7.3 Statistical framework
7.3.1.Statistical methodologies
Surveys must be designed taking into account the fact that fish assemblages and sessile resources associated with artificial reefs are both extremely patchy in distribution and abundance and variable in time. Patchiness and temporal variation are caused by processes that are external to the assemblage, in particular disturbances, changes in environmental factors (e.g. temperature and current speed and direction) and recruitment, in addition to processes operating within the existing assemblage.
The statistical framework which should be developed to better evaluate the community/assemblage biomass associated with artificial reefs, and hence determine the effectiveness of artificial reefs for the development of benthic communities, stock enhancement and fishery management, should be related to new and comprehensive statistical methods such as:
• Before?after control?impact (BACI)/after control?impact (ACI) and beyond BACI designs; • Analysis of variance (ANOVA), multivariate analysis of variance (MANOVA), permutational multivariate analysis of variance (PERMANOVA) with uni? or multifactorial designs;
• Non?parametric methods (e.g. Kolmogorov?Smirnov test, Mann?Whitney U test, Kruskall?Wallis test, Wilcoxon matched pairs test, etc.);
• Time series analysis.
7.3.2.BACI/ACI and beyond BACI designs
The development of beyond BACI designs (Underwood, 1991) has led to significant advances in the detection of changes due to the deployment of artificial structures. Such designs use multiple reference locations and the data are usually analysed with an asymmetrical analysis of variance due to the presence of a single location interested by the deployment of a new structure (artificial reefs, offshore platforms, etc.). In this approach, the influence of the new structure, if it exists, can be detected as a statistical interaction in the difference between the area interested by the deployment and reference locations from before to after the placement. Thorough discussions of beyond BACI designs, including several examples and their interpretation, are provided by Underwood (1991, 1992 and 1993). Further examples of the performance of BACI and beyond BACI procedures are illustrated by Hewitt et al. (2001), whereas Benedetti?Cecchi (2001) discussed an approach based on Monte Carlo simulations to optimize such complex designs. Stewart?Oaten and Bence (2001) examined a number of potential problems of beyond BACI procedures and emphasized a model?based philosophy to the analysis of impacts (Terlizzi et al., 2010).
A possible advantage of beyond BACI designs is that they can be modified and applied in tests of impact when no data have been obtained before the purported impact and, thus, only “after’’ data are available. These ACI designs, though more limited in establishing cause? effect relationships between human interventions and responses of populations, have been widely used in environmental impact studies (Chapman et al., 1995; Roberts, 1996; Lardicci et al., 1999; Guidetti et al., 2002). More specifically, in the absence of “before’’ data, it may be possible to detect consistent differences between one or more modified locations and several reference locations, although it is generally not possible to attribute causation to any particular event, historical or ongoing, for such differences.
A detailed description of how to deal with asymmetrical data and a discussion of the problems associated with detecting impacts when only “after’’ data are available are provided by Glasby (1997).
7.3.3.ANOVA and MANOVA (PERMANOVA)
The analysis of variance has been utilized since the beginning of the development of studies about artificial reefs (Fabi and Fiorentini, 1994). When the replication is appropriately designed and the assumptions are fully met, this method provides a robust statistical framework to evaluate the changes in both fish and benthic communities. The main issue is that, especially in multivariate analysis (MANOVA), it is quite unrealistic that data are normally distributed. An alternative to this traditional approach that does not rely on such strict assumptions is to use a permutation test (PERMANOVA). A permutation test calculates the probability of getting a value equal to or more extreme than an observed value of a test statistic under a specified null hypothesis by recalculating the test statistic after random re? orderings (shuffling) of the data (Anderson, 2001).
Non?parametric multivariate and univariate procedures have emerged in recent years, providing useful statistical methods that have been widely adopted for analysing areas characterized by the deployment of artificial structures. Similarly to permutation tests, an important feature of these methods is that they do not require the assumption of normality. This is a requirement that very often is not met by data consisting of counts of species, abundances or percentage cover of organisms (Legendre and Legendre, 1998).
