Spatial ordination of vegetation data using a generalization of Wartenberg's multivariate spatial correlation

Question: Are there spatial structures in the composition of plant communities? Methods: Identification and measurement of spatial structures is a topic of great interest in plant ecology. Univariate measurements of spatial autocorrelation such as Moran's I and Geary's c are widely used, but extensions to the multivariate case (i.e. multi‐species) are rare. Here, we propose a multivariate spatial analysis based on Moran's I (MULTISPATI) by introducing a row‐sum standardized spatial weight matrix in the statistical triplet notation. This analysis, which is a generalization of Wartenberg's approach to multivariate spatial correlation, would imply a compromise between the relations among many variables (multivariate analysis) and their spatial structure (autocorrelation). MULTISPATI approach is very flexible and can handle various kinds of data (quantitative and/or qualitative data, contingency tables). A study is presented to illustrate the method using a spatial version of Correspondence Analysis. Location: Territoire d'Etude et d'Expérimentation de Trois‐Fontaines (eastern France). Results: Ordination of vegetation plots by this spatial analysis is quite robust with reference to rare species and highlights spatial patterns related to soil properties.     

The effects of non-homology in RAPD bands on similarity and multivariate statistical ordination in Brassica and Helianthus

 In order to estimate the impact of mis-coding non-homologous, co-migrating DNA bands as homologous, two sets of data were utilized. Analyses were conducted using three Helianthus species in which each co-migrating band had previously been confirmed. Comparisons of the similarities between these three Helianthus species using the original 177 RAPD bands and the corrected, homology verified, 197 RAPD band data set revealed that the triangular relationship among these three species was almost identical in both data sets. The non-homology errors in the Helianthanus data sets were found to be random. These random errors merely reduced the absolute similarities, but not the relative similarities nor the relationships among the taxa, in principal-coordinate-analysis ordination. Analyses of RAPDs for the classical Brassica U triangle were made by inserting random non-homologies for 5, 10, 15 and 20% of the original 220 RAPD bands. These analyses revealed a progressive decrease in similarities and less loading on the first two axes in principal coordinate analysis (PCO). However, the basic U triangle of relationships among these six Brassica species was maintained. It appears that if errors in homology of co-migrating DNA bands are random, this will have little effect on the relative similarities and on PCO ordination. This helps explain the successful use of RAPDs at the specific level. Received: 6 December 1997 / Accepted: 11 December 1997     

The multivariate egg: quantifying within- and among-clutch correlations between maternally derived yolk immunoglobulins and yolk androgens using multivariate mixed models

Egg components are important mediators of prenatal maternal effects in birds and other oviparous species. Because different egg components can have opposite effects on offspring phenotype, selection is expected to favour their mutual adjustment, resulting in a significant covariation between egg components within and/or among clutches. Here we tested for such correlations between maternally derived yolk immunoglobulins and yolk androgens in great tit (Parus major) eggs using a multivariate mixed-model approach. We found no association between yolk immunoglobulins and yolk androgens within clutches, indicating that within clutches the two egg components are deposited independently. Across clutches, however, there was a significant negative relationship between yolk immunoglobulins and yolk androgens, suggesting that selection has co-adjusted their deposition. Furthermore, an experimental manipulation of ectoparasite load affected patterns of covariance among egg components. Yolk immunoglobulins are known to play an important role in nestling immune defence shortly after hatching, whereas yolk androgens, although having growth-enhancing effects under many environmental conditions, can be immunosuppressive. We therefore speculate that variation in the risk of parasitism may play an important role in shaping optimal egg composition and may lead to the observed pattern of yolk immunoglobulin and yolk androgen deposition across clutches. More generally, our case study exemplifies how multivariate mixed-model methodology presents a flexible tool to not only quantify, but also test patterns of (co)variation across different organisational levels and environments, allowing for powerful hypothesis testing in ecophysiology.     

