Multivariate analyses are well known and widely used to identify and understand structures of ecological communities. The ade4 package for the R statistical environment proposes a great number of multivariate methods. Its implementation follows the tradition of the French school of "Analyse des Donnees" and is based on the use of the duality diagram. We present the theory of the duality diagram and discuss its implementation in ade4. Classes and main functions are presented. An example is given to illustrate the ade4 philosophy.

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The ade4 Package: Implementing the Duality Diagram for Ecologists

This paper examines how to obtain species biplots in unconstrained or constrained ordination without resorting to the Euclidean distance [used in principal-component analysis (PCA) and redundancy analysis (RDA)] or the chi-square distance [preserved in correspondence analysis (CA) and canonical correspondence analysis (CCA)] which are not always appropriate for the analysis of community composition data. To achieve this goal, transformations are proposed for species data tables. They allow ecologists to use ordination methods such as PCA and RDA, which are Euclidean-based, for the analysis of community data, while circumventing the problems associated with the Euclidean distance, and avoiding CA and CCA which present problems of their own in some cases. This allows the use of the original (transformed) species data in RDA carried out to test for relationships with explanatory variables (i.e. environmental variables, or factors of a multifactorial analysis-of-variance model); ecologists can then draw biplots displaying the relationships of the species to the explanatory variables. Another application allows the use of species data in other methods of multivariate data analysis which optimize a least-squares loss function; an example is K-means partitioning.

https://www.umass.edu/landeco/teaching/multivariate/readings/LegendreandGallagher2001.pdf

Ecologically meaningful transformations for ordination of species data

Beginning with Emlen (1966) and MacArthur and Pianka (1966) and extending through the last ten years, several authors have sought to predict the foraging behavior of animals by means of mathematical models. These models are very similar,in that they all assume that the fitness of a foraging animal is a function of the efficiency of foraging measured in terms of some "currency" (Schoener, 1971) -usually energy- and that natural selection has resulted in animals that forage so as to maximize this fitness. As a result of these similarities, the models have become known as "optimal foraging models"; and the theory that embodies them, "optimal foraging theory." The situations to which optimal foraging theory has been applied, with the exception of a few recent studies, can be divided into the following four categories: (1) choice by an animal of which food types to eat (i.e., optimal diet); (2) choice of which patch type to feed in (i.e., optimal patch choice); (3) optimal allocation of time to different patches; and (4) optimal patterns and speed of movements. In this review we discuss each of these categories separately, dealing with both the theoretical developments and the data that permit tests of the predictions. The review is selective in the sense that we emphasize studies that either develop testable predictions or that attempt to test predictions in a precise quantitative manner. We also discuss what we see to be some of the future developments in the area of optimal foraging theory and how this theory can be related to other areas of biology. Our general conclusion is that the simple models so far formulated are supported are supported reasonably well by available data and that we are optimistic about the value both now and in the future of optimal foraging theory. We argue, however, that these simple models will requre much modification, espicially to deal with situations that either cannot easily be put into one or another of the above four categories or entail currencies more complicated that just energy.

Citation classic - optimal foraging - a selective review of theory and tests

The traditional likelihood-based test for differences in multivariate dispersions is known to be sensitive to nonnormality. It is also impossible to use when the number of variables exceeds the number of observations. Many biological and ecological data sets have many variables, are highly skewed, and are zero-inflated. The traditional test and even some more robust alternatives are also unreasonable in many contexts where measures of dispersion based on a non-Euclidean dissimilarity would be more appropriate. Distance-based tests of homogeneity of multivariate dispersions, which can be based on any dissimilarity measure of choice, are proposed here. They rely on the rotational invariance of either the multivariate centroid or the spatial median to obtain measures of spread using principal coordinate axes. The tests are straightforward multivariate extensions of Levene's test, with P-values obtained either using the traditional F-distribution or using permutation of either least-squares or LAD residuals. Examples illustrate the utility of the approach, including the analysis of stabilizing selection in sparrows, biodiversity of New Zealand fish assemblages, and the response of Indonesian reef corals to an El Nino. Monte Carlo simulations from the real data sets show that the distance-based tests are robust and powerful for relevant alternative hypotheses of real differences in spread.

Distance-based tests for homogeneity of multivariate dispersions.

A flexible method is needed for constrained ordination on the basis of any distance or dissimilarity measure, which will display a cloud of multivariate points by reference to a specific a priori hypothesis. We suggest the use of principal coordinate analysis (PCO, metric MDS), followed by either a canonical discriminant analysis (CDA, when the hypothesis concerns groups) or a canonical correlation analysis (CCorA, when the hypothesis concerns relationships with environmental or other variables), to provide a flexible and meaningful constrained ordination of ecological species abundance data. Called “CAP” for “Canonical Analysis of Principal coordinates,” this method will allow a constrained ordination to be done on the basis of any distance or dissimilarity measure. We describe CAP in detail, including how it can uncover patterns that are masked in an unconstrained MDS ordination. Canonical tests using permutations are also given, and we show how the method can be used (1) to place a new observation into...

