## 3 Results and Discussion
The evaluation of the parameters evaluated in this study indicated the presence of a significant negative correlation between the potential for the synthesis of silver nanoparticles \(\times\) production of fungal biomass, as well as the potential for synthesis of silver nanoparticles \(\times\) LT50, suggesting that, with the increase in values for biomass production and LT50, there is a tendency to reduce the potential for the synthesis of silver nanoparticles (Table 4). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Fungi/Isolate** & **Diameter (nm) \({}^{\star}\)** & **Polydispersity Index** \\ \hline \multicolumn{3}{c}{_Beauveria bussiana_} \\ SE101 & 127.8 \(\pm\) 0.63 & 0.262 \(\pm\) 0.01 \\ SE103 & 77.08 \(\pm\) 1.31 & 0.255 \(\pm\) 0.01 \\ SE104 & 173.63 \(\pm\) 16.11 & 0.635 \(\pm\) 0.12 \\ SE106 & 111.16 \(\pm\) 5.73 & 0.282 \(\pm\) 0.01 \\ SE107 & 136.63 \(\pm\) 9.41 & 0.627 \(\pm\) 0.02 \\ SE109 & 61.14 \(\pm\) 2.00 & 0.474 \(\pm\) 0.02 \\ SE110 & 90.29 \(\pm\) 5.50 & 0.250 \(\pm\) 0.01 \\ SE111 & 148.7 \(\pm\) 7.19 & 0.482 \(\pm\) 0.04 \\ Psi & 289.13 \(\pm\) 7.85 & 0.598 \(\pm\) 0.01 \\
447 & 40.14 \(\pm\) 0.61 & 0.467 \(\pm\) 0.004 \\
1213 & 69.36 \(\pm\) 1.57 & 0.342 \(\pm\) 0.05 \\
1260 & 77.56 \(\pm\) 2.14 & 0.306 \(\pm\) 0.05 \\
1258 & 126.06 \(\pm\) 0.57 & 0.165 \(\pm\) 0.01 \\ \multicolumn{3}{c}{_Metahizium anisopliae_} \\ SE202 & 132.3 \(\pm\) 10.86 & 0.279 \(\pm\) 0.04 \\ \multicolumn{3}{c}{_Isaria fumosorosea_} \\ SE301 & 131.3 \(\pm\) 12.39 & 0.551 \(\pm\) 0.11 \\ \hline \hline \multicolumn{3}{c}{\({}^{\dagger}\)Mean values with standard error.} \\ \end{tabular}
\end{table} 
Table 3: Average diameter and polydispersity index of silver nanoparticles synthesized by entomopathogenic fungi extracts. The effect of Pearson's correlation between variables is represented by the correlation coefficient (r) values that vary between \(-1\) to \(+1\), where zero indicates no correlation. Positive correlation coefficients represent the existence of a direct correlation between the variables, where both present the same trend (when the value of one variable increases, the value of the other variable also increases), and negative coefficients indicate the presence of an inverse correlation (when the value of one variable increases, the value of the other variable decreases). Moreover, Pearson's coefficients can be classified by their values. Therefore, values between 0 and 0.3 (or 0 and \(-0.3\)) are considered weak and biologically negligible; values between 0.31 and 0.5 (or \(-0.31\) and \(-0.5\)) refer to the presence of weak correlations; values between 0.51 and 0.7 (or \(-0.51\) and \(-0.7\)) indicate moderate correlations; values between 0.71 and 0.9 (or \(-0.71\) and \(-0.9\)) indicate strong correlations; and values >0.9 (or \(<\)\(-0.9\)) indicate the presence of very strong correlations [31]. The significance of the values calculated for [PERSON]'s coefficient demonstrates the presence of a strong negative correlation between the production of fungal biomass and synthesis of silver nanoparticles (\(-0.864\), \(p<0.05\)), indicating that an increase in the production of fungal biomass had a large influence in reducing the synthesis potential of the entomopathogenic fungi isolates. In addition, a moderate negative correlation was observed between the fungus virulence (LT50) and the potential for synthesis (\(-0.504\), \(p<0.01\)). Mycelial growth, pathogenicity, and virulence of entomopathogenic fungi are biological aspects associated with the ability of the microorganism to secrete enzymes that assist in the degradation of nutrients in the environment, and subsequent absorption, and in the processes of penetration and colonization of the fungus in the insect host body. Lipases, proteases, and chitinases are the main enzymes that influence entomopathogenic fungi in their pathogen-host interaction, and their activation and regulation can promote the development of greater specificity of action between the microorganism and the target