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Time series distribution at the diferent Locations for both the Reserve and the fished areas at

Comparison of the distribution between Fished and Reserve Areas

Comparison of the regression slopes by means of an ANCOVA.

Plot of the linear model fit for both Zones

Linear model fit for Reserve Areas

## 
## Call:
## lm(formula = Mean ~ Year, data = spp.reserve)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -0.8836 -0.2228 -0.1577  0.1462  1.3500 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 457.8929    77.2029   5.931 1.30e-05 ***
## Year         -0.2273     0.0384  -5.918 1.33e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4933 on 18 degrees of freedom
## Multiple R-squared:  0.6605, Adjusted R-squared:  0.6417 
## F-statistic: 35.02 on 1 and 18 DF,  p-value: 1.334e-05

Linear model fit for Fished Areas

## 
## Call:
## lm(formula = Mean ~ Year, data = spp.fished)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.82537 -0.38552 -0.05845  0.34717  1.64959 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 470.07857   69.17378   6.796 1.55e-07 ***
## Year         -0.23337    0.03441  -6.783 1.60e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5415 on 30 degrees of freedom
## Multiple R-squared:  0.6053, Adjusted R-squared:  0.5921 
## F-statistic:    46 on 1 and 30 DF,  p-value: 1.602e-07

ANCOVA model, the “Mean abundnace” is modeled as the dependent variable with “Zone (Fished or Reserve)” as the factor and Year as the covariate. The summary of the results show a significant effect of Year, but no significant interaction. These results suggest that the slope of the regression between Year-mean at both Fished and Reserve areas is similar.

##             Df Sum Sq Mean Sq F value   Pr(>F)    
## Year         1 21.946  21.946  81.581 5.28e-12 ***
## Zone         1  0.204   0.204   0.758    0.388    
## Residuals   49 13.181   0.269                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Call:
##    aov(formula = Mean ~ Year + Zone, data = spp)
## 
## Terms:
##                      Year      Zone Residuals
## Sum of Squares  21.945735  0.203862 13.181337
## Deg. of Freedom         1         1        49
## 
## Residual standard error: 0.5186587
## Estimated effects may be unbalanced

Compare the residuals

Standard model validation graphs are (i) residuals versus fitted values to verify homogeneity, (ii) a QQ-plot or histogram of the residuals for normality, and (iii) residuals versus each explanatory variable to check independence and (iv) Residuals versus Year

Reserves, Fished.