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Community Ecology
"Test how environmental gradients structure my species communities" -> Constrained ordination (CCA / RDA / db-RDA) with explicit dispersion testing alongside PERMANOVA, indicator-species analysis with group-size correction, Joint Species Distribution Models for residual covariance and prediction, and trait-environment testing with statistically corrected permutation schemes.
R: vegan::rda(), vegan::dbrda(), vegan::adonis2() for ordination and PERMANOVA
R: vegan::betadisper() for the mandatory PERMDISP companion to PERMANOVA
R: Hmsc or sjSDM for joint species distribution modeling
R: indicspecies::multipatt(..., func = 'IndVal.g') for indicator species
The Single Most Important Modern Insight -- Always run PERMDISP alongside PERMANOVA
Anderson & Walsh 2013 Ecol Monogr 83(4):557-574 established that PERMANOVA's pseudo-F is sensitive to dispersion heterogeneity — a significant PERMANOVA can reflect centroid difference, dispersion difference, or both. Running PERMANOVA without PERMDISP is the single most common methodological failure in community-ecology papers. If betadisper is significant alongside a significant PERMANOVA, the location-difference conclusion is not supported by the data alone; the two could be entirely a dispersion artifact.
A second cornerstone insight: residual species-species covariance in Joint Species Distribution Models is NOT a clean estimator of biotic interaction (Pollock 2014, reaffirmed by Zurell 2018 and Poggiato 2021). It reflects unmeasured covariates, dispersal limitation, sampling artifacts, AND any genuine biotic interactions, in unknown proportions. Skills that interpret residual covariance as interaction are over-interpreting.
Algorithmic Taxonomy
Method
Estimand
Strength
Fails when
CCA
Species-environment unimodal
Standard for chi-square data; fits bell-shaped responses
Linear gradients (use RDA); does not handle short gradients well
RDA
Species-environment linear
High power with short gradients; Hellinger-friendly
Long unimodal gradients (>3 SD DCA axis 1); needs no missing data
Different output structure than HMSC; not directly comparable
IndVal (Dufrene-Legendre)
Species-group association
Combines specificity AND fidelity
Biased by group size unless func='IndVal.g'
SES_MPD / SES_MNTD
Phylogenetic structure vs null
Tests whether communities are clustered or overdispersed
Interpretation of sign requires trait-conservatism check (Mayfield & Levine 2010)
RLQ + fourth-corner
Trait-environment relationship
Tests species-trait response to environment
Default modeltype gives inflated Type I; use modeltype=6
Decision Tree by Scenario
Scenario
Recommended approach
Why
Unimodal species responses, gradient > 3 SD (DCA axis 1)
CCA
Linear assumption fails for long gradients
Linear species responses, gradient <= 3 SD
RDA on Hellinger-transformed data
RDA assumes linearity; Hellinger solves double-zero problem
Bray-Curtis or other non-Euclidean distance preferred
db-RDA
Handles any distance metric while preserving constrained-ordination interpretation
Test "do these groups differ in community composition"
PERMANOVA (adonis2) AND PERMDISP (betadisper)
Never PERMANOVA alone; dispersion confound is non-negotiable
ANOSIM out of habit
Use PERMANOVA + PERMDISP instead
ANOSIM is biased by unbalanced N and dispersion
Mantel test for landscape genetics
dbRDA with spatial covariates OR GDM
Mantel has low power; partial Mantel inflates Type I
Joint species modeling with traits and phylogeny
HMSC (S < 500); sjSDM (S > 500)
HMSC encodes theory in priors; sjSDM is the only scalable option for high-S
Multi-species "association" structure
JSDM residual covariance
Interpret as ANY of (interaction, shared response to unmeasured driver, dispersal, sampling), NOT pure interaction
Indicator species with unbalanced group sizes
multipatt(..., func = 'IndVal.g')
IndVal is biased by group size; group-equalized form corrects
Phylogenetic community structure
SES_MPD with EXPLICIT null model + trait-conservatism test
Cite Mayfield & Levine 2010 for the "clustering = filtering" interpretation trap
Trait-environment hypothesis
RLQ + fourth-corner with modeltype=6
Default modeltype=2 or modeltype=4 gives inflated Type I error
Bipartite network nestedness/modularity
NODF2 + modularity with curveball null randomization
Strona 2014 curveball is exponentially faster and unbiased for binary matrices
CCA vs RDA — Gradient-Length Decision
Goal: Choose between unimodal (CCA) and linear (RDA) constrained ordination based on the dominant gradient length in the species data.
