Peter R. Minchin

Compositional dissimilarity as a robust measure of ecological distance

The robustness of quantitative measures of compositional dissimilarity between sites was evaluated using extensive computer simulations of species’ abundance patterns over one and two dimensional configurations of sample sites in ecological space. Robustness was equated with the strength, over a range of models, of the linear and monotonic (rank-order) relationship between the compositional dissimilarities and the corresponding Euclidean distances between sites measured in the ecological space. The range of models reflected different assumptions about species’ response curve shape, sampling pattern of sites, noise level of the data, species’ interactions, trends in total site abundance, and beta diversity of gradients.

An evaluation of the relative robustness of techniques for ecological ordination

Simulated vegetation data were used to assess the relative robustness of ordination techniques to variations in the model of community variation in relation to environment. The methods compared were local non-metric multidimensional scaling (LNMDS), detrended correspondence analysis (DCA), Gaussian ordination (GO), principal components analysis (PCA) and principal co-ordinates analysis (PCoA). Both LNMDS and PCoA were applied to a matrix of Bray-Curtis coefficients. The results clearly demonstrated the ineffectiveness of the linear techniques (PCA, PCoA), due to curvilinear distortion. Gaussian ordination proved very sensitive to noise and was not robust to marked departures from a symmetric, unimodal response model. The currently popular method of DCA displayed a lack of robustness to variations in the response model and the sampling pattern. Furthermore, DCA ordinations of two-dimensional models often exhibited marked distortions, even when response surfaces were unimodal and symmetric. LNMDS is recommended as a robust technique for indirect gradient analysis, which deserves more widespread use by community ecologists.

Continuum theory revisited: what shape are species responses along ecological gradients?

Abstract The shape of species’ responses along ecological gradients has important implications for both continuum theory and community analysis. Most current theories and analytical models in community ecology assume that responses are unimodal and symmetric. However, interactions between species and extreme environmental stress may cause skewed or non-unimodal responses. To date, statistical tools for evaluating response shapes have been either inappropriate, inefficient or biased. Using a data set on vascular plant distributions along an elevation gradient, we show that Huisman–Olff–Fresco (HOF) models are an effective method for this purpose, allowing models of various forms (skewed, symmetric, plateau, monotonic) to be tested for adequacy. HOF modeling was compared with alternative methods for response fitting, including Gaussian responses as Generalized linear model (GLMs), Generalized Additive Models (GAM) and Beta Functions with fixed or estimated endpoints. In our data set, skewed and plateau responses are less common than symmetric ones. Less than half of the species have skewed or plateau responses that can not be adequately modeled by Gaussian models. We show that Beta function models with fixed endpoints are biased, confounding skewness and the location of the mode and should not be used to test response shapes. Beta models with estimated endpoints are fairly consistent with other models. GAMs cannot provide clear tests of skewness or kurtosis of response curves, though we show that GAMs, in general, confirmed the shapes chosen by HOF modeling. We provide free software for fitting HOF models and encourage further applications to community data collected along different types of ecological gradients.

Instability of ordination results under changes in input data order: explanations and remedies

. Correspondence analysis (CA) and its Detrended form (DCA) produced by the program CANOCO are unstable under reordering of the species and sites in the input data matrix. In CA, the main cause of the instability is the use of insufficiently stringent convergence criteria in the power algorithm used to estimate the eigenvalues. The use of stricter criteria gives results that are acceptably stable. The divisive classification program TWINSPAN uses CA based on a similar algorithm, but with extremely lax convergence criteria, and is thus susceptible to extreme instability. We detected an order-dependent programming error in the non-linear rescaling procedure that forms part of DCA. When this bug is corrected, much of the instability in DCA disappears. The stability of DCA solutions is further enhanced by the use of strict convergence criteria. In our trials, much of the instability occurred on axes 3 and 4, but one should not assume that published two-dimensional ordinations are sufficiently accurate. Data sets which have pairs of almost equal eigenvalues among the first three axes could suffer from marked instability in the first two dimensions. We recommend that a debugged, strict version of CANOCO be released. Meanwhile, users can check the stability of their CA and DCA ordinations using the software that we have made available on the World Wide Web (http://www.helsinki.fi/jhoksane/). An accurate program for CA, a debugged, strict version of DECORANA (for DCA) and a strict version of TWINSPAN are also available at our site.

