Ecological Archives E085-116-A1

Elaine R. Hooper, Pierre Legendre, and Richard Condit. 2004. Factors affecting community composition of forest regeneration in deforested, abandoned land in Panama. Ecology 85:3313–3326.

Appendix A. Details of the statistical methods.

INTRODUCTION

We utilized multivariate methods to determine the effect of the experimental factors distance from the forest, Saccharum competition, time and fire on species composition; in a companion paper, we investigated their effects on the density and diversity of tree species recruitment (Hooper et al., in review). While multivariate analyses have been successfully used in studies of tropical succession to distinguish temporal trends from environmental patterns and randomness and to estimate successional vectors of species composition (for example, see Healey and Gara 200, Mesquita et al. 2001, Aide et al. 2000, Sheil 1999, Aide et al. 1996, Purata 1986, Knight 1975, and Williams et al. 1969), multivariate approaches have been criticized because they are often merely descriptive instead of experimental and thus have not increased our ability for prediction or control of succession (Austin 1977). Distance measures utilized in conventional ordination analyses are often not appropriate for tropical data which is characterized by the presence of a high number of rare species. To address these issues, we used an experimental approach and were able to assess the significance of our experimental factors in determining species composition through the use of a recently developed method, distance-based redundancy analysis (db-RDA, Legendre and Anderson 1999). This method is advantageous because it allowed us to use distance measures appropriate in the presence of a high number of rare species. We used 4th corner analysis, another recently developed method, to correlate the species attributes associated with successional stages (Legendre et al. 1997) and test the significance of these correlations.

We relate our results to previous tropical successional hypotheses, namely the initial floristic composition model (applied to tropical succession by Finegan 1996) and the nucleation model (Yarranton and Morrison 1974). To evaluate the importance of succession following the nucleation model, we determined the effect of trees, shrubs and large-leaved monocots on natural tree regeneration by documenting their locations and measuring their proximity to each naturally-regenerating seedling. We used a chronosequence, or space-for-time substitution approach, by studying floristic composition on plots at sites with known time since disturbance (fire). We separated the effects of spatial and temporal variation by using contiguous plots at replicated sites, as recommended by Austin (1977), coupled with appropriate analyses designed to test separately for the effects of site and temporal trend; this separation is important in successional studies utilizing a space-for-time substitution approach (Williams et al. 1969, Austin 1977, Swaine and Greig Smith 1980). To ensure that the successional trend occupied more variance than the within-year differences (Legendre et al. 1985), we separated the effects of short- and long-term variation by using repeated measurements from the same plots over a year (short-term variation) and comparing this to the effect of time-since-fire at each site (long-term variation).

PROBLEMS WITH USE OF CONVENTIONAL MULTIVARIATE ANALYSES

A major problem with the use of multivariate techniques for studying secondary succession of tropical rainforest is the choice of an appropriate distance measure for simple or canonical ordination analysis. Species abundance data in the tropics often produce matrices (sites x species) characterized by the presence of many rare species, each of which is found in very few plots. For this type of data, the Euclidean distance measure preserved in principal component analysis (PCA) and canonical redundancy analysis (RDA) is inappropriate (Legendre and Legendre 1998, Legendre and Gallagher 2001). Correspondence analysis and its canonical form, CCA, utilize an appropriate distance measure for analyzing data with unimodal response curves and double-zeros. However they overemphasize rare species; therefore, ecological decisions using the results of these methods will be based on the characteristics of the rare species. Nonmetric multidimensional scaling and principal coordinate analysis (PCoA) are not canonical ordination methods. Therefore most of the classical multivariate methods are problematic for characterizing secondary tropical succession.

JUSTIFICATION FOR OUR USE OF DISTANCE-BASED REDUNDANCY ANALYSIS (DB-RDA)

We needed to test the results of field experiments, using community composition as the multivariate response variable. MANOVA cannot be used with this data because it violates the assumption of multivariate normality and homogeneity of within-group covariance matrices. As well, MANOVA cannot be used when the number of species is greater than the number of sites, as was the case in our study where we recorded 80 species at 45 sites. We could not use non-parametric statistical methods, such as the Mantel test, because they do not allow tests of multivariate interactions between factors in an ANOVA design. Distance-based redundancy analysis (db-RDA) provides a solution for data such as ours (Legendre and Anderson 1999). Db-RDA provides the flexibility of choosing a distance measure which is appropriate for community composition data containing a high number of rare species; it allows for testing the main factors as well as the interaction terms of an ANOVA model; it uses permutation testing which does not require multivariate normality; it can be used with response data containing more species than there are sites; and it allows users to draw biplots to represent the ANOVA results.

