We present $\frac{m^{2}}{4}+\frac{m}{2}+\frac{1-\left(-1\right)^{m}}{8}$ homogeneous $(3m-2)$-parameter families of Liouville integrable $(2m)$- and $(2m-1)$-dimensional Lotka-Volterra systems. We also study inhomogeneous versions of these systems.

37 pages, 37 references, 8 figures, in honour of Professor Jarmo Hietarinta on the occasion of his 80th birthday. Added historical context and concluding remarks in V2