7.3.4.Non?parametric methods
Non?parametric tests are numerous and have different purposes. In the following paragraph, short descriptions of the most utilized tests are provided. The Kolmogorov?Smirnov test assesses the hypothesis that two samples were drawn from different populations and it is usually employed to compare frequency distributions. Unlike the Mann?Whitney U test, which tests for differences in the location of two samples (differences in means, differences in average ranks, respectively), the Kolmogorov?Smirnov test is also sensitive to differences in the general shapes of the distributions in the two samples (i.e. to differences in dispersion, skewness, etc.). Thus, its interpretation is similar to that of the Wald?Wolfowitz runs test. The Kruskal?Wallis ANOVA by ranks test assumes that the variable under consideration is continuous and that it was measured on at least an ordinal (rank order) scale. The test assesses the hypothesis that the different samples in the comparison were drawn from the same distribution or from distributions with the same median. Thus, the interpretation of the Kruskal?Wallis test is basically identical to that of the parametric one? way ANOVA, except that it is based on ranks rather than means. The Wilcoxon matched pairs test assumes that the variables under consideration were measured on a scale that allows the rank ordering of observations based on each variable (i.e. ordinal scale) and that allows rank ordering of the differences between variables (this type of scale is sometimes referred to as an ordered metric scale).
7.3.5.Time series analysis
Time series analysis is used when observations on artificial reefs are made repeatedly and over long time periods (more than 20–25 years). One goal of this analysis is to identify patterns in the sequence of samples over time, which are correlated with themselves. Another goal in many research applications is to test the impact of one or more interventions (for example the enlargement of an artificial reef or the opening of the reef to fishers). Time series analysis is also used to forecast future patterns of events or to compare series of different kinds of events and find out possible cause?effect correlations between habitat and environmental parameters.
7.3.6.Spatial and temporal replication
The temporal and spatial scale of sampling is essential to separate reef effects from background variability. While some studies have examined how the distribution of artificial reefs relates to habitat use and to the development of prey resources for resident species, few have explicitly attempted to isolate reef effects. An absence of background pre? deployment data (Clark and Edwards, 1999), erroneous and inappropriate experimental design (Alevizon and Gorham, 1989), as well as infrequent sampling, e.g. only once per season (Santos and Monteiro, 1998), have also cast doubts over recorded changes in fish abundances.
The spatial extent of sampling depends on the size of the area designated for artificial reef placement. Obviously, a number of reference sites without any artificial reef and having the same environmental characteristics (e.g. grain?size, depth) should be sampled at the same time in order to assess the effects of the artificial reef in the environment. Indicating the correct number of reference sites is quite challenging because it depends on a variety of factors, first of all the aim of the study and the spatial scale considered. However, as a rule of thumb, reference site number should not be less than three to provide enough data to apply one of the statistical methods listed before.
Whatever the typology of the study, the hypothesis to be tested and the ultimate use of the data from sampling, spatial replication is a mandatory component of any kind of investigation. The large variability in numbers and varieties of species from place to place at many spatial scales creates fundamental problems for determining which scale of replication is necessary. When there is a doubt about the relevant spatial scale, it is suggested to use a design that can detect changes or differences at one or more of the possible scales.
In studies with frequent sampling, the high variability in abundances of individual species is an evidence of key events such as settlement, migration and mortality. The same experimental design sampled at less frequent intervals will fail to detect these events, which are fundamental to distinguish attraction and production. Artificial reefs and reference sites should be visited at intervals that are relevant to life history events, e.g. every month or every two months, to permit comparisons between and within seasons and detect abundance changes related to recruitment and mortality.
To test seasonal or other a priori selected scales of temporal variation, temporal variation among the factors of interest should be compared to temporal variation within each factor of interest. In other words, the temporal variation among seasons must be compared to the magnitudes of variation that occur in each season. To measure such variability, it is essential to collect samples at an adequate number of times within each season. With two or more scales of temporal sampling, seasonal or other long?term trends can be identified against background noise. Where there is no measure of shorter?term temporal variation and such variation is large, quite spurious seasonal (or other temporal) patterns will be seen in the data. Moreover, at a shorter temporal time scale, the variability due to the photoperiod needs to be considered in studies on the horizontal and vertical movements of reef fish through the water column.
Different scales of temporal sampling are extremely important to identify environmental impacts. Disturbances to the environment may either be short?lived (pulse disturbances) or persist for long periods of time (press disturbances) (Bender et al., 1984). The responses of organisms to either type of disturbance may be relatively short?term (i.e. a pulse response); for example, abundance may rapidly increase but soon drop to normal levels, irrespective of whether the disturbance persists or ceases. Alternatively, populations may show long?term responses (i.e. press responses) to continuing disturbances (because the disturbance continues to exert an effect) or to pulse disturbances (because the disturbance, although ended long ago, caused long?term changes to some other environmental or biological variables).