An Ordination of the Upland Forest Communities of Southern Wisconsin, J. Roger Bray and J. T. Curtis (1957)

Atmospheric distributions!

Remember G. Evelyn Hutchinson’s definition of the fundamental niche as an n-dimensional hypervolume? In October of 1957, the same year Hutchinson makes his concluding remarks, Bray and Curtis publish a description of three dimensions constructed from quantitative plant community data. In contrast to the confined reductionist approach of C. S. Holling, Bray and Curtis seem animated by the spirit of exploration of the unknown, and a willingness to try to describe whatever they find. They have no hypotheses. Their stated goals are 1) to describe the compositional structure of a community; and 2) to look at patterns of interaction between biotic and abiotic phenomena. Their project is to map the complexity of “a field of interrelated units and events,” to build a broad foundation on which future scientists might discover causal connections.

In the introduction to this section, James H. Brown mentions that some people are less than enthusiastic about the impact of plant ordination studies. However, according to googlescholar.com, Bray and Curtis’ ordination paper has had 6,197 citations, 355 of them in 2015. Multivariate analysis, although begun using only adding machines and hole punches, must have had some impact.

In their brief literature review, Bray and Curtis go all the way back to Gleason’s 1910 prescient vision for a quantitative description of plant communities. They outline three basic schools of thought that have arisen since then, with different foci: 1) relationships of species to each other; 2) relationships of whole stands to each other; 3) demonstration of degree of relationship directly from analysis of quantitative data. They decide to combine relationships of whole stands with direct analysis of data.

Source and Treatment of Data

Bray and Curtis gather data from 59 representative, relatively undisturbed stands of vegetation in the southwestern half of Wisconsin. Using a random sampling technique, for each of the 59 stands, they make 38 measurements: density for 12 species of trees and total basal area for those 12 species (basal area, according to the USDA Forest Service glossary, is tree area in square feet of the cross section at breast height of a single tree), and frequency of 14 species of shrubs and herbaceous plants in regularly placed 1 m. quadrats. Scores for each stand are adjusted to relative values.

For their pairwise comparisons between stands, the plant ecologists discard the traditional correlation coefficient, “r,” as too insensitive. Instead, they use the Gleasonian coefficient of community “w,” the ratio of the species in common to the adjusted index for one stand (80). They arrive at 1711 values of w, and arrange them in a matrix.

Application of the Method

Rejecting previous analytical methods, they then constructed a 3-dimensional ordinate system with x, y, and z-axes, in which to project the data from their matrix. They inverted the values of the 1171 coefficients in the matrix (subtracted them from 80) to reflect their assumption that the greater the similarity of species between stands, the less distance there will be between those stands when plotted in the theoretical space. They constructed the scales for the axes using stands with farthest apart values (lowest w coefficients). A unit on any axis is defined as 1.

Results

The plots on pages 580 and 581 show 3-dimensional axes of tree species; the plots on pages 582 and 583 show herbs and understory plants in 2 dimensions. All plots depict pairwise “distance” relationships between stands. Each dot or circle represents a stand; the size of dot or circle reflects species dominance as measured by basal area. For each species, the stands are plotted on three 2-dimensional graphs (the three possible combinations of the x, y, and z axes) that can be thought of as cubes, with the three graphs forming the front, top, and side of the cube. Please excuse me if I pause just a moment to say this is REALLY COOL! Please see the 3D model (Figure 7) on page 584, and the diagram (Figure 8) on page 586.

Discussion

Mechanical Validity of the Ordination

Bray and Curtis test the accuracy of the 3-dimensional ordinate system by using a 3D version of the Pythagorean theorem. Distances in the ordinate system are compared to the coefficients of community in the matrix. A significant correlation is found (1% for 58 stand pairs and .1% for 11 reference stands). When the axes are tested for their ability to supply meaningful separation of the strands, however, the “z” axis is found lacking. It is retained for several reasons. The axes are also tested for their ability to produce random orientation of stands. They pass this test (they do not produce randomness).

Biologic Validity of the Ordination

By visualizing the 3D graphs, the species show all or part of an “atmospheric distribution,” where there is a center of concentration, and a diminishing radiation outward from that center. This is reminiscent of Gleason’s dune vegetation descriptions. Bray and Curtis point out that they have shown a 3D version of the concept of ecologic amplitude, and that compression into 2D gives contour-shaped patterns, while compression into 1D gives bell-shaped curves. They characterize the distribution and relationship of the patterns as “continuous variation,” and suggest that this is “evidence for individualistic theory of species distribution and for the continuum nature of community structure,” listing many past studies supported by their model.

While exercising caution about attributing causality, Bray and Curtis speculate about possible biologic meanings of their constructed axes. Correlation tests are done for all available environmental variables with the three axes. Patterns emerge:  for x, light, moisture, and temperature, relative to past fires; for y, soil moisture and aeration; for z, recent disturbance and amount of organic matter.

Questions

A. A couple of the assumptions in this paper are: 1) it makes sense to depict similarity of species as nearness in space; 2) the three types of measured quantities have equal weight (understory plant frequency, tree density, tree dominance). Are these good assumptions?

B. Would someone in our class please demonstrate the geometric technique of arc projection Bray and Curtis used for constructing their y and z-axes?

C. What do you think about this type of study in general? No hypothesis, no prediction, no testing of prediction—just an exploration.

D. Bray and Curtis write, “The nature of the causal role of factors shaping a community is an ultimate goal in ecology.” Do you agree? Why or why not?