A multivariate approach to predicting knee extensor performance

The impact of two predictor variables (estimated knee extensor fast-twitch fiber percentage, body mass) on performance measures (vertical jump power output, leg press peak angular velocity) were examined. Subjects (25 men, 27 women) performed 5 workouts involving 2 vertical jump, leg press, and 50-repetition isokinetic tests (to estimate knee extensor fast-twitch fiber percentage). Multivariate regression determined the following significant (p < 0.05) vertical jump equations: predicted male power output = -59.3464 + 1.566 (estimated knee extensor fast-twitch muscle fiber percent) + 15.7884 (body mass), predicted female power output = 36.1574 + 3.4248 (estimated knee extensor fast-twitch muscle fiber percent) + 9.8633 (body mass). Leg press peak angular velocity equations were insignificant by gender; thus, pooled data yielded the following: predicted leg press peak angular velocity = 18.6187 + 0.235 (estimated knee extensor fast-twitch muscle fiber percent) + 0.3801 (body mass). Body mass explained more variance for each performance measure.     

Statistical analysis for the classification and ordination of the vegetation of Chour valley. A multivariate approach

The study was designed to document the phytodiversity and vegetation dynamics of Chour Valley, Hazara Division, Pakistan during 2018–19. Sum of 115 plant species belonged to 48 families were documented. The leading family was Rosaceae with 14 plant species followed by Asteraceae (11 species). The data were analyzed for classification through two way indicator species Analysis and ordination through CCA and DCA to find differences in directories of plants communities and their habitats kind. Five plants communities were identified including, Abies-Pinus-Rheum, Picea-Cyperus-Oxalis, Rumex-Urtica-Cyperus, Picea-Betula-Viburnum and Berberis-Clematis-Potentilla communities. It was observed that the distribution of species and community structure was directly correlated to altitude, slope aspect and soil characteristics. It was also noticed that forest in the study area are continuously degraded and will go in vanishing, until conservation and restoration measures are adopted in priority basis.     

On the variation explained by ordination and constrained ordination axes

Abstract. Total inertia (TI), the sum of eigenvalues for all ordination axes, is often used as a measure of total variation in a data set. By use of simulated data sets, I demonstrate that lack-of-fit of data to the response model implicit in any eigenvector ordination method results in polynomial distortion ordination axes, with eigenvalues that normally contribute 30–70% to TI (depending on data set properties). The amount of compositional variation extracted on ecologically interpretable ordination axes (structure axes) is thus underestimated by the eigenvalue-to-total-inertia ratio. I recommend that the current use of total inertia as a measure of compositional variation is discontinued. Eigenvalues of structure axes can, however, be used with some caution to indicate their relative importance. I also demonstrate that when the total inertia is partitioned on different sets of explanatory variables and unexplained variation by use of (partial) constrained ordination, (35) 50–85% of the variation ‘unexplained’ by the supplied explanatory variables represents lack-of-fit of data to model. Thus, the common interpretation of ‘unexplained variation’ as random variation (‘noise’) or coenoclinal variation caused by unmeasured explanatory variables, is generally inappropriate. I recommend a change of focus from the variation-explained-to-total inertia ratio and ‘unexplained’ variation to relative amounts of variation explained by different sets of explanatory variables.     

Remotely sensed vegetation phenology for describing and predicting the biomes of South Africa

Questions: What are the patterns of remotely sensed vegetation phenology, including their inter‐annual variability, across South Africa? What are the phenological attributes that contribute most to distinguishing the different biomes? How well can the distribution of the recently redefined biomes be predicted based on remotely sensed, phenology and productivity metrics? Location: South Africa. Method: Ten‐day, 1 km, NDVI AVHRR were analysed for the period 1985 to 2000. Phenological metrics such as start, end and length of the growing season and estimates of productivity, based on small and large integral (SI, LI) of NDVI curve, were extracted and long‐term means calculated. A random forest regression tree was run using the metrics as the input variables and the biomes as the dependent variable. A map of the predicted biomes was reproduced and the differentiating importance of each metric assessed. Results: The phenology metrics (e.g. start of growing season) showed a clear relationship with the seasonality of rainfall, i.e. winter and summer growing seasons. The distribution of the productivity metrics, LI and SI were significantly correlated with mean annual precipitation. The regression tree initially split the biomes based on vegetation production and then by the seasonality of growth. A regression tree was used to produce a predicted biome map with a high level of accuracy (73%). Main conclusion: Regression tree analysis based on remotely sensed metrics performed as good as, or better than, previous climate‐based predictors of biome distribution. The results confirm that the remotely sensed metrics capture sufficient functional diversity to classify and map biome level vegetation patterns and function.     