DETAILS OF METHODOLOGY

I. Effect of distance from the forest, Saccharum competition, time, site and fire on community composition.—Distance-based redundancy analysis (db-RDA) was used to test the significance of these experimental factors and their interaction terms in an ANOVA model, using species assemblage (a table of species abundances by subplots) as the response variable. Details of the procedure are outlined in Legendre and Anderson (1999). The experimental factors of distance from the forest, treatment of the Saccharum spontaneum, site, fire, and time were coded as orthogonal dummy variables. The effect of all five experimental factors could not be analyzed in a single analysis; different data were needed to test for time, site and fire (Table A1). We therefore analyzed our data using db-RDA with various three-way ANOVA designs: (1) To test for the effect of time, distance from the forest, Saccharum competition, and their interactions, data from all four time periods at the three sites that were not burned by wildfire, or by prescribed burn, were utilized (108 subplots). (2) To test for the effect of site, distance from the forest, and Saccharum competition, only the December 1996 data could be used because site replication was achieved by using the data collected before the prescribed burn on both sides of the firebreak at each site (90 subplots). (3) To test for the effect of fire, we used two response variable data tables: (A) burned vs. unburned. This was done as the experiment was originally planned, comparing the data collected in the final census in the burned (prescribed burn) and unburned sides of the two sites that received a prescribed burn and escaped uncontrolled fires (36 subplots). Because of this lack of power, we also conducted an alternative analysis (B) and compared before vs. after the burn on all plots that were burned regardless of whether it was as a result of wild or prescribed fires (108 subplots). The response data tables in all analyses included total number of individuals per species and number of recruits per species. Two additional response tables were also utilized for the fire analyses: total number of root sprouts per species, and a combined data table of the total number of root sprouts and recruits per species. The latter analysis is used to differentiate the effect of fire on the two mechanisms of regeneration in a single analysis; it treats the same species with two origins (root sprout and recruit) as if they were two different species. To de-emphasize rare species, this final analysis was performed using only those species where 10 or more individuals had been recorded.

TABLE A1. Data matrices used in the 10 three-way db-RDA analyses.


Factors tested

Response

Aug. 96

Dec. 96

April 97

Aug. 97


Time, distance, treatment

Total

+

+

+

+

Time, distance, treatment

Recruits

+

+

+

+

Site, distance, treatment

Total

+

Site, distance, treatment

Recruits

+

Fire, distance, treatment

Total

+

*

Fire, distance, treatment

Recruits

+

*

Fire, distance, treatment

Rootsprouts

+

*

Fire, distance, treatment

Rootsprouts and recruits

+

*

Fire, distance, treatment

Total

*, +

Fire, distance, treatment

Recruits

*, +

   Note: Response = response variables: Total = all data; Recruits; Rootsprouts; Rootsprouts and recruits = rootsprouts and recruits included in this analysis, but coded differently for each species. + = unburned plots, * = burned plots.

 

Redundancy analysis (RDA) was applied to the set of all principal coordinates (PCoA, Gower 1966) derived from the Bray-Curtis distance matrix among sites to test the significance of the main factors and the interactions. We used the Bray-Curtis distance measure within the db-RDA analyses because it does not give disproportionate weight to rare species (Legendre and Legendre 1998). The principal coordinates were corrected for negative eigenvalues using the Lingoes method (Gower and Legendre 1986, Legendre and Anderson 1999).

A special procedure was utilized for biplot representation, because the identity of the original species is lost when principal coordinates are computed from the Bray-Curtis distance matrix in the db-RDA procedure. The original species data were transformed using the chord transformation described by Legendre and Gallagher (2001), chosen because it does not give disproportionate weight to the rare species. The transformed data table was analyzed using RDA and utilized to produce ordination biplots. To further de-emphasize rare species, only those species represented by 5 or more individuals were represented in the biplots.

II. Effect of time since fire.—To test the significance of time since fire on species composition, and relate it to our experimental factors (distance from the forest and Saccharum treatment), forward selection of the (ln + 0.01)-transformed environmental variables (time since fire, distance from the forest, and both live and dead Saccharum biomass) was performed using RDA. This was carried out on the species matrix of number of individuals (chord-transformed) recorded per site in December 1996. A Monte-Carlo permutation test with 999 permutations was used to assess the statistical significance of each variable, as was the case for all multivariate analyses we utilized.

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