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Introduction

Methods

Background and Design

Data Preperation

Analyses

Results

Discussion

Literature Cited

Throughout the data exploration and analysis stages of my project I explored a number of different multivariate statistical techniques. Below I present summaries of both univariate and multivariate methods used in this project.

Univariate Techniques:

Individual Based Rarefaction:

Individual based rarefactions help to overcome the problems which have traditionally challenged many diversity indices such as Shannon-Weiner or Simpsons (Buddle et al., 2005). Rarefaction effectively standardizes the richness between treatments for a reliable comparison of heterogeneous datasets. The analysis produces a simple species accumulation type graph which enables us to compare the estimated species richness between study treatments. To interpret, the estimated species richness must be compared at an equal number of individuals (indicated by black arrow in all figures) to control for differences in abundances between treatments.

Data Transformations:

When working with community data, one of the greatest challenges is dealing with rare species versus common species. Data transformations are commonly used to address this issue by down weighting the importance of the most common species, and up weighting the importance of rarer species. This helps ensure we are seeing patterns of the community, rather than a few dominant species in the data set. I explored the use of arcsine, logarithmic, and square root transformations for this project. After reviewing the results, I decided to use a generalized logarithmic procedure as was recommended by McCune and Grace (2002). This transformation was used in most of the analyses presented on this site.

Multivariate Analyses:

Non-metric Multidimensional Scaling (NMS) Ordination:

This is recognized as the most effective ordination technique for ecological community data (McCune and Grace, 2002). By avoiding the assumption of a linear relationship among variables and effectively handling data sets with multiple zeros (such as many rare species within a community data set) NMS is very powerful for use with community data. In addition, the analysis is non-parametric, thus the requirement of normality is avoided. The NMS technique first creates a dissimilarity matrix based on a chosen distance measure (Bray-Curtis used here). The technique then balances the number of axes which are required to effectively display the community data with the ranked order of the dissimilarity matrix, while minimizing the stress in the final ordination. A NMS is easily interpreted as points closer together represent points more similar, whereas points farther apart represent sites less similar.

Hierarchichal Clustering Analyses:

When groups are sought from ecological data, hierarchical clustering analysis can provide a very effective means of accomplishing this goal. In its simplest form, the clustering analysis forms groups of data based on their similarity as illustrated by a particular distance measure (Bray-Curtis dissimilarity index used here). The analysis then progressively splits the data into smaller groups based on their similarity to one another (McCune and Grace, 2002). The result is a fusion of branches which creates a dendrogram, or tree like structure, from which the data groups are easily interpreted.

Non-linear Canonical Analysis of Principal Coordinates (NCAP):

The NCAP is a general distance based analysis which enables effective modeling of changes in community composition along environmental gradients. The analysis has many advantages for multivariate community data in that it is robust to non-normality and multiple zero values in the dataset, and permits effective non-linear analysis. The method first uses a distance matrix (Bray-Curtis dissimilarity index used here) to calculate the principal co-ordinates of the data matrix. A non-linear canonical correlation analysis is then performed on the matrix of principal co-ordinates to determine the nonlinear gradient which "maximizes the canonical correlation with the principal co-ordinates" (Millar et al. 2005). Thus, the output from the analysis is a comparison of the gradient correlation compared to the distance along the environmental gradient. The analysis is flexible and enables a suite of non-linear gradients to be fitted to the dataset. I selected the logistic function as we would expect community composition to change quickest at or near the edge with less rapid change further into the forest. Although a rather new analysis, this technique is very well received in the published literature on edge effects and environmental gradients (Baker et al., 2007; Millar et al., 2005).

Bray-Curtis (Polar) Ordination:

While a highly contested analysis which has undergone substantial scrutiny throughout the evolution of ordination techniques (McCune and Grace, 2002), Bray-Curtis ordination is still viewed today as an effective technique for extracting ecological gradients from community data. Like the NMS, Bray Curtis ordinations use a distance matrix (Bray-Curtis dissimilarity index used here) as the basis of the technique. The analysis then selects two points which are the least similar (ie: farthest apart in ordination space) and places all remaining points within these two extremes (McCune and Grace, 2002). The ordination output is interpreted just like the NMS in that points closer together represent points which are more similar to each other. With its high utility for analyzing gradients where two endpoints might be expected from the inherent nature of the experimental design, I thought this method was worth exploring for this study.

All analyses were conducted in PC-ORD Version 5.0, with the exception of the NCAP and rarefaction analyses which were performed within R version 2.5.1.