## 2 Materials and Methods  
A systematic search of published literature on Google Scholar and EBSCOhost from 1999 to 2019 was carried out using the following terms or phrases: Fishmeal replacements in fish feeds, fishmeal alternatives in fish diets, animal protein sources in aquaculture, insects in fish feeds, terrestrial by-product, and fishery by-products. By reading through the titles and abstracts, the papers were found and screened. In addition, of the selected articles, the reference and bibliographic lists were screened as potential leads to additional relevant studies for inclusion. In Endnote reference manager version x7.7.1 (Clarivate Analytics, Philadelphia, PA, USA), full-text articles for studies including animal protein sources, were retrieved and managed. An article was included in the review if published between 1999 and 2019 and reported on 3 or all 4 of the following on experimental animals: Specific growth rate, final weight, feed conversion ratio, and survival rate. Studies with less than 4 protein levels tested, and those with no standard error on results were excluded. Furthermore, editorial material, book chapters, and conference papers were excluded. Meta-analysis was conducted for final weight, specific growth rate, feed conversion ratio, and survival rate, separately in a Microsoft Excel Spreadsheet using formulas and procedure described by [20] as follows after entering study Authors and year, events, and sample size for each study included:  
1. Calculated the outcome (es) = number of events/the sample size
2. Calculated Standard Error (SE) = Square root of the outcomes/sample size
3. Variance (Var) =SE2
4. Computed the individual study weights (W) = 1/SE2
5. Computed each weighted effect size (W*es) =each effect size multiplied by study weight
6. W*es2 and W2 were calculated. All values of each variable were added to have the sum.
7. Calculated Q = \(\sum\)(W*ES2)-[\(\sum\)(W*ES)]2/\(\sum\)W, Q test to measure heterogeneity among studies.
8. I2 index = (Q-degree of freedom (df)/Q*100, was calculated to quantify heterogeneity, Degree of freedom (df) was calculated as the total number of studies minus 1. If values of I2 index were 0%, \(\leq\)25%, 50%, or 75%, the I2 index was interpreted as no, low, moderate, or high heterogeneity, respectively.  
9. Decided on the effect summary model. Random Effect Model was used because we assumed that the variability in studies was not due to sampling errors only but also in the population of effects. Furthermore, the Random Effect Model was used to measure the variability between studies, considering that other studies, which were not included in the meta-analysis at hand, could be unpublished, ignored in the systematic literature quest, or to be conducted in the future [21]. The weight of each study was adjusted with a constant (V) = Q-df)/\(\sum\)W-(\(\sum\)W\({}^{2}\)/\(\sum\)W). However, we computed w\({}^{2}\) first and then the sum of w\({}^{2}\) (\(\sum\)W\({}^{2}\)), which was not computed yet.
10. New weight for each study was calculated using W\({}_{\rm v}\) = 1/(SE\({}^{2}\) + V).
11. Weighted effect size (W*es), W*es\({}^{2}\), Wv\({}^{2}\), Q\({}_{\rm v}\), and I\({}^{2}\)v were computed using the new weight (W\({}_{\rm v}\)) as in steps 5-8.
12. Calculated the effect summary as es\({}_{\rm v}\) = \(\sum\)(Wv*es)/\(\sum\)W\({}_{\rm v}\) and standard error as SES\({}_{\rm v}\) = \(\surd\)1/\(\sum\)W\({}_{\rm v}\)
13. The lower and upper confidence intervals were calculated as es\({}_{\rm v}\) - (1.96*SEes\({}_{\rm v}\)) and es\({}_{\rm v}\) + (1.96*SEes\({}_{\rm v}\)), respectively.
14. Figures in results (excluding Figure 1) were drawn using the weights, prevalence, and confidence intervals calculated above.