Ecological guilds represent groups of species within a community that share common resources (Root 1967). Species within a guild may be more likely to interact or compete for resources than are species in different guilds (e.g., owls vs. hummingbirds). How can we incorporate guild structure into our analyses?
One approach would be to create separate presence-absence matrices for each guild in the assemblage and analyze each matrix separately using EcoSim's co-occurrence analysis. However, we might also want to test for patterns among the guilds as a group. This module allows you to carry out such simple tests.
The tests in this section assume that you have already designated the guilds according to biologically realistic criteria. All species in an assemblage are assigned to a guild, and each species can be assigned to only one guild. Approaches to defining guilds include using taxonomic groupings (all the species within a genus), resource-based groupings (all the species that use a particular food resource), and functional groupings (all the species with similar morphology that exploit a shared resource) (Simberloff and Dayan 1991). This module of EcoSim does not contain tests for classifying or recognizing guilds, but for testing hypotheses about guilds that have been designated a-priori by the user. If you have not done so already, you should study the Co-occurrence Module, which explains the methods for quantifying species co-occurrence patterns in a presence-absence matrix. We will use the same measures of community structure (C-score, V-ratio, number of checkerboard pairs, and number of species combinations) that were introduced in the Co-occurrence Module in the analysis of guild structure.
In these analyses, EcoSim measures the significance patterns of the co-occurrence indices among the different guilds. It tests whether the mean co-occurrence index among guilds is larger or smaller than expected by chance. It also tests the variance of the co-occurrence index among guilds. An unusually large variance would mean that the guilds differ significantly from one another in their levels of co-occurrence: some guilds have species with high levels of co-occurrence and other guilds have species with low levels of co-occurrence. An unusually small variance would mean that guilds are strikingly similar to one another in the level of co-occurrence observed. A random result for the variance means that the level of co-occurrence among guilds is about what would be expected if the species were assigned randomly to different guilds.
Finally, this module provides a test of the "favored states hypothesis" (Fox 1987, 1999, Fox and Brown 1993), which is that the distribution of species among guilds is unusually uniform or even among communities. If communities are formed by sequentially adding species in different guilds or functional groups, there should be an unusually large number of favored states compared to the null model.
Species | Site1 | Site2 | Site3 | Site4 |
---|---|---|---|---|
SpeciesA | 1 | 1 | 0 | 0 |
SpeciesB | 0 | 0 | 1 | 0 |
SpeciesC | 0 | 0 | 0 | 1 |
SpeciesD | 1 | 1 | 1 | 1 |
SpeciesE | 0 | 1 | 1 | 0 |
SpeciesF | 0 | 1 | 0 | 0 |
SpeciesG | 1 | 1 | 1 | 0 |
SpeciesH | 0 | 0 | 0 | 1 |
SpeciesI | 1 | 1 | 0 | 1 |
SpeciesJ | 1 | 0 | 1 | 1 |
SpeciesK | 1 | 0 | 0 | 1 |
For the analysis of guild structure, we need to add an additional column of data to indicate guild designation for each species in the matrix:
Species | Guilds | Site1 | Site2 | Site3 | Site4 |
---|---|---|---|---|---|
SpeciesA | GuildX | 1 | 1 | 0 | 0 |
SpeciesB | GuildX | 0 | 0 | 1 | 0 |
SpeciesC | GuildY | 0 | 0 | 0 | 1 |
SpeciesD | GuildX | 1 | 1 | 1 | 1 |
SpeciesE | GuildY | 0 | 1 | 1 | 0 |
SpeciesF | GuildY | 0 | 1 | 0 | 0 |
SpeciesG | GuildZ | 1 | 1 | 1 | 0 |
SpeciesH | GuildZ | 0 | 0 | 0 | 1 |
SpeciesI | GuildZ | 1 | 1 | 0 | 1 |
SpeciesJ | GuildZ | 1 | 0 | 1 | 1 |
SpeciesK | GuildX | 1 | 0 | 0 | 1 |
In this matrix, we have designated 3 different guilds (x,y, and z), and every species is assigned to one of these three guilds. The guild label always belongs in the second column of your data matrix, following the species names. The standard rules for EcoSim data entry apply here: each of the different guilds requires a unique label, and labels cannot contain spaces or commas. It is not necessary to order the species within the guilds; EcoSim will do that for you when it makes its calculations. There must be at least two species represent in every guild, as it is not possible to calculate co-occurrence statistics for a single species!
