is not required to explain the distribution and relative abundance of the 109 mountain species mapped by Gjlerevoll(l990) or of plant distributional groups long considered to be "glacial survivors'' in Norway, such as the west arctic, the bicentric, and the northern and southern unicentric groups (Dahl 1955, 1990). In this paper I focus solely on the patterns of mountain species richness, or diversity. in Norway. I take advantage of the two developments discussed above Fig. I. The number of mountain plant species. as mapped by qae and of a third statistical one. namely partial least Gjaprevoll (19%) in 75 grid s u r s in Noway. ECOGRAPHY 1 9 2 11996) Table I. Explanatory “predictor” variables recorded for each grid square and used in the statistical analyses. Type of variable Geography and topography Latitude Longitude Maximum elevation Land area in grid square Bedrock geology Abundance of schist and/or Iimeston e Climate Maximum summer temperature Continuous Continuous Categorical ( 5 500 m classes) Proportional Categorical (4 abundance classes) Continuous 1°C classes Continuous Categorical (4 lo00 mm classes) Continuous IoC classes Continuous 1°C classes Accumulated respiration Total annual precipitation Mean January temperature Mean July temperature History Unglachted areas Categorical (3 abundance classes) See Birks (1993) for further details. partial regression analyses (ter Braak 1988, Legendre 1993. Sokal and Rohlf 1995) were also done with area Statistical analyses were performed in an attempt to and area + latitude + longitude entered first (as “coanswer the following four questions: variables” in the CANOCO program) as these variables I ) Are any of the eleven variables (Table 1) Statisti- are well known predictors of species richness. In the cally significant explanatory variables in explaining the context of multiple regression, as implemented by patterns of species richness (Fig. I)? A multiple regres- CANOCO, a covariable here is simply a predictor sion analysis was done using all I1 explanatory vari- variable that is entered first into the regression model. ables with forward selection of variables (Miller 1990, The EFA and HFA series were repeated with these ter Braak 1990b). At each step the variable that adds variables entered first. In such analyses, the aim is to most to the explained variance in the richness data is estimate the amount of variance in species richness that selected and the statistical significance of that variable is explained by history, elevation, geology + elevation. tested by means of a Monte Carlo permutation test (ter geology history, climate + geology + elevation, hisBriak 1990b, 1992) using 999 unrestricted permuta- tory + climate + geology + elevation, etc. after the tions. The forward selection procedure is stopped when effects of land area within the grid squares, latitude. the additional effect of the chosen variable is not signifi- and longitude are considered first statistically. The cant at the a“ = a/v level (where a = 0.05, v = number statistical significance of each model was assessed by of multiple tests performed at each step in the forward Monte Carlo permutation tests (999 unrestricted perselection, namely 1,2,3, .... v), according to the Bonfer- mutations). roni method of correcting for multiple tests (Cooper 3) D e history (relative abundance of unglaciated os 1968, Legendre and Fortin 1989). areas) make a unique and statistically significant contri2) How much of the variance in the richness data is bution to the variance of the species-richness patterns explained by the four groups of predictor variables when the effects of variables operative today (bedrock, (Table l)? A series of multiple regressions was done. In geology, climate, etc.) are considered first and allowed the “Ecology First Analysis” (EFA series), the groups for statistically? The variance in the richness data was of explanatory variables were used in the order 1) decomposed into different components using partial geography topography, 2) geology geography regression analysis (Whittaker 1984, Borcard et al. topography, 3) climate + geology + geography + topo- 1992, Legendre 1993, ter Braak and Wiertz 1994). graphy, and 4) history + climate + geology + geo- Initially the variance was partitioned into three nongraphy topography, thereby defining four different independent components: 1) the variance explained by multiple regression model specifications (see Table 3). all 11 predictor variables, 2) the variance explained by In a second series, (“History First Analysis” - HFA), history alone, and 3) the unexplained variance. As the the order of groups of variables was 1) history, 2) Occurrence of unglaciated areas may, to some degree, geology history, 3) climate + geology history, 4) be related to bedrock geology, elevation, latitude, and geography + topography + climate + geology + history longitude, a more realistic variance decomposition is (see Birks (1993) for a