Combining data from different monitoring schemes is the only realistic option to assess the global state and trends of biodiversity. When measurement units and statistical distribution of data are the same across monitoring schemes, raw data can easily be combined and analysed within a single parametric statistical model, which produces an average estimated trend across all monitoring data despite heterogeneities in sampling units and scales. Summary statistics are also straightforward to compute from the integrated dataset. When the nature of data differs among monitoring schemes, information complexity can be reduced to the lowest level. This enables uncomplicated data integration, although much of the original information and precision contained in the data is lost. This is true for one species or several species. Here we outline basic principles and statistical methods for analysis if data can be combined. Meta-Analyses are required, if estimates need to be combined.
Basic principles and benefits
Approaches that combine monitoring data across ecological scales are particularly powerful to design global indicators of spatiotemporal trends of biodiversity and to explore the mechanisms underlying spatiotemporal responses of species and communities facing global change. If different species or taxonomic groups are to be combined, differences in biological coverage between monitoring schemes have to be accounted for in statistical analyses by appropriate weighting or averaging if contributions are not equal among species. Several weighting rationales can be considered. First, no weighting is used when biological knowledge of the relationship among species and taxa is insufficient. This is often done in practice, e.g. in the Living Planet Index. Second, weights can be used to give priority to a given characteristic (e.g. biological property: degree of specialization, rarity, originality, ecosystem function, or trophic level; conservation priorities; phylogenetic non-independence across species). Integration across species or taxa with similar ecological characteristics is informative when traits provide complementary information on the response of species to environmental change. Good examples of integration across species that differentiate specialist vs. generalist species are, for example, the European Bird Indicator and the European Butterfly Indicator. These and other approaches have demonstrated that specialist species are more sensitive to global change than generalist species. Thus, community analyses that build upon statistical models of "intactness" are expected to yield more accurate information on the expected trends of rare species than individual analyses of species. Furthermore, results indicate that an integrative approach based on functional traits rather than taxonomy alone may boost our understanding of patterns and processes, and enhance our predictive ability.
The most widely used techniques for statistical modelling of abundance data are General(ized) Linear Models (GLM), Generalized Additive Models (GAM) and their derivatives, such as Generalized Additive Mixed Models (GAMM). For example the classic way to analyse standardized large-scale monitoring schemes, such as Breeding Bird Surveys (BBS), is the use of Poisson regression analysis. To minimize the consequences of design deficiencies, analyses of such data tend to be model-based, using covariates in analyses to model factors that influence individual detectability and observer- or habitat-based differences in detection probabilities. Most models usually contain site and year effects, as well as possible effects of other covariates, and estimate missing values from available data.
Note that hierarchical (log linear) models can also be used to estimate regional population change from count data directly. In contrast to classical regressions, explanatory variables in hierarchical models (such as year, stratum or observer effects) are not considered fixed parameters, but are instead drawn from distributions, which may differ across higher hierarchical levels (state, region). The influence of regions, observers, and other factors is modelled directly on the distributions of parameters influencing counts, rather than on the counts themselves.
Bayesian methods are also increasingly used to describe the relationship between counts and control variables. Several features make Bayesian approaches particularly attractive for analysing meta-data: (1) ability to deal with missing values and unknown variances in a formal way; (2) ability to make belief statements that are relevant for management via a quantification of the likelihood of alternative hypotheses; (3) natural structuring of hierarchical data. Hierarchical Bayesian Models (HBM) hence allow integration of multiple sources of data and handling of missing data to study ecological processes at different scales in a unique and consistent framework. They appear to be promising tools to assess causes of trends in biodiversity using heterogeneous data across monitoring schemes and scales. A highly informative community modelling website, providing examples of various models as well as software code for implementing them, is: www.mbr-pwrc.usgs.gov/pubanalysis/communitymodeling
For further methods that may be suitable to analyse monitoring data, be they counts, presence/absence, or estimates of populations size, see Estimating trends from monitoring data.
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EuMon core team; August 2014