A second form of analysis is available in this module. Rather than analyze for differences among guilds, we can compare patterns among "regions" or groups of sites. For example, we might wish to test whether species co-occurrence patterns are different for "intact" sites or sites that have been "invaded" by a non-native species. In this case, we a unique row label to designate the regions in the analysis. For example:
Species | Site1 | Site2 | Site3 | Site4 |
---|---|---|---|---|
Regions | Intact | Intact | Invaded | Invaded |
SpeciesA | 1 | 1 | 0 | 0 |
SpeciesB | 0 | 0 | 1 | 0 |
SpeciesC | 0 | 0 | 0 | 1 |
SpeciesD | 1 | 1 | 1 | 1 |
SpeciesE | 0 | 1 | 1 | 0 |
SpeciesF | 0 | 1 | 0 | 0 |
SpeciesG | 1 | 1 | 1 | 0 |
SpeciesH | 0 | 0 | 0 | 1 |
SpeciesI | 1 | 1 | 0 | 1 |
SpeciesJ | 1 | 0 | 1 | 1 |
SpeciesK | 1 | 0 | 0 | 1 |
In this analysis, we would be comparing the co-occurrence pattern in intact vs. invaded sites.
The default co-occurrence index is the C-score, which is described in the Co-occurrence Module.
The default grouping is by guild(=row), so EcoSim is expecting your matrix to contain properly formatted guild labels.
The Favored States Analysis is not calculated in the default.
1) Stone and Roberts' (1990) C-score This is EcoSim's default index. The C-score measures the average number of "checkerboard units" between all possible pairs of species. A checkerboard unit is any submatrix of the form:
10
01
or
01
10
The number of checkerboard units (CU) for each species pair is calculated as:
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where is S is the number of shared sites (sites containing both species) and ri and rj are the row totals for species i and j. The C-score is the average of all possible checkerboard pairs, calculated for species that occur at least once in the matrix.
In a competitively structured community, the C-score should be significantly larger than expected by chance.
2) The number of checkerboard species pairs This index follows directly from Diamond's (1975) assembly rules analysis. For this index, EcoSim scans the rows of the matrix and tabulates the number of species pairs that never co-occur in any site.
In a competitively structured community, there should be more checkerboard pairs of species than expected by chance.
3) The number of species combinations For this index, EcoSim scans the columns of the presence-absence matrix and keeps track of the number of unique species combinations that are represented in different sites. For an assemblage of n species, there are 2n possible species combinations, including the combination of no species being present (Pielou and Pielou 1968). In most real matrices, the number of sites (= columns) is usually substantially less than 2n, which places an upper bound on the number of species combinations that can be found in both the observed and the simulated matrices.
In a competitively structured community, there should be fewer species combinations than expected by chance.
4) The variance ratio The V-ratio was first proposed by Robson (1972) and popularized by Schluter (1984) who recommended it as an index of species co-occurrence. The ratio is calculated as the ratio of the variance of the column sums to the sum of the row variances. For a presence-absence matrix, this is the ratio of the variance in species richness to the sum of the variance in species occurrence. If the species are distributed independently and the sites are equiprobable, the expected value of the ratio is 1.0. If there is strong negative covariance between species pairs, the variance will ratio will be < 1.0 and if there is positive covariance between species pairs, the variance ratio will be > 1.0. Unlike the other three indices, the variance ratio does not actually depend on the species co-occurrence patterns, but is determined solely by the marginal totals of the matrix. For this reason, it cannot be tested with EcoSim's default algorithm, which maintains observed marginal totals.
The variance ratio is best thought of as an index of variability in species richness per site. If niche limitation constrains the number of coexisting species, the variance in species richness among sites will be small relative to the null model.
In a competitively structured community, the observed variance ratio should be significantly smaller than expected by chance.
By region(=columns) This analysis expects a data matrix in which each site is classified into a unique region. Region designations are given in the second row of the data matrix. The simulation does not alter the structure of the matrix, but instead reshuffles the region labels among the different sites.