discussion of the rationale for into four independent components: 1) the variance exadding these groups of explanatory variables in differ- plained by geography, topography, climate, and geolent orders into the regression models). Several series of ogy after taking account of unglaciated areas (history). Methods ECOGRAPHY 193 (1996) Table 2. Results of forward selection in multiple regression analysis to find a minimal set of statistically significant explanatory predictor variables among the eleven variables (Table I ) for the observed patterns of species richness. Only significant variables are shown ( p 5 0.05 with Bonferroni corrections for multiple tests) in order of selection. Explanatory variable Mean July temperature Mean January tcmperature Abundance of schist and/or limestone Maximum summer temperature Total model Percentage variance explained (R’x loo)+ 61 4 5 4 75 -0.78 -0.49 0.52 Regression coeficieritt -0.26 -0.36 + 0.27 -0.65 - 0.35 - P = Exact Monte Carlo significance level (ter Braak 1990a) r = Correlation coefficient = Regression coefficients of the regression of the response variable on standardised explanatory variables * = Additional explained variance at each step in the regression 2) the variance explained by history after taking account of geography, topography, climate, and geology, 3) the variance explained by history that covaries, to some extent, with geography, topography, climate, and geology, and 4) the unexplained variance. As area is often an important predictor of species richness, the variance partitionings were repeated with the effects of area allowed for statistically by entering area first into the podels. In all these analyses, a cubic trend-surface of latitude and longitude was used (Legendre 1990, Borcard et al. 1992) to ensure that complex spatial patterns requiring quadratic or cubic terms and interaction terms of their spatial coordinates were adequately modelled (Birks 1993). To avoid overfitting of explanatory variables, the nine terms of the cubic surface were screened by forward selection to retain only statistically significant variables, as identified by Monte Carlo permutation tests (999 unrestricted permutations; ter Braak 1990b). Only two terms had p s 0.05 (with Bonferroni correction) (latitude, longitude2) and. were included as spatial variables in the variance decompositions. 4) How well can the eleven explanatory variables (Table 1) and all the variables except history predict total species richness in the grid squares? In other words, what is the predictive value of the explanatory variables with and without history included? Partial least squares (PLS) regression (Martens and Nzes 1989) was used to answer this question. In PLS a large number of correlated explanatory variables are replaced by a few latent variables or orthogonal components chosen to have maximum covariance with the response variable and hence to maximise predictive power. These components are used in a regression of the response variable and the significance of each component is assessed by cross-validation on the basis of empirical predictive power (prediction error sum-of-squares, PRESS). PLS is related to ordinary least squares regression, principal components regression (PCR), and ridge regression (RR) (Stone and Brooks 1990, Sundberg 1993, de Jong and Farebrother 1994). However, PLS usually gives the lowest prediction error, as estimated ECOGRAPHY 1 9 3 (IY96) by the root mean square error of prediction (RMSEP) derived by the cross-validation procedure of “leaveone-out’’ jack-knifing (Martens and Nres 1989). With a data-set of 75 grid squares, PLS was done 75 times using a set of 74 squares, leaving out each square in turn. The regression model based on the 74 squares was applied to the one excluded grid to give a predicted species richness and, by subtraction from the observed value, a prediction error. The prediction errors are accumulated to give a leave-one-out root mean square error which is a consistent estimate of the true RMSEP (Marten and Nres 1993). PLS, like PCR and RR, are biased regression methods that guard against multicollinearity among explanatory vdriubles. Such techniques have, rather surprisingly, hardly been used in biogeography. Examples include McCoy and Connor (1976) (RR), Mauriello and Roskowski (1974) (RR), and Nilsson et al. (1994) (PLS). All computations were done with CANOCO version 3.12 (ter Braak 1990a. b) except for PLS that was done using CALI version 0.54 (Juggins and ter Braak unpubl.). It should be noted that, although CANOCO is primarily a program for multivariate data analysis, simple multiple regression with Monte Carlo permutation tests can be implemented in CANOCO as a redundancy analysis (RDA) with only one response variable and with appropriate scaling of fitted values (ter Braak 1990a). Ter Braak (1990a) shows how the multivariate methodology of RDA with one response variable reduces to standard multiple regression