Simulation of multidimensional community patterns: towards a comprehensive model

Simulated data, derived from descriptive models of community variation along ecological gradients, are useful for the evaluation of ordination techniques and other numerical methods for the analysis of community data. Existing approaches to the simulation of community patterns are based on restrictive assumptions, although there is evidence supporting several alternative models. Simulation studies should aim to assess the robustness of analytical techniques to variations in model properties. This paper describes a modelling procedure which encompasses most current concepts and hypotheses about the properties of community patterns. The procedure has been used to assess the comparative robustness of several ordination techniques and to examine the effectiveness of alternative coefficients of compositional dissimilarity. COMPAS, a FORTRAN 77 computer program which implements the modelling procedure, is available on application to the author.

An analysis of epiphytic lichen communities in Tasmanian cool temperate rainforest

A three-dimensional compositional pattern in the epiphytic lichen vegetation in Tasmanian cool temperate rainforest is demonstrated using the robust ordination technique, hybrid multidimensional scaling (HMDS). The first two dimensions are correlated with the age of the host tree (and the concomitant change in bark texture) and wetness of the substrate. No measured environmental variable is related to the third dimension, which is tentatively attributed to a gradient in the constancy of the microclimate. Patterns of richness of lichen growth forms and the cover of bryophytes are correlated with the three putative environmental gradients. Possible successional trends between 12 community groups derived by numerical classification are described with respect to changes in substrate age, wetness and microclimatic constancy. Temporal variation of these factors due to tree growth, together with the slow establishment and long persistence of some lichen species, make succession in epiphytic communities very complex. This study demonstrates the value of HMDS in identifying compositional patterns and generating hypotheses about the causal ecological factors. The existence of the postulated microclimatic constancy gradient was not appreciated before the analysis and its discovery illustrates the risk of relying on constrained ordination methods, such as canonical correspondence analysis.

Correlations between sea surface temperature, circulation patterns and the distribution of hermatypic corals of Japan

Abstract Techniques of multivariate exploratory data analysis and regression are used to examine correlations between patterns of distribution of the hermatypic corals of the Ryukyu Islands and mainland Japan, sea surface temperature (SST) and dispersal time. The species composition of all localities is highly correlated with geographic position, with species richness decreasing with latitude. There is an abrupt decrease in diversity between reefal (Ryukyu Islands) and non-reefal (mainland) localities. The compositional data are strongly unidimensional and this dimension is correlated with SST. There are eight high latitude endemic species as well as other species “locked-up” in northern localities as a result of the northward-flowing Kuroshio Current. On a broad scale, overall similarity in coral species composition can be predicted solely from absolute differences in SST and dispersal time makes no significant contribution. Except for short term or localized chilling, the minimum SST for coral reef development is 18°C. Of all Japanese species, 22.5% tolerate a minimum SST of 10.4°C, 27% tolerate 13.2°C and 48% tolerate 14.1°C. Thus, approximately half of all species tolerate temperatures 4°C below the 18°C minimum required for reef development.

Montane vegetation of the Mt. Field massif, Tasmania: a test of some hypotheses about properties of community patterns

direct gradient analysis was applied to the montane vegetation of the Mt. Field massif, Tasmania. Ecological response surface were constructed, describing the relationship between the mean % cover of each of 100 vascular plant species and two major environmental complex-gradients represented by soil drainage and altitude. The hypotheses tested were that: (1) the ecological responses of species are generally of Gaussian form; (2) the modes of ‘minor’ species have a uniform random distribution along gradients; (3) the modes of ‘major’ species are evenly distributed; (4) the frequency distribution over species of modal abundance is either lograndom or lognormal; and (5) alpha diversity has a unimodal trend along environmental gradients. The hypotheses were tested both for the full site of vascular species and for each of five species groups defined by structural form. Hypothesis (1) was rejected: only 45% of species had response surface which appeared unimodal and symmetric. Hypotheses (2) and (4) were rejected for the full set of species, but each was supported for all but one of the structural groups. The modes of herb species were clumped, rather than random and the frequency distribution of modal percentage cover for shrubs was inconsistent with both lograndom and lognormal hypotheses. Contrary to hypothesis (3), the modes of ‘major’ species were randomly distributed. Although total alpha diversity had a complex trend surface, the patterns for the alpha diversities of each structural group were unimodal, in accordance with hypothesis (5). The results suggest that an adequate model of community variation along environmental gradients must take into account differences in response patterns between species groups.

