On reaching adulthood the young animal faces the problem of settling into the patch of habitat which may be its home for the rest of its life. The selection of an area is crucial to the individual's genetic fitness since it may affect both survival and breeding success and thus the total number of progeny produced in the animal's lifetime. Many individuals settle preferentially in their natal area, but others emigrate and face a choice between different regions for settlement. Selection of an area may depend mainly on assessment of the resources available but should also take into account the degree of competition for them. The response of individuals to increasing competition may limit the total number of young which settle in a local population and this may be important in the limitation of density.

In many territorial species, recruitment occurs in two stages, firstly to the non-territorial flock and then from there to the attainment of a breeding territory, sometimes several years later (Charles, 1972). In this chapter I will describe the return of young adult shelducks to the flock, the factors affecting settlement and the possible consequences for population density.

Return of the young

After dispersing for their first winter, many young shelducks return to their natal area, mostly when about one year old. Of 60 Ythan-reared ducklings (ringed before fledging) which returned, 45 per cent were first seen as yearlings, 40 per cent as two-year-olds and 15 per cent at three years old (Patterson et al., in press b).

Classification is the assignment of entities to classes or groups. In community ecology, the customary input data are species abundances in a two-way samples-by-species data matrix. The resultant output from classification is either a nonhierarchical or hierarchical arrangement of samples, species, or both, as illustrated earlier in the introduction. An arranged data matrix may be viewed formally as merely a particular option for presenting the results of a hierarchical classification, but this option merits special consideration because it is quite useful and has had an important role from the beginnings of community classification. There are uncountable individual techniques for classification, but the central purpose of community classification is to summarize large community data sets.

Classification is a fundamental, ubiquitous mental activity (Goodall 1953; Sokal 1974; Blashfield & Aldenderfer 1978). Even simple animals must classify past sensory experiences as a prerequisite for future avoidance of deleterious actions and places and for seeking useful foods and habitats. The existence of language is predicated upon the classification of similar entities or concepts under words serving as class labels. It is not surprising that the first conceptual framework used to organize quantitative community data was classification. Becking (1957), Whittaker (1962), and Westhoff & Maarel (1978) trace the earliest origins of relevant concepts to about 1800 and the earliest substantial community classification to about 1900.

Early classification techniques were informal and subjective (Goodall 1953; Whittaker 1962; Sokal 1974). Several limitations were felt.

Multivariate analyses routinely require millions of mathematical steps and hence necessitate solution by computers. The algorithms are often complex, however, requiring mathematical and computing expertise for programming them and sometimes many weeks of programming labor. Consequently, the development of computer programs for multivariate analysis has occurred mainly at a relatively small number of laboratories, and the programs are distributed to numerous other laboratories. This Appendix will list several sources of computer programs for multivariate analysis of community data.

The Cornell Ecology Program, series, edited by the author, is perhaps the most widely used package, having been used in hundreds of laboratories in over 30 countries. Information on these programs is available upon request from the author. All programs are written in FORTRAN. Several of the commonly used programs are as follows: ORDIFLEX, a flexible ordination program performing weighted averages, polar ordination, principal components analysis, and reciprocal averaging; DECORANA, providing reciprocal averaging and detrended correspondence analysis ordinations; TWINSPAN, producing hierarchical classifications by two-way indicator species analysis; COMPCLUS, performing nonhierarchical classifications by composite clustering; DATAEDIT, offering a variety of data–matrix-editing options, along the lines discussed in Chapter 6; and CONDENSE, a utility program for reading data matrices keypunched in a wide variety of convenient formats and copying them into a single standardized format efficient for computer processing. There are additional programs, including one for Gaussian ordination and two for simulating community data.

In this book multivariate analysis in community ecology has been reviewed and the theory, methods, and applications of direct gradient analysis, ordination, and classification have been presented. In conclusion, a few comments will be offered concerning inherent limitations, model accuracy, and prospectus.