analysis (cf. Borcard et al. 1992). Results Forward selection of statistically significant predictor variables for a multiple regression model for species richness (Table 2) identifies mean July temperature as the major explanatory variable (61% variance explained), and with mean January temperature, the abundance of schist and/or limestone, and maximum 335 summer temperature (Dahl 1955) as minor explanatory variables. each explaining 4-5% variance only. The regression equation suggests, not surprisingly, that species richness of mountain plants in Norway decreases with high maximum summer, mean January, and mean July temperatures and increases with high amounts of schist and/or limestone. The model predicts that highest species richness will occur in areas of low mean and maximum summer and low mean winter temperatures and with an abundance of calcareous bedrock. Other variables, including history, make no statistically significant contribution (p > 0.05). The results of the “ecology first analysis” (EFA) and the “history first analysis” (HFA) series of regressions are given in Table 3. In the EFA series, geography and topography explain a large amount of the variance in species richness (73.5%). increasing to 85% when geology (6.3‘X), climate (5.1%1), and history (0.1%) are added. If the order of variable addition is changed, as in the HFA series, history by itself explains 7.6?4 of the variance but this is not statistically significant (p = 0.072). When geology is added, the variance in species richness explained increases to 3 I .6‘%1,and when climate is added 77.8% variance is explained. Addition of topography and latitude and longitude results in a small increase in variance (7.7%). When the effects of the amount of land area in each grid square are allowed for statistically (Table 3). the results for the EFA and HFA series of regressions are virtually unchanged. When the effects of area, latitude, and longitude are allowed for statistically (Table 3), variables such as elevation. geology, and climate still remain as the most important variables in explaining the observed patterns of species richness. The results of the EFA and HFA series of regressions and their partial counterparts (Table 3) consistently show that for the explanatory variables considered (Table 1). history (relative abundance of unglaciated areas) explains the smallest amount of variance (0.I 7.6%) in the species richness data. The amount explained is not, however, significant statistically (p = 0.072-0.083). Modem ecological variables such as bedrock geology, climate, topography, and geography are considerably more effective explanatory variables of species richness than history is. Results of the variance decomposition are given in Tables 4 and 5. In none of the analyses (history by itself (Table 41, history after taking account of modem ecological factors (Table 5), or history after taking account of modem ecological factors when the effects of land area are allowed for statistically (Table 5) does the ) history variable contribute a statistically significant component of variance (p = 0.072.0.532, 0.381, respectively) in the species-richness patterns. Modem ecological variables account for over 75% of the variance in species richness. There is a small component (7.5%) of variance explained by ecological variables that covary 336 with the history variable. As discussed by Birks (1993). this common variation could possibly result from areas of deeply weathered bedrock having a higher species richness than other areas. More likely, it could be noncausal and may simply result from the spatial coincidence of unglaciated areas with high elevations, western coastal areas, and certain types of bedrock. hence the description “ecology” covarying with history ( = unglaciated areas). The unexplained variance is low (15%). Additional factors that might help explain further the patterns in species richness include local soil factors, maximum forest extent during the postglacial, topographical diversity, biotic factors, and recording effort. The overall conclusion from the variance partitionings is that present-day patterns of species richness are largely explained by modem ecological variables and that there is no statistically significant explanatory contribution from the history variable. Partial least squares regression results (Table 6) show that the lowest RMSEP, as assessed by leave-one-out cross-validation occurs with 4 PLS components irrespective of whether the history variable is included or excluded. The predictive models (Fig. 2) are good, with a R’ between observed species richness and predicted species richness in leave-one-out jack-knifing of 0.79 (r = 0.89). There is no significant difference in the predictive abilities of the models with or without the history variable included (RMSEP = 10.99 and 10.90, respectively). The PLS models (Fig. 2) show that species richness is well modelled and predicted by the l l