Favored States Analysis This checkbox provides an additional analysis that can be performed on data sets that are organized as guilds. The analysis tests the hypothesis of Fox (1987, 1999) that species are added sequentially to a community so that different "functional groups" or guilds are represented as evenly as possible. Communities can then be classified as to whether they are in a "favored" or an "unfavored" state. For example, suppose the data matrix has 4 guilds, each with 3 species. Each local community consists of subsets of these twelve species, and the local community exists in either a favored or an unfavored state, depending on how uniform the distribution of species is among the guilds. Thus, if a community had 7 species, a "favored state" would have the guilds filled with (1,2,2,2) species. However, an "unfavored state" would be (0,1,3,3). This example is unfavored because the guilds are not filled as evenly as possible- the first guild has no species present in the community, and the second guild has only one species.
In this analysis, EcoSim reshuffles the guild labels, then examines each column of the matrix and designates it as a favored or an unfavored state. Thus, the number of favored states in matrix is an integer that can range from a minimum of 0 to a maximum of C, the number of columns in the data matrix. Communities that have 0 or 1 species or communities in which all species are present or only 1 species is missing are counted as neither favored nor unfavored states.
The next three columns form the histogram window, which summarizes the distribution of the co-occurrence indices for the simulated communities. The first two columns give the low and high boundaries of 12 evenly spaced histogram bins. In the right-hand column, the number of simulations tells you how many of the simulated indices were in each bin. These integers sum up to the total number of iterations that were specified for the run.
The placement of the observed index shows you, graphically, where the observation fell in the histogram distribution. You can use these data to plot the histogram and the observed value if you want to illustrate your results with a graph.
The lower window gives summary statistics (mean and variance) for the co-occurrence index of the simulated communities. It then tells you the tail probability that the observed index was greater than or less than expected by chance. Remember that this analysis is testing whether the mean co-occurrence index among guilds is larger or smaller than expected by chance.
The summary window also supplies you with the standardized effect size, which is calculated as:
observed index - mean(simulated indices)/standard deviation(simulated indices)
This metric is analagous to the standardized effect size that is used in meta-analyses (Gurevitch et al. 1992). It scales the results in units of standard deviations, which allows for meaningful comparisons among different tests. Roughly speaking a standardized effect size that is greater than 2 or less than -2 is statistically significant with a tail probability of less than 0.05. However, this is only an approximation, and it assumes that the data are normally distributed, which is often not the case for null model tests. For any individual study, you should always report the actual tail probability, which is calculated directly from the simulation, and does not require any assumptions about normality of the data.
Finally, the summary tab shows the original data matrix, including the row and column labels.
All of these data can be edited, deleted, or annotated. The output can then be saved (Save to File) or discarded (Close). There is also a small time clock in the lower right-hand corner so you can tell how long your simulation took.
Stone et al. (1996) introduced this test for the favored states hypothesis and found that desert rodent communities were marginally non-signficant. Brown et al. (2000) recently challenged these results and found a significantly large number of favored states using a different algorithm, in which species are randomly drawn from regional source pools. They suggested that the reshuffling algorithm has weak statistical power. However, these issues cannot be resolved by comparison with empirical data sets (which contains unknown amounts of randomness and structure). It is not clear to us that the reshuffling test is prone to Type II errors (incorrectly accepting a false null hypothesis). In fact, the test may actually be prone to Type I errors (incorrectly rejecting a true null hypothesis). This is because the test does not control for the occurrence frequencies of species in different guilds. Because occurrence frequencies can affect co-occurrence indices, the null hypothesis might be rejected on a "random" data set in which species occurrence frequencies are much higher in some guilds than in others. More testing needs to be done.
Another caution is that the results of the guild tests won't necessarily correspond to the results of co-occurrence tests conducted within guilds. The null hypotheses are not the same in both cases. There might be data sets in which co-occurrence appears random within guilds, but is non-random across guilds. Such patterns might just reflect the smaller sample sizes, and hence weaker statistical power, within individual guilds.
Check the favored states box and run the analysis, which should take only a few seconds to run 1000 simulations.
In the output window, click back and forth between the Input and Simulation Tabs. You will see that the matrix is the same for both, but the guild labels have been reshuffled in the Simulation Tab.
Next, move to the Guild/Regions Tab. This tab gives the observed C-score for each of the guilds. The larger the C-score, the more segregation between species. The observed C-score ranged from 0.67 for the Lasius guild to 11.00 for the Formica guild. For the 1000 simulated assemblages, the average C-score was approximately 6.1 for all the guilds.
