Statistical methods to analyze ecological data

We provide a variety of statistical methods and simulation techniques in order to analyze ecological data. 

Overview:

Frequently used methods:

• Graphical analyses: scatterplots, histograms, box plots, coplots, Cleveland plots, pair plots, density plots, 3D-plots, variograms, residual plots, h-scatterplots.
• Correlations: Pearson’s, Kendall’s, Spearman’s, biserial, point-biserial, temporal autocorrelation, spatial autocorrelation (Moran I, Geary C), cross-correlation, Q-analysis, R-analysis, Mantel test, ANOSIM.
• Comparing means: t-Tests, ANOVA, ANCOVA, factorial ANOVA, post hoc tests, defined contrasts.
• Regressions: linear regression, multiple regression, multinomial regression, partial regression, generalized linear (mixed) models, generalized additive (mixed) models, linear mixed models, generalized least squares, generalized estimation equations, mixture models, zero-inflated models (z.B. ZIP), regression diagnostics.
• Classification and regression trees, discriminant function analysis.
• Multivariate/ordination-techniques: MANOVA, multinomial logistic regression, principal component analysis, linear discriminant analysis, redundancy analysis, correspondence analysis, de-trended correspondence analysis, canonical correspondence analysis, explanatory factor analysis, principal coordinate analysis, non-metric multidimensional scaling, dynamic factor analysis, Mantel test, Bray-Curtis ordination.
• Time series: ANOSIM, autoregressive models, moving average models, ARMA, ARIMA, ARIMAX models, multivariate trend analyses, min/max autocorrelation factor analysis, dynamic factor analysis, chronological clustering, univariate trend analysis with complex regression methods.
• Spatial statistics: Mantel test, analysis of raster data, geo-statistics, Moran’s I index, correlograms, spatial autoregressive models, SMA models, LM(ce) models, kriging/variogram models, explanatory variogram analysis, AM-trend models, AM(ce) models, home ranges.
• Non-parametric statistical methods: robust Wilcoxon methods, resampling, bootstrap, trimmed mean, Monte-Carlo simulations, permutation tests, M estimators, Kendall's tau, Spearman’s correlation, χ² test, log-linear analysis, Fisher’s exact test, Wilcoxon rank-sum and signed-rank tests, Kruskal-Wallis test, Jonckheere-Terpsra test, Friedman's ANOVA.
• Model selection: AIC, DIC, BIC, cAIC, AICc, WAIC, Bayes factors, LASSO, ridge regression, model averaging.
• Differential equations: ordinary differential equations, partial differential equations.
• Simulation techniques: finite difference methods, finite elements methods.
• Bayesian data analysis: posterior predictive model checking, Markov chain Monte Carlo simulations.
• Imputing missing values: kriging, multiple imputation.
• Power analyses (e.g. to determine optimal sample sizes): a priori, post hoc, compromise.
• Ecological applications: morphometry, impact studies, e.g. before-after control-impact studies, alpha-diversity indices (Simpson, Evenness, Shannon), beta-diversity indices (Bray-Curtis, Jaccard), home ranges, distance correction, survival rates, mark-recapture studies, Cormack-Jolly-Seber models, analysis of tracking/logger data using point process models (PPMs), integrates Step Selection Analysis (iSSA) or Hidden Markov Models (HMMs).