  Non-reciprocal interactions between microscopic constituents can profoundly
shape the large-scale properties of complex systems. Here, we investigate the
effects of non-reciprocity in the context of theoretical ecology by analyzing a
generalization of MacArthur's consumer-resource model with asymmetric
interactions between species and resources. Using a mixture of analytic cavity
calculations and numerical simulations, we show that such ecosystems
generically undergo a phase transition to chaotic dynamics as the amount of
non-reciprocity is increased. We analytically construct the phase diagram for
this model and show that the emergence of chaos is controlled by a single
quantity: the ratio of surviving species to surviving resources. We also
numerically calculate the Lyapunov exponents in the chaotic phase and carefully
analyze finite-size effects. Our findings show how non-reciprocal interactions
can give rise to complex and unpredictable dynamical behaviors even in the
simplest ecological consumer-resource models.
