The activity of a neural network is defined by patterns of spiking and silence from the individual neurons. Because spikes are (relatively) sparse, patterns of activity with increasing numbers of spikes are less probable, but, with more spikes, the number of possible patterns increases. This tradeoff between probability and numerosity is mathematically equivalent to the relationship between entropy and energy in statistical physics. We construct this relationship for populations of up to N = 160 neurons in a small patch of the vertebrate retina, using a combination of direct and model-based analyses of experiments on the response of this network to naturalistic movies. We see signs of a thermodynamic limit, where the entropy per neuron approaches a smooth function of the energy per neuron as N increases. The form of this function corresponds to the distribution of activity being poised near an unusual kind of critical point. We suggest further tests of criticality, and give a brief discussion of its functional significance.entropy | information | neural networks | Monte Carlo | correlation

Guiding behavior requires the brain to make predictions about the future values of sensory inputs. Here, we show that efficient predictive computation starts at the earliest stages of the visual system. We compute how much information groups of retinal ganglion cells carry about the future state of their visual inputs and show that nearly every cell in the retina participates in a group of cells for which this predictive information is close to the physical limit set by the statistical structure of the inputs themselves. Groups of cells in the retina carry information about the future state of their own activity, and we show that this information can be compressed further and encoded by downstream predictor neurons that exhibit feature selectivity that would support predictive computations. Efficient representation of predictive information is a candidate principle that can be applied at each stage of neural computation.neural coding | retina | information theory A lmost all neural computations involve making predictions. Whether we are trying to catch prey, avoid predators, or simply move through a complex environment, the data we collect through our senses can guide our actions only to the extent that these data provide information about the future state of the world. Although it is natural to focus on the prediction of rewards (1), prediction is a much broader problem, ranging from the extrapolation of the trajectories of moving objects to the learning of abstract rules that describe the unfolding pattern of events around us (2-4). An essential aspect of the problem in all these forms is that not all features of the past carry predictive power. Because there are costs associated with representing and transmitting information, it is natural to suggest that sensory systems have optimized coding strategies to keep only a limited number of bits of information about the past, ensuring that these bits are maximally informative about the future. This principle can be applied at successive stages of signal processing, as the brain attempts to predict future patterns of neural activity. We explore these ideas in the context of the vertebrate retina, provide evidence for nearoptimal coding, and find that this performance cannot be explained by classical models of ganglion cell firing. Coding for the Position of a Single Visual ObjectThe structure of the prediction problem depends on the structure of the world around us. In a world of completely random stimuli, for example, prediction is impossible. Consider a simple visual world such that, in the small patch of space represented by the neurons from which we record, there is just one object (a dark horizontal bar against a light background) moving along a trajectory x t . We want to construct trajectories that are predictable, but not completely; the moving object has some inertia, so that the velocities υ t are correlated across time, but is also "kicked" by unseen random forces. A mathematically tractable example (Eqs. 4 and 5 in Materials and Methods) is shown in Fig...

eTOC blurb Westerman, VanKuren et al. show that butterfly wing color maps to a putative cis-regulatory element adjacent to two aristaless genes. The genes are differentially expressed between white and yellow wings and CRISPR knockout of aristaless1 causes white wings to develop yellow. Both colors have been shared among species via hybridization.

We have used a combination of theory and experiment to assess how information is represented in a realistic cortical population response, examining how motion direction and timing is encoded in groups of neurons in cortical area MT. Combining data from several single-unit experiments, we constructed model population responses in small time windows and represented the response in each window as a binary vector of 1s or 0s signifying spikes or no spikes from each cell. We found that patterns of spikes and silence across a population of nominally redundant neurons can carry up to twice as much information about visual motion than does population spike count, even when the neurons respond independently to their sensory inputs. This extra information arises by virtue of the broad diversity of firing rate dynamics found in even very similarly tuned groups of MT neurons. Additionally, specific patterns of spiking and silence can carry more information than the sum of their parts (synergy), opening up the possibility for combinatorial coding in cortex. These results also held for populations in which we imposed levels of nonindependence (correlation) comparable to those found in cortical recordings. Our findings suggest that combinatorial codes are advantageous for representing stimulus information on short time scales, even when neurons have no complicated, stimulus-dependent correlation structure.

Supergene mimicry is a striking phenomenon but we know little about the evolution of this trait in any species. Here, by studying genomes of butterflies from a recent radiation in which supergene mimicry has been isolated to the gene doublesex, we show that sexually dimorphic mimicry and female-limited polymorphism are evolutionarily related as a result of ancient balancing selection combined with independent origins of similar morphs in different lineages and secondary loss of polymorphism in other lineages. Evolutionary loss of polymorphism appears to have resulted from an interaction between natural selection and genetic drift. Furthermore, molecular evolution of the supergene is dominated not by adaptive protein evolution or balancing selection, but by extensive hitchhiking of linked variants on the mimetic dsx haplotype that occurred at the origin of mimicry. Our results suggest that chance events have played important and possibly opposing roles throughout the history of this classic example of adaptation.