Canonical analysis of principal coordinates: a useful method of constrained ordination for ecology

2School of Oceanography, University of Washington,Seattle, Washington 98195 USAAbstract. Controlled field experiments were used to test the effects of surface-deposit feederson succession at the Skagit flats, an intertidal sandflat in northern Puget Sound . The tube buildersHobsonio florida (Polychaeta, Ampharetidae), Pseudopolydora kempi japonica (Polychaeta, Spioni-dae), and Tanais sp. (Crustacea, Peracarida) facilitate the recruitment of other taxa to 10-cm 2 azoicpatches. Simulated animal tubes facilitated the immigration of Tanais sp. and oligochaetes. Macomabalthica, a tellinid bivalve, facilitated the immigration of H. Florida, while inhibiting that of Tanaissp. These experiments clearly documented that facilitation rather than inhibition is the dominantprocess governing succession in the Skagit community. The facilitation model of succession offers aviable alternate explanation for many soft-bottom benthic processes previously explained by theinhibition model.Key words: community structure; controlled manipulations; facilitation; infauna; polychaetes;succession; tube builders.

Facilitation of soft-bottom benthic succession by tube builders'

The benthic infaunal mudflat community of Boston Harbor’s Savin Hill Cove was sampled every other week from January though December 1986. Eighty replicate samples per date allowed precise estimates of the abundances of juvenile and adult stages of all macrofaunal taxa and many meiofaunal taxa. We describe the multivariate structure of%the seasonal succession of this community with a faunal distance metric approach. There were three groups of species that produced a three-stage or triangular succession pattern. Stage 1 is defined by a March bloom of harpacticoid copepods that closely follows a benthic diatom bloom. Harpacticoid copepod abundance rapidly declines in late spring and is followed by the recruitment of four opportunistic annelids, marking the break between stages 1 and 2. Stage 2 is a dense assemblage of four surface-deposit feeding and shallow subsurface-deposit-feeding annelids that reach peak abundance in June and decline in late summer, marking the break between stages 2 and 3. Stage 3 populations are more diverse than stage 2, reach peak abundance in fall, and decline in late fall. The infaunal community structure of December resembles that of the community the previous January. Succession on this mudflat is a fast-paced and dynamic process affected by epipelic diatom production, the timing and duration of juvenile recruitment, and the ability of the infauna to survive in dense assemblages of tube builders.

https://aslopubs.onlinelibrary.wiley.com/doi/pdf/10.4319/lo.1994.39.6.1440

Three stages of seasonal succession on the Savin Hill Cove mudflat, Boston Harbor

Basic to nearly any prediction concerning the behavior and structure of entire communities or of their components is knowledge of trophic connections among species. A major impediment to such understanding of soft-bottom benthos is methodological. Because none of the routinely available methods of food web analysis (e.g. visual gut content analysis, direct observation of feeding, tracer techniques) is generally suitable for examining all trophic interactions of benthic infauna, we rought to evaluate the potential of immunological methods for identifying predatorprey relationships in one typical, estuarine, intertidal sand flat. Whole-organism extracts of individual macro- and meiofaunal taxa were injected into rabbits to produce antisera of varying specificity. Double immunodiffusion precipitin tests of antiserum specificity revealed both phyletic and trophic relationships among 20 taxa. Using relatively unspecific antisera, preliminary analysis of the stomach contents of a few surface deposit-feeders and particle browsers was successful, giving positive identification of several trophic links which would otherwise have gone undetected. The production of taxon-specific antisera is expected to provide the methodological tool necessary to document the breadth of trophic connections in a marine benthic food web.

Immunological methods for food web analysis in a soft-bottom benthic community

The impact of a sewage point source on the bacterial densities in an intertidal mud flat in Boston Harbor, Mass, was investigated The area, Savin Hill Cove, acts as a receiving basin for a combined storm and sewage outlet (CSO) Preliminary examination of sediments and overlying water at high tide demonstrated that fecal coliforms were present in sediments at abundances 2 to 4 orders of magnitude higher than in the overlying water column The following bacterial counts were determined from sediments along a sampling transect extending 460 m from the CSO: total bacteria by epifluorescent microscopy, heterotrophic bacteria by plate counts on nutrient-rich and nutrient-poor media, fecal coliforms and enterococci by membrane filtration, and Vibrio parahaemolyticus by a most-probable-number technique with a resuscitation step Median sediment grain size, average tidal exposure, carbon/nitrogen ratio, and total organic carbon were also measured All bacterial indices, except for V parahaemolyticus, declined significantly with distance from the outfall Multiple regression analysis indicated that tidal exposure (low tides) may affect densities of total bacteria Fecal coliforms and enterococci were still present in appreciable numbers in sediments as far as 460 m away from the CSO In contrast, V parahaemolyticus densities did not correlate with the other bacterial counts nor with any of the environmental parameters examined These results indicate that intertidal sediments which adjoin point sources of pollution are severely contaminated and should be considered as potentially hazardous reservoirs of sewage-borne diseases

Eugene D. Gallagher

Papers

Ecologically meaningful transformations for ordination of species data

Facilitation of soft-bottom benthic succession by tube builders'

Three stages of seasonal succession on the Savin Hill Cove mudflat, Boston Harbor

Immunological methods for food web analysis in a soft-bottom benthic community

Distribution of indicator bacteria and Vibrio parahaemolyticus in sewage-polluted intertidal sediments.