Several inherent limitations should be acknowledged in community ecology. They may be mitigated in part by strenuous efforts but cannot be eliminated. These limitations must be recognized or the likely result will be unrealistic and ineffective research. (1) Community ecology field data are noisy. (2) Multivariate analysis summarizes community data and functions because numerous species abundances are controlled largely by a relatively small number of environmental and historical factors. The word largely is required, however, because each species is unique and individual (Gleason 1926; Whittaker, Levin, & Root 1973; Macfadyen 1975; Mclntosh 1975, 1980; Simberloff 1980; Strong 1980), and likewise, each site and each environmental factor are to some degree unique. Consequently, any general community description, even the best possible such description, can capture only a fraction of the total variation. In contrast, the objects of other sciences may be more uniform, such as in chemistry, where trillions of atoms of carbon or iron may be treated as identical for many purposes. (3) Community ecology is partially subjective. The origins of subjectivity include the choices of research purposes and perspectives, the field data collection procedures, the multivariate analyses, and the methods of interpreting the results.

Community ecology concerns assemblages of plants and animals living together and the environmental and historical factors with which they interact. The domain of community ecology within biology as a whole may be characterized better by the spatial and temporal scales of principal interest rather than by other criteria such as conceptual viewpoint or methodology (Osmond, Björkman, & Anderson 1980). Community ecologists study living things principally on a spatial scale of meters to kilometers and a time scale of weeks to centuries. Phenomena beyond these spatial and temporal scales although relevant to community ecology and its interdisciplinary character, are studied mainly by biologists who would not be classified as community ecologists.

The community-level viewpoint is a major sector of ecology, receiving attention for many theoretical and applied purposes. Even when an ecologist's principal interest is more specific, however, such as the distribution of a particular species or the impact of a particular pollutant, much insight may result from preliminary or complementary community studies (Poore 1956, 1962; Foin & Jain 1977).

Multivariate analysis is the branch of mathematics that deals with the examination of numerous variables simultaneously: “The need for multivariate analysis arises whenever more than one characteristic is measured on a number of individuals, and relationships among the characteristics make it necessary for them to be studied simultaneously” (Krzanowski 1972). Community data are multivariate because each sample site is described by the abundances of a number of species, because numerous environmental factors affect communities, and so on.

A review of multivariate analysis in community ecology is timely for several reasons. This field has been extensively developed recently, with many preferred methods only a few years old. Also, multivariate analysis is receiving wider usage in applied ecology and allied fields. Finally, this topic is timely because of the urgency of making wise choices concerning ecological problems. In tackling these problems, multivariate analysis is a major research approach because many ecological problems involve numerous variables and numerous individuals or samples (and hence involve multivariate data), and many problems cannot be investigated experimentally because of practical restraints. Multivariate analysis of community data cannot replace experimental manipulation, for example, but neither can experimentation replace multivariate analysis. Each research methodology has unique advantages, and the strongest research strategy employs all methodologies.

Two decisions were fundamental to the planning of this book. First, this book is relatively brief and emphasizes the preferred techniques of multivariate analysis. Such a strategy is possible because comparative tests have demonstrated the superiority of relatively few of the many proposed techniques. Furthermore, the primary concerns of most readers are with ecological or related subject matter, not with methods. This book is complementary to longer and more technical treatments by Orlóci (1978a) and Whittaker (1978a,c). Direct gradient analysis, ordination, and classification are presented as a methodological triad, and an integrated approach is described for solving research problems. Second, this book stresses both principles and applications.

Community ecologists often analyze data by a methodological triad consisting of direct gradient analysis, ordination, and classification. These three methods have the common goal of organizing data for purposes of description, discussion, understanding, and management of communities. They vary in strategy. Direct gradient analysis portrays species and community variables along recognized environmental gradients. By contrast, ordination and classification techniques organize community data on species abundances exclusively, apart from environmental data, leaving environmental interpretation to a subsequent, independent step (with a few exceptions, as will be noted later). The result of ordination is the arrangement of species and samples in a low-dimensional space such that similar entities are close by and dissimilar entities far apart. The result of classification is the assignment of species and samples to classes; the classes may or may not be arranged in a hierarchy. These three approaches are complementary, as was shown by examples in the first chapter.

