Algebraic independence of solutions to multiple Lotka-Volterra systems

Consider some non-zero complex numbers $a_i,b_i,c_i,d_i$ with $1\le i\le n$ and the associated classical Lotka-Volterra systems $$\{\begin{array}{l}{x}^{\mathrm{\prime }}=a_{i}xy+b_{i}y\\ y^{\mathrm{\prime }}=c_{i}xy+d_{i}y\text{ .}\end{array}$$ We show that as long as $b_i\mathrm{\ne }{d}_i$ for all $i$ and $\{b_i,d_i\}\mathrm{\ne }\{b_j,d_j\}$ for $i\mathrm{\ne }j$, any tuples $(x_1,y_1),\cdots ,(x_m,y_m)$ of pairwise distinct, non-degenerate solutions of these systems are algebraically independent over $\mathbb{C}$, meaning $\mathrm{t}\mathrm{r}\mathrm{d}\mathrm{e}\mathrm{g}((x_1,y_1),\cdots ,(x_m,y_m)\mathrm{/}\mathbb{C})=2m$. Our proof relies on extending recent work of Duan and Nagloo by showing strong minimality of these systems, as long as $b_i\mathrm{\ne }{d}_i$. We also generalize a theorem of Brestovski which allows us to control algebraic relations using invariant volume forms. Finally, we completely classify all invariant algebraic curves in the non-strongly minimal, $b_i=d_i$ case by using machinery from geometric stability theory.