Let $(x_1,y_1),\ldots,(x_n,y_n)$ be distinct non-constant and non-degenerate solutions of the classical Lotka-Volterra system \begin{ equation}\notag \begin{ split} x'&= axy + bx\\ y'&= cxy + dy, \end{ split} \end{ equation} where $a,b,c,d\in\mathbb{ C}\setminus\{ 0\}$. We show that if $d$ and $b$ are linearly independent over $\mathbb{ Q}$, then the solutions are algebraically independent over $\mathbb{ C}$, that is $tr.deg_{ \mathbb{ C}}\mathbb{ C}(x_1,y_1,\ldots,x_n,y_n)=2n$. As a main part of the proof, we show that the set defined by the system in universal differential fields, with $d$ and $b$ linearly independent over $\mathbb{ Q}$, is strongly minimal and geometrically trivial. Our techniques also allows us to obtain partial results for some of the more general $2d$-Lotka-Volterra system.
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