ESTUDIO FINANCIERO

All statistical analyses were carried out using R (R Development Core Team, 2008).

3.2.9.1 Analysis of scale-loss scores

Fisher’s exact test was used for comparisons between TREATMENT and CONTROL groups of the frequencies of changes to scale loss scores between release and recapture at the three defined score-change conditions, and for changes in pectoral fin score.

Generalized linear mixed effect models (GLMM) were used to check for potential influences on scale loss by other measured covariates which could not be controlled as part of the experimental design. Logistic GLMMs were performed with each of the three score-change conditions as a response. The covariates included were: treatment group, turbine speed category, lag between release and recapture, method of capture, average scale-loss score over the two sides of the fish before the trial, fork length and Fulton’s condition factor (100 x mass (g)/[fork length (cm)]3_{. Release batch was included as a random effect. The}

minimally adequate model was selected by the sequential deletion of covariates which caused no significant decrease in the fit of the model when omitted, as tested by likelihood ratio tests. The threshold for retention of covariates was p < 0.1, and the threshold for significance was p < 0.05.

Estimates for the probability of each score-change condition were based on the assumption that each fish was an independent trial with a probability of a change in score resulting from the process of the trial. The estimate of that probability is the number of fish with a change in score divided by the number of trials. Ninety-five percent confidence intervals were calculated from the binomial distribution for each probability and sample size.

3.2.9.2 Analyses of blood-chemistry data

Kruskal-Wallis tests were used to check for differences in blood analyte activities between UNHANDLED, CONTROL and TREATMENT groups. Mann- Whitney U-tests were used to check for differences between TREATMENT and CONTROL groups. These non-parametric tests were used because of the non- normal distributions of the data.

During the trials, there were potential influences on blood chemistry which were not part of the experimental design. Additional variation in response may also have arisen from lab analysis techniques. In order to account for these potential sources of systematic variation, generalized linear model regressions were performed which included recorded potential covariates. These regressions were carried out only on the data from the TREATMENT and CONTROL fish, not including the UNHANDLED fish, since these were not exposed to trial conditions.

Potential uncontrolled covariates identified and measured during the trials were: release batch (corresponding to a date and time of release); date and time of recapture (blood sampling time); the lag between release and recapture of each fish; temperature and temperature deviance (calculated for the 24 hour period

Table 3.3. Thresholds of detection for enolase, and distribution of data over thresholds. These data include Saprolegnia infected fish. The lowest detected value was 1.58, but the calculated lower limit of detection was 5.83.

Lowest detected value 1.58

Lower limit of detection 5.83

Proportion of sample below lowest value 0.53 Proportion of sample below limit of detection 0.90

Upper limit of detection 140

Proportion of sample above upper limit 0.01

Total N 223

prior to sampling); fish length; condition factor; method of capture (seine, recapture box, crowding); and actual turbine speed during the release-recapture period for each fish (summarized as mean and range). Assay plate for enolase was identified as a source of systematic variation from the laboratory analysis.

The enolase data were bounded by limits of detection, were zero inflated and had a left skewed distribution (Table 3.3). Therefore three regressions were carried out for these data: a logistic regression on the binary data dichotomised around the lower limit of detection, an ordinary regression on the continuous part of the data, and a logistic regression on the data dichotomised around a chosen threshold, the median enolase activity for the UNHANDLED group.

Collinearity

Covariates were checked for collinearity using the corvif function from the R library “HighstatLibV6” (Zuur et al., 2009). Sampling time, lag, batch, speed category, and average speed were found to be collinear (variance inflation factor > 3). Release-recapture lag is calculated from batch release time and sampling time, and so these three variables are not independent. Batch was selected for use in the models as the most pertinent potential covariate. Removing sampling time resulted in acceptable levels of collinearity (Variance inflation factor < 3) for lag. Whilst there may have been a temporal trend in blood chemistry, the random effect of batch was deemed more important for the analysis, and since batch is really a temporal categorical variable it would be expected that any underlying temporal differences would be captured. Average turbine speed is clearly not independent of the speed category, and so speed category was selected as the simplest variable.

Model selection

Stepwise model-selection was carried out for each separate regression to reduce the number of coefficients to the minimally adequate model. Covariates were removed on the basis of likelihood ratio tests between the current model and the models reduced by each of the remaining covariates in turn. Covariates resulting in p<0.1 on deletion were retained in the model.

3.2.9.3 Correlation between scale loss and blood responses

Once the final regression models for the blood responses had been selected, scale-loss scores were included to test for correlation between these and the

blood responses. The average scale-loss score before release, and change to average scores between release and recapture were selected for use.

3.2.9.4 Post-hoc power analysis

Post-hoc power analysis was carried out by simulating data with a range of assumed effect sizes, given the sample sizes attained in the trials, followed by analysis using the statistics described. The power was calculated as the proportion of 1000 simulated datasets at each effect size which yielded a significant treatment effect at the p=0.05 level. The effect size which would be reliably detected was taken as that which resulted in a significant result in 80% of simulations. For the blood chemistry analytes, the following model was used to simulate data: unperturbed enzyme activity levels were assumed to be normally distributed with the mean and standard deviation of the UNHANDLED group. A portion of CONTROL group activities were altered with a binomial probability pc, at an effect size ec. A portion of TREATMENT group activities were

altered with a binomial probability pt at an effect size et. Data were simulated

at four control effect prevalences (0.01, 0.05, 0.1 and 0.5) and two control effect sizes (a factor of 1.5 and 3, corresponding to a low and high effect size). The treatment effect prevalence necessary for 80% power using a t-test for a range of treatment effect sizes was then calculated and graphed. A t-test was used since this is the equivalent of a linear model with only one two-category covariate. Thus the power calculated is that of the model to detect a treatment effect with the partial effects due to other covariates already accounted for.

3.3 Results

3.3.1 Turbine and river state

The overall sample mean of the average turbine speed between introduction and recapture of each fish was 21.88 RPM (sd = 3.85, range: 11.68 - 25.60) for the FAST speed, and 9.96 RPM (sd = 2.13, range: 7.96 - 14.51) for the SLOW speed. Mid-channel water velocity in the intake basin at the SLOW and FAST speeds were 0.22 ms-1 _{and 0.61 ms}-1 _{respectively. Turbine discharge calculated from a}

velocity-depth profile at the FAST speed was 2.54 m3s-1, with a mean water velocity in the intake basin of 0.43 ms-1. Assuming maximum flow of 4 m3s-1 at 26 RPM at ideal channel depth, mean velocity entering the turbine mouth calculated from channel cross section (measured depth and known turbine diameter) and fractional filling of the turbine intake was 0.37 ms-1 at the SLOW speed and 1.21 ms-1 at the FAST speed. Using the measured discharge and fractional filled area resulted in a mean velocity at the turbine mouth of 1.24 ms-1 at the FAST speed. Fifteen-minute logged turbine and river discharge data are shown in Appendix A3.5. Average mean daily water temperature during the trials was 8.6 oC (range: 7.5-10.2), and average daily temperature deviance was 3.4 o_{C (range: 1.5-6) Fifteen-minute logged temperature data are shown in}

Appendix A3.5.