Null matrices and the analysis of species co-occurrences

Patterns in species occurrences on islands have been analyzed by several authors. At issue is the number of non-occurring pairs of species (also known as checkerboards). Previous authors have suggested that if the number of checkerboards differs from what is expected by chance, then island communities might have been structured by competition. Investigators have pursued this problem by first generating random (or null) matrices and then testing a metric derived from the collection of null matrices against the metric calculated from the actual species co-occurrence matrix. The random matrices were constrained by requiring the number of species on each island, and the number of islands on which each species occurred to be equal to their observed values. We show that results from previous studies are generally flawed. We present a fast, efficient algorithm to generate null matrices for any set of fixed row and column sums, and propose a modification of a previously proposed metric as a test statistic. We evaluated the efficacy of our construction method for null creation and our metric using incidence matrices from the avifauna of Vanuatu (formerly New Hebrides). Received: 31 March 1997 / Accepted: 8 April 1998     

Methods for detecting non-randomness in species co-occurrences: a contribution

Summary Comparison of co-occurrences between species on a group of islands with those expected from a randombased null model could provide evidence on community structure. However, it is difficult to decide on the appropriate null model. Gilpin and Diamond proposed a model and a test for departure from it, but this test is shown to indicate significant structure even when applied to a matrix of random numbers. An alternative method is suggested, using the distribution of Gilpin and Diamond's deviation as test statistic, but determining the expected distribution by Monto Carlo simulation, and using many such simulations as a randomisation test of significance. The null model used accepts the observed totals of occurrences for islands and species; it therefore offers a somewhat conservative test. Applied to the Vanuatu bird data that Gilpin and Diamond used, significant departure from a null model is seen, but with an excess of extreme negative associations, the opposite result from that given by Gilpin and Diamond's method. It is not possible to tell whether the negative associations are due to autecology, biogeography, or to interactions between species.     

Maximum-likelihood estimation of familial correlations from multivariate quantitative data on pedigrees: a general method and examples

A general method for maximum-likelihood estimation of familial correlations from pedigree data is presented. The method is applicable to any type of data structure, including pedigrees in which variable numbers of individuals are present within classes of relatives, data in which multiple phenotypic measures are obtained on each individual, and multiple group analyses in which some correlations are equated across groups. The method is applied to data on high-density lipoprotein cholesterol and total cholesterol levels obtained from participants in the Swedish Twin Family Study. Results indicate that there is strong familial resemblance for both traits but little cross-trait resemblance.     

Study of circadian correlations between acetylcholine muscarinic receptor and brain glycosyltransferases by multivariate analysis

Circadian variations of the acetylcholine muscarinic receptor and some glycosyltransferases were studied in brain using multivariate analysis. Highly significant correlations exist between fucosyltransferase, sialyltransferase and galactosyltransferase and to a lesser extent between both of these enzymes and acetylcholine receptor. No correlation appeared between these enzymes and dolichol phosphate mannose synthase.     

Species co-occurrences and neutral models: reassessing J. M. Diamond's assembly rules

The question whether species co-occurrence patterns are non-random has intrigued ecology for more than two decades. Recently Gotelli and McCabe used meta-analysis to show that natural assemblages indeed tend to have non-random species co-occurrence patterns and that these patterns are in line with the predictions of Diamond's assembly rule model. Here I show that neutral ecological drift models are able to generate patterns in line with Diamond's assembly rules and very similar to the empirical results in Gotelli and McCabe. Ecological drift shifted species co-occurrence patterns (measured by C-scores, checkerboard scores and species combination scores) of model species placed into a grid of the 25 cells (sites; metacommunity sizes 5 to 25 species with 100 individuals each) significantly from an initial random pattern towards a pattern predicted by the assembly rule model of Diamond. These findings imply that instead of asking whether natural communities are structured according to some assembly rules we should ask whether these non-random patterns are generated by species interactions or by stochastic drift processes.     

Analytic and simulation models predicting positive genetic correlations between traits linked by trade-offs

Summary Using a two-loci multiplicative model of resource allocation, we show how the existence of several levels of resource allocation may affect the sign of the genetic correlations between traits linked by trade-offs. Positive genetic correlations between components of fitness affected by genetic trade-offs may result from different amounts of genetic variability at the pleiotropic loci determining the allocation of resources. Thus positive genetic correlations may be obtained in the absence both of environmental variation and of differences between individuals in resource acquisition. Nevertheless, positive correlations between all components of fitness at the same time cannot be obtained without variability in the acquisition of resources.     