Although the observed C-scores appear to differ among the guilds, this variation is within the range expected by chance. The Means Tab shows that the mean C-score, measured across all guilds, was 4.82, which is not much smaller than the average of the simulated assemblages (simulated mean = 6.14, p = 0.142). Similarly, the Variance Tab shows that the observed variance in C-score among guilds (19.60) was not very different from the simulated variance (20.41, p = 0.354).
The Favored States Tab shows that, of the 22 sites, 9 had species distributed in a favored state. If you study the input matrix very carefully, you will see that the favored states occur in sites 13T, 14T, 16T, 21T, 22T, 25T, 26T, 27T, and 31T. The other sites were unfavored states (sites 12T, 18T, 19T, 20T, 23T, 24T,and 29T) or undefined (sites 15T, 17T, 28T, 30T, 32T, and 33T). However, 9 favored states is about what is expected in this matrix (mean = 7.26) and is not an unusually large number (p = 0.248).
Finally, the Summary Tab gives all of the standard EcoSim output in a text box that can be edited and annotated. This information can be saved to disk as an ASCII text file.
Our conclusion from this analysis is that co-occurrence patterns do not differ among forest ant genera.
Select the By region(= columns) grouping and run the analysis, which will take only a few seconds.
The tabs are similar to those in the first data set, but now we are comparing co-occurence patterns between regions with and without fire ants, rather than comparing co-occurrence patterns among guilds.
The Input Tab and the Simulation Tab demonstrate that the region labels were randomly reshuffled among the different columns.
The Guild/Regions tab shows that the observed C-score was larger for the intact sites (6.99) than for the invaded sites (2.24). However, the sample sizes were rather different (22 sites vs. 11 sites), and there were also differences in the simulated data sets (intact C-score = 5.45 vs. invaded C-score = 2.41), so we need to examine the simulation results before deciding whether this result is unusual or not.
The Mean Tab shows that the overall mean C-score of 4.61 was larger than all but 5 of the simulated mean C-scores (p = 0.005), indicating non-randomness in this data set.
The Variance Tab tests the specific hypothesis that the C-scores of the intact and invaded sites are significantly different. The observed variance in C-scores (11.26) was significantly larger than the simulated values (p = 0.006), indicating that co-occurrence structure was significantly different in the two regions. This result reinforces the conclusions of Gotelli and Arnett (2000), who analyzed each data matrix separately.
The Summary Tab again contains all of the simulation results. This text box can be annotated and saved to disk.
We conclude from this analysis that native ant species co-occur significantly less (large C-score) among intact sites than among sites that have been invaded by S. invicta.
Brown, J. H., Fox, B. J. and Kelt, D. A. 2000. Assembly rules: desert rodent communities are structured at scales from local to continental. The American Naturalist 156: 314-321.
Fox, B. J. 1987. Species assembly and the evolution of community structure. Evolutionary Ecology 1: 201-213.
Fox, B. J., and J. H. Brown. 1993. Assembly rules for functional groups in North American desert rodent communities. Oikos 67: 358-370.
Fox, B. J. 1999. The genesis and development of guild assembly rules. Pages 23-57 in E. Weiher and P. Keddy, eds. Ecological assembly rules: Perspectives, advances, retreats. Cambridge University Press, Cambridge.
Gotelli, N. J., and A. E. Arnett. 2000. Biogeographic effects of red fire ant invasion. Ecology Letters 3: 257-261.
Gurevitch, J., L. L. Morrow., A. Wallace, and J. S. Walsh. 1992. A meta-analysis of field experiments on competition. The American Naturalist 140: 539-572.
Robson, D. S. 1972. Appendix: Statistical tests of significance. Journal of Theoretical Biology 34: 350-352.
Root, R. B. 1967. The niche exploitation pattern of the blue-gray gnatcatcher. Ecological Monographs 37: 95-124.
Schluter, D. 1984. A variance test for detecting species associations, with some example applications. Ecology 65: 998-1005.
Simberloff, D., and T. Dayan. 1991. The guild concept and the structure of ecological communities. Annual Review of Ecology and Systematics 22: 115-143.
Stone, L., and A. Roberts. 1990. The checkerboard score and species distributions. Oecologia 85: 74-79.
Stone, L., T. Dayan, and D. Simberloff. 1996. Community-wide assembly patterns unmasked: the importance of species' differing geographical ranges. The American Naturalist 148: 997-1015.