predictor variables (Table I ) but that the history variable does not improve the predictions. In fact its inclusion results in a very small decrease in the predictive power of the PLS model, raising the RMSEP by 0.09! Discussion The results of the statistical analyses presented here provide no reason for suggesting that the hypothesis of plant survival on glacial nunataks is necessary to explain the present-day patterns of species richness of Norwegian mountain plants. All the analyses are consistent in suggesting that there is no statistically significant contribution from the history variable irrespective of whether the effects of modem topography, geology, geography, and climate are considered first (cf. Birks 1993). The observed patterns of species richness (Fig. 1) are well explained by modern geology, climate, and topography, a view first presented by Blytt (1876) and repeated by Fsgri (1963) and Berg (1963) but frequently disregarded in favour of the nunatak hypothesis (e.g. Gjarevoll 1990, Dahl 1990). The results presented here and in Birks (1993) provide an answer to Fzgri’s (1963) question “is centricity anything more ECOGRAPHY 193 (1996) Table 3. Percentages of variance in species richness explained by groups of predictor variables in (partial) multiple regression analysis in the “Ecology First Analysis”(EFA) and the ”History First Analysis” (HFA) series of regression models. The change in R’ as groups of explanatory variables are added into the regression is also listed, along with the statistical significance (p) of each overall regression model. Analysis Explanatory variables included in model Explanatory variables included initially (covariables) in model Percentage variance explained Change in R- (R’) EFA EFA 84.9 E FA 85.0 .................................................. E FA H FA H FA H FA H FA H FA , . Geography topography As above + geology As above + climate As above+ history 6.3 5. I 0.1 0.00I ... ...... ........................................... EFA E FA Elevation + latitude+ longitude As above+ geology As above+ climate As above+ History Area Area Area Area Area Area Area Area History As above+ geology As above+ climate As above+ topography As above+ fAeograPhY ....... 24.0 445.2 3.7 4.0 ..... 0.00I .............. ......... E FA EFA ...... H FA H FA H FA H FA ........................................... History As above+ !J~h3Y As above+ climate As above+ elevation + latitude+ longitude Elevation As above+ geology As above+ climate As above+ history History As above+ geology As above+ climate As above+ elevation ......... ........ 0.00I 0.00I ...... ............. EFA EFA EFA EFA ..................... Area, latitude, longitude A5 above .... ... ..... As above As above Area, latitude, longitude As above As above As above ...... H FA H FA ................... ............................... ...... H FA H FA p = Exact Monte Carlo significance level for each overall model as assessed by Monte Carlo mutation tests (999 unrestricted permutations) (ter Braak 1990a. b). It is the significance level of R’ for each overarregression model. It is not the significance level for the change in R’ as groups of explanatory variables are added into the regression models. ECOGRAPHY 1 9 3 (1996) Table 4. Variance decomposition into I ) total variance explained by all explanatory variables including statistically significant terms of a cubic trend-surface of latitude and longitude 2) variance explained by history alone, and 3) the total unexplained variance in species richness. The statistical significance (p) of the explained components was assessed by Monte Carlo permutation tests (999 unrestricted permutations). Note that as History is included in the Total explained component of variance, the column sum exceeds 100?!1. ‘% Table 6. Predictive abilities of the explanatory variables listed in Table I in estimating species richness in relation to the number of PLS components. The abilities are assessed by apparent RMSE. apparent R2, leave-one-out RMSEP, and leave-one-out R2 (see ter Braak and Juggins (1993) for details). All 1 1 variables PLS components RMSE R2 RMSEP R2 (leavesne-out) Total explained variance Unexplained variance History I5 All variables excluding history PLS components RMSE R2 RMSEP R2 (leavesne-out) than one might expect from actual ecological condi0.12 12.01 0.75 12.62 tions?’ The statistical results suggest that the centric 1 0.77 10.50 0.81 11.33 patterns in species richness are indeed nothing more 2 0.19 3 9.90 0.83 11.05 than one might predict from the modem topography, 4 0.19 9.51 0.84 10.90* climate, and geology of Norway. The nunatak hypothe- 5 0.19 9.43 0.84 10.92 0.79 9.32 0.85 10.89 sis as an explanation for the observed present-day 6 patterns of species richness and distributions of moun=model with lowest RMSEP tain plants is an example of not maintaining the critical distinction in biogeography between observed patterns and inferred processes, and of an apparent disregard conditions result in a range of natural disturbances and for alternative, simpler explanatory hypotheses. The open habitats resulting from solifluction processes, a patterns of modem plant distributions were described variety of open spring and flush habitats, an abundance in terms of the assumed causal processes and were used of open screes, wind-blasted plateaux, and late snowto suggest the existence of unglaciated areas (e.g. Dahl beds, and thus a high habitat diversity. High habitat 1955). These areas were then used to “explain” the diversity commonly results in a high species richness observed distribution patterns (e.g. Gjzrevoll 1963, (Williamson 1988, Hart and Horwitz 1991). Nordhagen 1963). An increasing body of palaeobotanical evidence It is clear from Fig. 1 that certain areas of Norway (Birks 1994) independently indicates it is not necessary are richer in mountain plant species than others. Multi- to invoke refugial survival to explain the present-day ple regression analysis (Table 2) identifies those vari- distribution of Norwegian mountain plants. Many ables that best explain, in a statistical sense, the mountain species grew beyond the ice-sheet margins in species-richness patterns. Besides low mean January, the last glaciation and were clearly capable of rapid mean July, and maximum summer temperatures and an migration as new habitats became available soon after abundance of calcareous schist or limestone, the spe- the ice melted. They were able to colonise their present cies-rich mountain areas are also extensive and high mountain habitats, but their widespread lowland lateand often have gentle, rather subdued slopes. These glacial distributions were subsequently restricted by Table 5. Variance decomposition into 1) total variance explained by the climate, geology, geography, and topography variables after taking account of the history variable, 2) variance explained by the history variable after taking account of geography, topography, climate, and geology (“ecology”), 3) variance explained by the history variable that is itself influenced by and covanes with climate, geology, geography, and topography (“ecology”), and 4) total unexplained variance in species richness. Statistically significant terms of a cubic trend-surface of latitude and longitude were included in the geography variables. In a second analysis the effects of land area within each grid square were partialled out by entering area into the regression model first. The statistical significance (p) of component 2 (history after taking account of other explanatory variables) was assessed by Monte Carlo permutation tests (999 unrestricted permutations). Component “Ecology” aRer taking account of history History after taking account of “ecology” “Ecology” covarying with history Unexplained 338 Percentage variance Effects of area allowed for statistically ECOGRAPHY I93 (1996) . . .=. . . . r A rA -i -w . . .. * . a2 .rA rA ._ L . I B 0 0-b -1 2 a Observed species richness Observed species richness Fig. 2. Plot of predicted species richness, as estimated by leave-one-out jack-knifing and a 4component PLS model. against observed species richness when (a) all eleven predictor variables are included in the PLS regression and (b) all predictor variables with the exception of the history variable (unglaciated areas) are included in the PLS regression. post-glacial climatic warming, by the resulting competition from forest development, and by soil stabilisation and deterioration through leaching and podsolisation (Pigott and Walters 1954, Fsgri 1963). Although biogeographers have rarely been able to resist the temptation of interpreting hotspots of species richness as resulting from survival in glacial refugia (e.g. Dahl 1990), all such refugial hypotheses have turned out to be unproven or unnecessary when examined statistically, palaeobotanically, or biosystematically (see Birks 1993). Examples of such statistical analyses include Endler (1982a, b), and Beven et al. (l984), and Birks (1993). With detailed biogeographical data and statistical techniques of (partial) regression and constrained ordination and Monte Carlo permutation tests to evaluate the statistical significance of the statistical results, biogeographers have powerful means of exploring patterns in biodiversity data and of considering and testing alternative hypotheses to explain patterns in species richness. I am indebted to Y. Haila for the invitation to participate in the 1994 Pori Workshop on Quantitative surveys in biodiversity evaluation, to M. P. Austin, H. H. Birks. A. 0. Nicholls, and Y. Haila for helpful discussions, to P. Legendre and C. J. F. ter Braak for valuable comments as journal reviewers, to S. M. Peglar for drafting Fig. I. and to A. B. Ruud Hage for word-processing the manuscript. Acknoidedgemenrs ECOGRAPHY I93 (19961

Journal

EcographyWiley

Published: Jan 1, 1996

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