maths 101 Essay

maths 101 Essay maths 101 Essay 1ABSTRACT: A strategy is presented for analysing marine biological survey data and relating the biotic patterns to environmental data. To avoid circular argument, biotic and environmental data are kept separate. The strategy is illustrated by a worked example using data on the distribution of 182 nematode species in 107 samples in the River Exe estuary. Nineteen stations are grouped Into 4 main clusters using complementary classification and multi-dimensional scaling (MDS) ordination tech- niques. These are both based on root-root transformed abundance data with the Bray-Curtis measure of similarity. Indicator species characterising each group are extracted using information statistics. Inverse analyses give clusters of CO-occurnng species which are strongly related to the station groups. Relationships of station groups to environmental variables are revealed by superimposing data for one variable at a time on the MDS plot, showing that some station groups differ in sediment granulometry and others in salinity, for example. Some of the other factors plotted show no difference between station groups. Similarly, physiognomic charactcrlstics of the species are superimposed on the MDS plots of the inverse analysis of species groups, revealing differences in setal length and trophic status between the species groups. Finally, the 4 major station groups and species groups are related to one another in terms of morphological adaptation to the habitat. INTRODUCTION Biological surveys whether of benthos, plankton or nekton, usually result in complex bodies of biotic and environmental data from which patterns and relation- ships need to be extracted. Although such multispecles data sets have much in common, a confusing variety of numerical techniques has been used in the marine ecological literature, often simply because a computer program happened to be handy and without considera- tion of its suitability for the data. Numerical techniques have been most commonly applied to benthic data (e.g. Sanders, 1958; Cassie and Michael, 1968; Lie and Kelley, 1970; Day et al., 1971; Hughes and Thomas, 1971; Popham and Ellis, 1971 ; Stephenson et al., 1972; Poore and Mobley, 1980; Shin, 1982; and several other recent papers). Plankton workers have also used num- erical methods (e.g. Cassie, 1961; Fager and McGo- wan, 1963; McConnaughey, 1964; Thorrington-Smith, 1971; Angel and Fasham, 1975), and some similar analyses have been done on fish distribution (e.g. Fager and Longhurst, 1968; Peters, 1971; Haedrich et al., 1980). O Inter-Research/Printed in F. R. Germany In this paper we present an overall strategy for the analysis of multispecies data and the associated environmental variables which we believe has wide applicability in marine ecology. A set of robust and tested numerical techniques is presented stage by stage and illustrated by a simple example. We do not claim to review all the useful techniques available, but merely to outline numerical methods which we have successfully applied to a variety of ecological data. For a more complete review of many of the techniques see Clifford and Stephenson (1975). Walker et al. (1979) have summarized the 3 alterna- tive