A comparison of taxonomic composition and diversity between reef coral life and death assemblages in Madang Lagoon, Papua New Guinea

Abstract The comparative taphonomy of reef coral life and death assemblages makes an important contribution in estimating bias in the taxonomic composition of fossil reef ecosystems. In Madang Lagoon, Papua New Guinea, the taxonomic composition of reef coral death assemblages shows varying degrees of congruence with adjacent life assemblages in fringing reefs. The original composition of coral communities from low energy reef crest sites appears to be more faithfully represented by their correspondent death assemblages than do those from high-energy reef crest sites where mixing of populations obscures the original coral composition. Coral death assemblages from low energy reef crest habitats may represent autochthonous deposits retaining some of the original community structure, whereas those from high energy reef crest habitats may represent detrital deposits retaining little of their original ecological information. In addition, coral zonation patterns appear to be better preserved at broad than local spatial scales. Species richness, Shannon-Wiener index of diversity and evenness of life and death assemblages were constant between sites and depths in Madang Lagoon. For all three parameters, however, diversity of reef coral death assemblages is significantly less than that of the corresponding life assemblages. This may be due to the unique life history attributes of reef corals. The great longevity of many reef corals may exceed the amount of time needed to degrade their skeletons. Alternatively, only a subset of the life assemblage is being selectively incorporated into the death assemblage. Published measures of fidelity for non-reef marine environments are different from those found in the reefs of Madang Lagoon. In Madang Lagoon reef corals, many live taxa are not found dead, but most taxa in the death assemblage are found alive. The situation is reversed in shelly faunas from non-reef open marine, coastal and intertidal settings: most live taxa are found dead and few taxa in the death assemblage are found alive. As with the diversity results, this probably has to do with the unique life history of reef corals and/or selective preservation of a subset of taxa in the death assemblage. It may be, however, that the present study is not directly comparable to the other marine studies because (1) corals may undergo very different taphonomic processes from both reef and non-reef molluscs; and (2) the sampling regime of the present study, in targeting within- and between-habitat variability in preservation of taxonomic composition and diversity, may be different from previous studies. The community ecology approach utilized in the present comparative taphonomic study was sufficient to capture the high variability inherent in marine life and death assemblages.

Sixteen years of old-field succession and reestablishment of a bottomland hardwood forest in the Lower Mississippi Alluvial Valley

In the Lower Mississippi Alluvial Valley (LMAV), losses of bottomland hardwood forests have been severe, with less than 30% of the original 10 million ha remaining. Reforestation of abandoned farmland is occurring, but there has been little research on natural reestablishment of these forests. We examined understory succession and tree establishment patterns in a 3.2-ha field in northeast Louisiana, USA, abandoned in 1984. Relative elevation, strongly correlated with flooding depth and frequency, varied by approximately 1m. Ground-layer composition was monitored from 1985 to 1999 in twenty 1-m2 quadrats stratified along the elevation gradient. In 2000, shrubs and tree saplings were mapped and their relative elevations determined. Ordination of the ground-layer data revealed that the major trends in species composition were related to time-since-abandonment and elevation. Annual species gradually declined, woody perennials became more abundant, and a shrub and young tree layer emerged from beneath the ground layer, but species composition in low and high elevation plots did not converge. Obligate species were more common at lower elevations, while facultative species were more common at upper elevations. By 16 years after abandonment, a total of 16 tree and shrub species had established in the field; eleven of these had potential local seed sources on levees adjacent to the study site. Abundance of dominant species was significantly related to elevation in most cases. In addition, distance to seed source influenced density and spatial distribution of Celtis laevigata and Fraxinus pennsylvanica. Our study suggests that rate and pattern of secondary succession in LMAV bottomlands are strongly influenced by elevation, dispersal mode of species, and the composition and proximity of forest remnants. Successful restoration of bottomland forests will require an improved understanding of these factors