Approach: Run a Detrended Correspondence Analysis (DCA) on the raw community matrix; use the axis-1 SD length as the gradient-length metric. > 3 SD suggests unimodal CCA; < 3 SD suggests linear RDA on Hellinger-transformed data; 2-3 SD is a gray zone where either is defensible.
library(vegan)# Step 1: Check gradient length
dca <- decorana(species_matrix)
dca # axis 1 length in SD units# Step 2a: Long gradient -> CCA
cca_result <- cca(species_matrix ~ temperature + precipitation + pH + elevation,
data = env_data)
anova(cca_result, by ='margin', permutations =999)# Step 2b: Short gradient -> RDA with Hellinger transformation# Hellinger (Legendre & Gallagher 2001) is MANDATORY before RDA on community data
species_hell <- decostand(species_matrix, method ='hellinger')
rda_result <- rda(species_hell ~ temperature + precipitation + pH + elevation,
data = env_data)
RsquareAdj(rda_result)$adj.r.squared
anova(rda_result, by ='margin', permutations =999)# Forward selection with adjusted R-squared criterion (Peres-Neto 2006 Ecology 87:2614)
rda_null <- rda(species_hell ~1, data = env_data)
rda_full <- rda(species_hell ~ ., data = env_data)
rda_sel <- ordiR2step(rda_null, scope = formula(rda_full),
direction ='forward', permutations =999)# VIF check: > 10 indicates problematic multicollinearity
vif.cca(rda_sel)
PERMANOVA with the Mandatory PERMDISP Companion
Goal: Test whether community composition differs across groups while detecting the dispersion-heterogeneity confound.
Approach: Run adonis2 (modern PERMANOVA per Anderson 2001 Austral Ecol) on Hellinger or Bray-Curtis distances; THEN run betadisper (PERMDISP per Anderson 2006 Biometrics) to test whether group dispersions are unequal. Report BOTH results. If betadisper is significant, the adonis2 conclusion of centroid difference is not supported — the apparent "group difference" may be entirely a dispersion artifact.
library(vegan)# Distance matrix
bray_dist <- vegdist(species_matrix, method ='bray')# PERMANOVA via adonis2 (modern API; adonis() is deprecated)# by='margin' for unbalanced designs (sequential SS gives wrong result)
permanova <- adonis2(bray_dist ~ habitat + soil_pH, data = env_data,
by ='margin', permutations =999)
permanova
# MANDATORY companion: PERMDISP via betadisper# Tests homogeneity of multivariate dispersions across groups
disp <- betadisper(bray_dist, env_data$habitat)
disp_test <- permutest(disp, permutations =999)
disp_test
# Interpretation rule:# PERMANOVA p < 0.05 AND betadisper p > 0.05 -> location difference is real# PERMANOVA p < 0.05 AND betadisper p < 0.05 -> CONFOUNDED, cannot conclude location difference# PERMANOVA p > 0.05 -> no group difference detected# Visualize dispersions
plot(disp)
boxplot(disp)# For pairwise group comparisons, do NOT use Bonferroni-corrected pairwise PERMANOVA# (permutation tests with overlapping sets do not give nominal FWER from Bonferroni);# use pairwiseAdonis::pairwise.adonis2 with FDR correction instead# install.packages('pairwiseAdonis')
Joint Species Distribution Models — HMSC vs sjSDM
Goal: Model species occurrences jointly to capture environmental responses, traits, phylogeny, and residual covariance among species.