Work in organizing data matrices pertinent to ordination began early in this century, and substantial ordination work was done around 1950, using simple algorithms and hand calculations (for reviews, see Becking 1957 and Whittaker 1967). By 1970, computers were available to most ecologists, and a great number of ordination techniques had been developed. Ordination techniques were introduced more rapidly than they were tested, however, until the 1970s, when ordination comparisons were made leading to reliable recommendations and preferences.

Direct gradient analysis is used to display the distribution of organisms along gradients of important environmental factors. By contrast, ordination and classification techniques generally start with the analysis of community data alone and, only later, use environmental data for interpretation. Direct gradient analysis is a major research approach in community ecology, forming a methodological triad with ordination and classification. Ramensky (1930) and Gause (1930) originated direct gradient analysis, but active research began around 1950 (Whittaker 1948, 1967, 1978b). The results of numerous direct gradient analyses have become the foundation for the Gaussian model of community structure, and this model has served an important role in testing and designing multivariate methods.

Basic purposes and example

Before presenting the methods and results of direct gradient analysis in detail, a typical example will be considered to introduce basic purposes and methods.

Figure 3.1 depicts the native vegetation and topography of Nelson County, North Dakota, at a hypothetical site. Prairie, meadow, and marsh occur on a rolling plain of low relief with soil drainage appearing to be the major environmental factor (Dix & Smeins 1967). As one might gather from Figure 3.1, mere reconnaissance of Nelson County would suffice to ascertain the primary importance of drainage. Likewise, it would be easy to determine the characteristic species of prairie, meadow, and marsh. Casual inspection, however, resolves only the easiest questions; a quantitative approach is required for more difficult questions.

Community sampling is the initial, observational phase of community studies. The inherent strength or weakness of a study and the range of potential data analyses that will be subsequently appropriate are determined and fixed to a great degree at this first step, data collection (Cain & Castro 1959:2; Poore 1962; Greig-Smith 1964:20; Mueller- Dombois & Ellenberg 1974:32). An investigator planning a sampling procedure faces three questions, which will be considered in detail in the following three sections. (1) What general considerations and tradeoffs affect the practicality and effectiveness of sampling procedures? (2) What community sampling procedure is best for a particular study? (3) What corroborative environmental and historical data should be gathered at each sample site?

The first question involves general principles, which can be treated reasonably well in this chapter. They will be discussed primarily in the context of terrestrial vascular plants, but other kinds of communities will be discussed later in this chapter. The second and third questions involve so many permutations of research purpose, level of accuracy, scope of study, kind or kinds of communities, intended subsequent analysis, and so on, that thorough treatment here is impractical. Thus, for these questions, only a sketchy response will be offered, with the burden carried by references to the literature. This is fair enough because an investigator planning a project on, say, phytoplankton communities in small lakes should begin with a survey of relevant literature, which will reveal customary sampling procedures, which may be adopted or else adapted in view of the investigator's particular needs.

This chapter will be concerned with the applications of multivariate analysis. First, general recommendations will be given for community ecology applications regarding data editing in preparation for multivariate analysis and selecting multivariate techniques appropriate for a given data set and purpose. These are based on the theory and evaluations presented in earlier chapters on direct gradient analysis, ordination, and classification. Then, representative literature references will be given for applications of multivariate analysis in applied community ecology and in related and distant fields.

General recommendations

First, general recommendations will be given for multivariate analysis in community ecology. Although presented in the context of community ecology, these recommendations, for the most part, concern common features of any kind of two-way individuals-by-attributes matrix and, consequently, apply to many kinds of data.

Especially for applied researchers, multivariate analysis is just one of many tools serving as a means to specific ends. An applied researcher's time for learning multivariate techniques and for analyzing a particular data set is limited, so it is necessary to provide straightforward, general recommendations that usually work. Given the greater robustness of recent multivariate techniques, such recommendations are now possible. As Williams (1976:28) notes, “Where a subject is ancillary to one's own discipline, the important thing is not how much, but how little, one needs to learn.”

Data editing

A samples-by-species community data matrix may be edited prior to multivariate analysis (Singer 1980).