  We present a method to construct superintegrable $n$-component Lotka-Volterra
systems with $3n-2$ parameters. We apply the method to Lotka-Volterra systems
with $n$ components for $1 < n < 6$, and present several $n$-dimensional
superintegrable families. The Lotka-Volterra systems are in one-to-one
correspondence with trees on $n$ vertices.