Approach: For S < 500 species with rich theory and traits/phylogeny: use HMSC (Ovaskainen 2017 Ecol Lett 20:561-576; current R package Tikhonov 2020 Methods Ecol Evol 11:442-447) for Bayesian inference with explicit ecological priors. For S > 500 species (modern metabarcoding datasets): use sjSDM (Pichler & Hartig 2021 Methods Ecol Evol 12:2159-2173) which is orders of magnitude faster via Monte Carlo approximation of the joint likelihood with elastic-net regularization. The Wilkinson 2019 Methods Ecol Evol 10:198-211 benchmark is essential reading before picking among HMSC, sjSDM, gjam, and BayesComm. Do NOT interpret residual species-species covariance as biotic interaction (see Zurell 2018 Ecography 41:1812-1819; Poggiato 2021 Trends Ecol Evol 36:391-401).
library(Hmsc)# HMSC for moderate-S Bayesian JSDM# X: site x environment data# Y: site x species presence-absence or abundance# distr: 'probit' for presence-absence; 'lognormal poisson' for counts
m <- Hmsc(Y = species_matrix, XData = env_data, XFormula =~ temperature + soil_pH,
distr ='probit')# Sample posterior (production runs need thin >= 100, transient >= 1000, samples >= 1000)
m <- sampleMcmc(m, thin =10, samples =1000, transient =5000, nChains =4)# Variance partitioning into fixed (environment), random (latent factors), traits, phylogeny
VP <- computeVariancePartitioning(m)
plotVariancePartitioning(m, VP = VP)# Predict to new environment
pred <- predict(m, XData = new_env_data, expected =TRUE)# For S > 500: switch to sjSDM# library(sjSDM)# m_sj <- sjSDM(Y = species_matrix, env = linear(env_data, ~ temperature + soil_pH),# family = binomial('probit'))# summary(m_sj); plot(m_sj)
Indicator Species with Group-Size Correction
Goal: Identify species statistically associated with site groups using an indicator value that combines specificity and fidelity, corrected for unequal group sizes.
Approach: Run indicspecies::multipatt with func = 'IndVal.g' (the group-size-equalized form per De Caceres & Legendre 2009 Ecology 90:3566-3574). The original IndVal is biased toward larger groups; the .g form corrects this. For continuous-vs-categorical or rank-based associations, use func = 'r.g' (point-biserial correlation, group-equalized).
library(indicspecies)# IndVal.g: group-size-equalized indicator value# multipatt tests species-group associations with permutation# duleg=TRUE: tests only single-group associations (not combinations)# duleg=FALSE: tests species against all group combinations (more powerful but more tests)
mp <- multipatt(species_matrix, site_groups,
func ='IndVal.g',# Group-equalized; NOT 'IndVal' (biased)
duleg =TRUE,
control = how(nperm =999))
summary(mp, alpha =0.05)# Extract significant indicators sorted by p-value
sig <- mp$sign[!is.na(mp$sign$p.value)& mp$sign$p.value <0.05,]
sig[order(sig$p.value),]
Mantel Replacement — dbRDA with Spatial Covariates
Goal: Test whether community/genetic distance correlates with environmental distance while controlling for spatial autocorrelation, replacing the low-power and bias-prone Mantel framework.
Approach: Use db-RDA with spatial predictors (PCNM eigenvectors or raw coordinates) as Condition() (Legendre & Fortin 2010 Mol Ecol Resour 10:831-844). Partial Mantel inflates Type I error under autocorrelation — do not use for landscape data.
library(vegan)
library(adespatial)# Build spatial predictors: PCNM (principal coordinates of neighbor matrices)
geo_dist <- dist(coords[,c('longitude','latitude')])
pcnm <- pcnm(geo_dist)
pcnm_vars <- pcnm$vectors # significant axes# db-RDA controlling for spatial structure
dbrda_result <- dbrda(bray_dist ~ temperature + precipitation +
Condition(as.matrix(pcnm_vars)),
data = env_data, add ='lingoes')# Test marginal significance of environment AFTER conditioning out space
anova(dbrda_result, by ='margin', permutations =999)# DO NOT use partial Mantel for this question; cite Legendre & Fortin 2010
Per-Method Failure Modes
PERMANOVA significant, betadisper also significant -> conclusion not supported
Trigger: Reporting PERMANOVA p < 0.05 as evidence of "community composition differs across groups" without running betadisper, OR running betadisper and finding it significant but ignoring the result.
