  Our main goal in this paper is to study the number of small-amplitude
isolated periodic orbits, so-called limit cycles, surrounding only one
equilibrium point a class of polynomial Kolmogorov systems. We denote by
$\mathcal M_{K}(n)$ the maximum number of limit cycles bifurcating from the
equilibrium point via a degenerate Hopf bifurcation for a polynomial Kolmogorov
vector field of degree $n$. In this work, we obtain another example such that $
\mathcal M_{K}(3)\geq 6$. In addition, we obtain new lower bounds for $\mathcal
M_{K}(n)$ proving that $\mathcal M_{K}(4)\geq 13$ and $\mathcal M_{K}(5)\geq
22$.
