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Gittens(1985) measured the abundance of 8 species of plants from 45 sites within 3 habitat types. Essentially, the plant ecologist wanted to be able to compare the sites according to their plant communities.
Open the veg data file (HINT). Note the format of the file, with variables in columns and samples/sites in rows.
The ecologist was not interested in teasing out the patterns based on each individual species in isolation. The ecologist wanted to see patterns between the plant communities, rather than individual species. Hence a multivariate approach was taken. You may have noticed that the patterns between sites (and habitats) based on SP1 and SP8 were very similar. The abundances of SP1 and SP2 appear to be correlated to one another. It is not surprising that different species might be correlated, as they are likely to respond similarly to similar conditions. If two or more species reveal exactly the same patterns (hypothetically), we could easily combine them into a single group that characterises the sites. Species are never likely to be exactly correlated, however we can still generate new groups that are the combinations of multiple species abundances. If we were to attempt to combine three species, two of which were highly correlated to one another and the other not correlated to either, then the two correlated species will contribute a lot to the new group and the other variable will contribute only little. In the example, lets say we wanted to reduce the 8 species variables down to just 2 groups. Based on how much each species is correlated to each other species, each species will contribute something to each of the two new groups. So each new group is a linear combination of original species variables. This sort of data combining (or reduction) can be done in a number of ways, however for it to work meaningfully, there must be a reasonable degree of correlation between the species.
Peet & Loucks (1977) examined the abundances of 8 species of trees (Bur oak, Black oak, White oak, Red oak, American elm, Basswood, Ironwood, Sugar maple) at 10 forest sites in southern Wisconsin, USA. The data (given below) are the mean measurements of canopy cover for eight species of north American trees in 10 samples (quadrats). For this question we will explore the relationships between the quadrats, in terms of tree species abundances using PCA. That is, which quadrats are most similar/dissimilar to one another.
Open the wisc data file (HINT). Note the format of the file, with variables in columns and samples/sites in rows.
The following data are the abundances of 3 species of gastropods in 5 quadrats (ranging from high shore marsh, Quadrat 1, to low shore marsh, Quadrat 5) in a saltmarsh.
Open the gastropod data file (HINT). Note the format of the file, with variables in columns and samples/sites in rows.
Question 4 - Mantel tests
Vare et al. (1995) measured the cover abundance of 44 plants from 24 sites so as to explore patterns in vegetation communities between these sites. They also measured a number of environmental variables (mainly concentration or various soil chemicals) from each site so as to also be able to characterise sites according to soil characteristics. Their primary interest was to investigate whether there was a correlation between the plant communities and the soil characteristics.
Open the vareveg (HINT) and vareenv (HINT) data files.
Jongman et al. (1987) presented a data set from a study in which the cover abundance of 30 plant species were measured on 20 rangeland dune sites. They also indicated what the form of management each site experienced (either biological farming, hobby farming, nature conservation management or standard farming. The major intension of the study was to determine whether the vegetation communities differed between the alternative management practices.
Open the dune data file (HINT).
Question 6 - Multidimensional scaling
The following example is designed to help you appreciate the link between distance measures and ordination space (MDS). The data set consists of distances (km) between major Australia cities (as the crow flies), and is in the form of a triangular matrix.
Open the austcities data file (HINT). Note the format of the file, it is a triangular distance matrix.
While the file is a distance matrix, at this stage R is unaware of it, we must manually make it aware (a round about way of saying that we must type a command to force R to treat the data set as a distance matrix. Convert the data frame into a distance matrix (HINT)
We are now ready to perform the MDS for the purpose of examining the ordination plot.
MacNally (1989) studied geographic variation in forest bird communities. His data set consists of the maximum abundance for 102 bird species from 37 sites that where further classified into five different forest types (Gippsland manna gum, montane forest, woodland, box-ironbark and river redgum and mixed forest). He was primarily interested in determining whether the bird assemblages differed between forest types.
Open the macnally data file HINT.
Peet & Loucks (1977) examined the abundances of 8 species of trees (Bur oak, Black oak, White oak, Red oak, American elm, Basswood, Ironwood, Sugar maple) at 10 forest sites in southern Wisconsin, USA. The data (given below) are the mean measurements of canopy cover for eight species of north American trees in 10 samples (quadrats). For this question we will explore the relationships between the quadrats via cluster analysis.