Mechanism: PERMANOVA's pseudo-F responds to BOTH centroid shifts AND dispersion heterogeneity (Anderson & Walsh 2013). When groups differ in dispersion but not centroid, PERMANOVA can return p < 0.05 from the dispersion difference alone.
Symptom: Reviewer asks "was dispersion checked?"; PCoA visualization shows overlapping centroids but one group is more dispersed; betadisper p < 0.05.
Fix: Report both PERMANOVA and betadisper. If betadisper is significant, the conclusion must be reframed: "Groups differ in either centroid or dispersion, with dispersion heterogeneity present." Consider db-RDA which is more dispersion-robust.
Mantel test reports low p but reflects spatial autocorrelation
Trigger: Using Mantel or partial Mantel to test "is genetic distance correlated with environmental distance" in a spatially-structured landscape.
Mechanism: Mantel statistics are biased downward by spatial autocorrelation in either distance matrix (Legendre & Fortin 2010). Partial Mantel further inflates Type I error rates under autocorrelation (see Guillot & Rousset 2013 Methods Ecol Evol 4:336-344 for the formal demonstration).
Symptom: Mantel p < 0.001 but no detectable signal when re-tested with dbRDA conditioning on geographic distance.
Fix: Use db-RDA with PCNM spatial eigenvectors as Condition(), OR GDM (Generalized Dissimilarity Modeling).
JSDM residual covariance interpreted as biotic interaction
Trigger: Reporting "species A and species B have residual covariance after fitting environment, indicating biotic interaction."
Mechanism: Residual covariance after environmental fitting reflects (a) unmeasured covariates, (b) dispersal limitation, (c) sampling artifacts, (d) shared response to unmeasured drivers, AND (e) any genuine biotic interactions, in unknown proportions. Without manipulative or independent corroboration, the interaction signal cannot be isolated.
Symptom: Reviewer challenges "interaction" interpretation; sensitivity tests with different environmental specifications change the residual structure dramatically.
Fix: Report residual covariance descriptively ("residual association after fitting environment"), explicitly acknowledge alternative explanations, and cite Zurell 2018 or Poggiato 2021 for the interpretation caveat.
IndVal biased by unequal group sizes
Trigger: Running multipatt(..., func = 'IndVal') with strongly unbalanced groups.
Mechanism: The original IndVal index from Dufrene & Legendre 1997 is biased toward larger groups because larger groups have higher average occupancy by chance.
Symptom: All indicators are assigned to the largest group; small-group indicators are undetected.
Fix: Use func = 'IndVal.g' (group-equalized) per De Caceres & Legendre 2009. The .g correction is the modern default.
SES_MPD sign interpreted as filtering vs competition without trait check
Mechanism: Mayfield & Levine 2010 Ecol Lett 13:1085-1093 showed competition can produce phylogenetic clustering (not just overdispersion) when ecologically similar species coexist via R*-rule trait differences. The Webb 2002 sign-to-process mapping is incomplete.
Symptom: Trait-similarity vs phylogenetic-similarity correlation has not been examined; reviewer asks about Mayfield-Levine alternative.
Fix: Compute Blomberg's K AND Pagel's lambda; if traits track phylogeny strongly, the clustering signal could be either filtering OR competition. Cite Mayfield & Levine 2010 in interpretation.
