  Both natural ecosystems and biochemical reaction networks involve populations
of heterogeneous agents whose cooperative and competitive interactions lead to
a rich dynamics of species' abundances, albeit at vastly different scales. The
maintenance of diversity in large ecosystems is a longstanding puzzle, towards
which recent progress has been made by the derivation of dynamical mean-field
theories of random models. In particular, it has recently been shown that these
random models have a chaotic phase in which abundances display wild
fluctuations. When modest spatial structure is included, these fluctuations are
stabilized and diversity is maintained. If and how these phenomena have
parallels in biochemical reaction networks is currently unknown. Making this
connection is of interest since life requires cooperation among a large number
of molecular species. In this work, we find a reaction network whose
large-scale behavior recovers the random Lotka-Volterra model recently
considered in theoretical ecology. We clarify the assumptions necessary to
derive its large-scale description, and reveal the underlying assumptions made
on the noise to recover previous dynamical mean-field theories. Then, we show
how local detailed balance and the positivity of reaction rates, which are key
physical requirements of chemical reaction networks, provide obstructions
towards the construction of an associated dynamical mean-field theory of
biochemical reaction networks. Finally, we outline prospects and challenges for
the future.