Detrended correspondence analysis: An improved ordination technique

Summary Detrended correspondence analysis (DCA) is an improvement upon the reciprocal averaging (RA) ordination technique. RA has two main faults: the second axis is often an arch or horseshoe distortion of the first axis, and distances in the ordination space do not have a consistent meaning in terms of compositional change (in particular, distances at the ends of the first RA axis are compressed relative to the middle). DCA corrects these two faults. Tests with simulated and field data show DCA superior to RA and to nonmetric multidimensional sealing in giving clear, interpretable results. DCA has several advantages. (a) Its performance is the best of the ordination techniques tested, and both species and sample ordinations are produced simultaneously. (b) The axes are scaled in standard deviation units with a definite meaning, (c) As implemented in a FORTRAN program called DECORANA, computing time rises only linearly with the amount of data analyzed, and only positive entries in the data matrix are stored in memory, so very large data sets present no difficulty. However, DCA has limitations, making it best to remove extreme outliers and discontinuities prior to analysis. DCA consistently gives the most interpretable ordination results, but as always the interpretation of results remains a matter of ecological insight and is improved by field experience and by integration of supplementary environmental data for the vegetation sample sites.This research was supported by the Institute of Terrestrial Ecology, Bangor, Wales, and by a grant from the National Science Foundation to R.H. Whittaker. We thank R.H. Whittaker for encouragement and comments, S.B. Singer for assistance with the Cornell computer, and H.J.B. Birks, S.R. Sabo, T.C.E. Wells, and R.H. Whittaker for data sets used for ordination tests.     

The development of numerical classification and ordination

Summary The paper reviews the constraints and influences which have affected the development of numerical classification and ordination of vegetation.Initial development of ordination techniques and their reception by ecologists was hindered by the mistaken idea that ordination involved acceptance of variation in vegetation as a continuum, as well as by a general suspicion of mathematical approaches.Three distinct approaches to ordination, largely unrecognised at the time, are apparent in earlier work: direct gradient analysis, reduction in dimensionality and path-seeking (catenation) (Dale 1975).Modifications of simple initial techniques made them more efficient at the cost of increased computation. Acceptance of heavier computation as computers increased in capacity and speed turned attention to prineipal component analysis and the superficially similar factor analysis. These have been widely misunderstood largely because they were initially applied in the same way as in the analysis of psychological data, in which different constraints and objectives apply. The initial failure to recognise that principal component analysis involves a preliminary data transformation, the form of which depends on answers to biological, not mathematical, questions, was particularly unfortunate.Principal component analysis has limitations as a technique of ordination resulting from its assumptions of linearity and additivity of plant responses. Attempts to devise more effective techniques raise questions about the practical importance of non-linearity if the objective is data-exploration rather than elucidating the nature of species-response curves and about the adequacy of using simulated data as test data when we do not know how to simulate realistic data.Data-exploration has been more prominent in practical uses of ordination but many methodological developments have concentrated rather on species-response curves.Numerical classification also met obstacles to its acceptance additional to a general aversion to numerical techniques. The first numerical techniques were presented in the context of the relationships of a particular set of data, rather than of a generally valid system, which was the more familiar concept in non-numerical classification.Both numerical and non-numerical classification aim to produce as homogeneous groups as possible. The distinctive contribution of numerical methods is to allow the data to indicate the most efficient criteria of classification; this was an unfamiliar idea.The strategy of classification may be either divisive or agglomerative and either monothetic or polythetic. Choice of strategy in earlier work was not only constrained by computational limitation but may also have been influenced by an author's previous experience of non-numerical classification. As with ordination, the distinction between preliminary data transformation and subsequent analysis was at first not appreciated.Numerical classification has been influenced by parallel numerical developments in formal taxonomy. Because objectives and assumptions are not always the same, this influence has not been altogether helpful.The limitations of real data suggest that developments of technique are at risk of becoming too concerned with refinements of methodology. Increasingly complex methods and increasing availability of programmes for such methods carry the risk that they may be used without adequate understanding of what they do.