Quantitative Thresholds
Threshold
Value
Source / rationale
DCA gradient length
< 3 SD: RDA; > 3 SD: CCA; 2-3 SD: gray zone
Standard ordination decision rule
VIF
> 10: collinearity problem
Hair et al. ecology convention
PERMANOVA + PERMDISP rule
Report BOTH; if both p < 0.05, location difference not supported
Anderson MJ (2001) A new method for non-parametric multivariate analysis of variance. Austral Ecol 26(1):32-46. doi:10.1111/j.1442-9993.2001.01070.pp.x
Anderson MJ (2006) Distance-based tests for homogeneity of multivariate dispersions. Biometrics 62(1):245-253. doi:10.1111/j.1541-0420.2005.00440.x
Anderson MJ, Walsh DCI (2013) PERMANOVA, ANOSIM, and the Mantel test in the face of heterogeneous dispersions. Ecol Monogr 83(4):557-574. doi:10.1890/12-2010.1
Legendre P, Fortin M-J (2010) Comparison of the Mantel test and alternative approaches for detecting complex multivariate relationships. Mol Ecol Resour 10(5):831-844. doi:10.1111/j.1755-0998.2010.02866.x
Legendre P, Gallagher ED (2001) Ecologically meaningful transformations for ordination of species data. Oecologia 129(2):271-280. doi:10.1007/s004420100716
Peres-Neto PR, Legendre P, Dray S, Borcard D (2006) Variation partitioning of species data matrices. Ecology 87(10):2614-2625. doi:10.1890/0012-9658(2006)87[2614:VPOSDM]2.0.CO;2
Dufrene M, Legendre P (1997) Species assemblages and indicator species. Ecol Monogr 67(3):345-366. doi:10.1890/0012-9615(1997)067[0345:SAAIST]2.0.CO;2
De Caceres M, Legendre P (2009) Associations between species and groups of sites. Ecology 90(12):3566-3574. doi:10.1890/08-1823.1
Pollock LJ, Tingley R, Morris WK et al. (2014) Joint Species Distribution Model (JSDM). Methods Ecol Evol 5(5):397-406. doi:10.1111/2041-210X.12180
Ovaskainen O, Tikhonov G, Norberg A et al. (2017) Hierarchical Modelling of Species Communities (HMSC). Ecol Lett 20(5):561-576. doi:10.1111/ele.12757
Tikhonov G, Opedal OH, Abrego N et al. (2020) Joint species distribution modelling with the R-package Hmsc. Methods Ecol Evol 11(3):442-447. doi:10.1111/2041-210X.13345
Pichler M, Hartig F (2021) A new joint species distribution model for faster and more accurate inference. Methods Ecol Evol 12(11):2159-2173. doi:10.1111/2041-210X.13687
Wilkinson DP, Golding N, Guillera-Arroita G et al. (2019) Comparison of joint species distribution models. Methods Ecol Evol 10(2):198-211. doi:10.1111/2041-210X.13106
Zurell D, Pollock LJ, Thuiller W (2018) Do joint species distribution models reliably detect interspecific interactions from co-occurrence data in homogenous environments? Ecography 41(11):1812-1819. doi:10.1111/ecog.03315
Poggiato G, Munkemuller T, Bystrova D et al. (2021) On the interpretations of joint modeling in community ecology. Trends Ecol Evol 36(5):391-401. doi:10.1016/j.tree.2021.01.002
Guillot G, Rousset F (2013) Dismantling the Mantel tests. Methods Ecol Evol 4(4):336-344. doi:10.1111/2041-210x.12018
Webb CO, Ackerly DD, McPeek MA, Donoghue MJ (2002) Phylogenies and community ecology. Annu Rev Ecol Syst 33:475-505. doi:10.1146/annurev.ecolsys.33.010802.150448
Mayfield MM, Levine JM (2010) Opposing effects of competitive exclusion on phylogenetic community structure. Ecol Lett 13(9):1085-1093. doi:10.1111/j.1461-0248.2010.01509.x
Dray S, Choler P, Doledec S et al. (2014) Combining fourth-corner and RLQ methods. Ecology 95(1):14-21. doi:10.1890/13-0196.1
Strona G, Nappo D, Boccacci F, Fattorini S, San-Miguel-Ayanz J (2014) A fast and unbiased procedure to randomize ecological binary matrices. Nat Commun 5:4114. doi:10.1038/ncomms5114
Related Skills
ecological-genomics/biodiversity-metrics - Alpha/beta diversity and Hill numbers prior to ordination
ecological-genomics/edna-metabarcoding - Generate community data from environmental samples
ecological-genomics/landscape-genomics - Genotype-environment associations (genetic analog of GEA)
microbiome/diversity-analysis - Unconstrained ordination alternative for 16S microbiome
data-visualization/ggplot2-fundamentals - Customize triplots, ordination plots, and indicator-species visualizations
