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In large, natural ecosystems, many (≳1) phenotypically relevant mutants can emerge over the characteristic turnover time of the population. When this is the case, there can be ‘eco-evolutionary feedback’ between the dynamical processes that underlie mutation, selection and ecology. We show that, owing to such feedback, the precise details of the mutational process can have a qualitative impact on the long-term behavior of an eco-evolutionary system, in contrast to the classical population genetic assumption that all mutations can be modeled with an effective, homogeneous rate. We demonstrate this in the context of a version of MacArthur’s consumer-resource model in which consumers mutate along a resource preference trait-space. Starting from a stochastic individual-based model, we simulate the system in the case where mutations are exogenously generated at a fixed rate (e.g. via external mutagens) and in the case where mutations are coupled to replication (e.g. via DNA copying errors). We find that, surprisingly, replication-coupled mutations are capable of generating a patterned phase in the limit of fast ecological relaxation – precisely the regime where classical population genetic models are expected to operate. We derive a mean-field description of the stochastic model and show that the patterned phase comes about due to a Turing-like mechanism driven by the non-reciprocal and nonlinear nature of replicative mutations. Furthermore, we show that additional interactions like those due to host defense mechanisms can extend the patterned regime to arbitrarily high dimensional phenotype spaces. We demonstrate that these results are robust to demographic noise and model choices and we discuss systems in which this phenomenology might be relevant. 

Biological systems with many components often exhibit seemingly critical behaviors, characterized by atypically large correlated fluctuations. Yet the underlying causes remain unclear. Here we define and examine two types of criticality. criticality arises from interactions within the system which are fine-tuned to a critical point. criticality, in contrast, emerges without fine-tuning when observable degrees of freedom are coupled to unobserved fluctuating variables. We unify both types of criticality using the language of learning and information theory. We show that critical correlations, intrinsic or extrinsic, lead to diverging mutual information between two halves of the system, and are a feature of learning problems, in which the unobserved fluctuations are inferred from the observable degrees of freedom. We argue that extrinsic criticality is equivalent to standard inference, whereas intrinsic criticality describes , in which the amount to be learned depends on the system size. We show further that both types of criticality are on the same continuum, connected by a smooth crossover. In addition, we investigate the observability of Zipf's law, a power-law rank-frequency distribution often used as an empirical signature of criticality. We find that Zipf's law is a robust feature of extrinsic criticality but can be nontrivial to observe for some intrinsically critical systems, including critical mean-field models. We further demonstrate that models with global dynamics, such as oscillatory models, can produce observable Zipf's law without relying on either external fluctuations or fine-tuning. Our findings suggest that while possible in theory, fine-tuning is not the only, nor the most likely, explanation for the apparent ubiquity of criticality in biological systems with many components. Our work offers an alternative interpretation in which criticality, specifically extrinsic criticality, results from the adaptation of collective behavior to external stimuli. 

Continuous attractors have been used to understand recent neuroscience experiments where persistent activity patterns encode internal representations of external attributes like head direction or spatial location. However, the conditions under which the emergent bump of neural activity in such networks can be manipulated by space and time-dependent external sensory or motor signals are not understood. Here, we find fundamental limits on how rapidly internal representations encoded along continuous attractors can be updated by an external signal. We apply these results to place cell networks to derive a velocity-dependent nonequilibrium memory capacity in neural networks. 

The information bottleneck (IB) approach to clustering takes a joint distribution [Formula: see text] and maps the data [Formula: see text] to cluster labels [Formula: see text], which retain maximal information about [Formula: see text] (Tishby, Pereira, & Bialek, 1999 ). This objective results in an algorithm that clusters data points based on the similarity of their conditional distributions [Formula: see text]. This is in contrast to classic geometric clustering algorithms such as [Formula: see text]-means and gaussian mixture models (GMMs), which take a set of observed data points [Formula: see text] and cluster them based on their geometric (typically Euclidean) distance from one another. Here, we show how to use the deterministic information bottleneck (DIB) (Strouse & Schwab, 2017 ), a variant of IB, to perform geometric clustering by choosing cluster labels that preserve information about data point location on a smoothed data set. We also introduce a novel intuitive method to choose the number of clusters via kinks in the information curve. We apply this approach to a variety of simple clustering problems, showing that DIB with our model selection procedure recovers the generative cluster labels. We also show that, in particular limits of our model parameters, clustering with DIB and IB is equivalent to [Formula: see text]-means and EM fitting of a GMM with hard and soft assignments, respectively. Thus, clustering with (D)IB generalizes and provides an information-theoretic perspective on these classic algorithms.