The brain processes information through multiple layers of neurons. This deep architecture is representationally powerful, but complicates learning because it is difficult to identify the responsible neurons when a mistake is made. In machine learning, the backpropagation algorithm assigns blame by multiplying error signals with all the synaptic weights on each neuron's axon and further downstream. However, this involves a precise, symmetric backward connectivity pattern, which is thought to be impossible in the brain. Here we demonstrate that this strong architectural constraint is not required for effective error propagation. We present a surprisingly simple mechanism that assigns blame by multiplying errors by even random synaptic weights. This mechanism can transmit teaching signals across multiple layers of neurons and performs as effectively as backpropagation on a variety of tasks. Our results help reopen questions about how the brain could use error signals and dispel long-held assumptions about algorithmic constraints on learning.

Social learning (learning through observation or interaction with other individuals) is widespread in nature and is central to the remarkable success of humanity, yet it remains unclear why it pays to copy, and how best to do so. To address these questions we organised a computer tournament in which entrants submitted strategies specifying how to use social learning and its asocial alternative (e.g. trial-and-error) to acquire adaptive behavior in a complex environment. Most current theory predicts the emergence of mixed strategies that rely on some combination of the two types of learning. In the tournament, however, strategies that relied heavily on social learning were found to be remarkably successful, even when asocial information was no more costly than social information. Social learning proved advantageous because individuals frequently demonstrated the highest-payoff behavior in their repertoire, inadvertently filtering information for copiers. The winning strategy (discountmachine) relied exclusively on social learning, and weighted information according to the time since acquisition.Human culture is widely thought to underlie the extraordinary demographic success of our species, manifest in virtually every terrestrial habitat (1-2). Cultural processes facilitate the spread of adaptive knowledge, accumulated over generations, allowing individuals to acquire vital life skills. One of the foundations of culture is social learning -learning influenced by observation or interaction with other individuals (3) -which occurs widely, in various forms, * To whom correspondence should be addressed. ler4@st-andrews.ac.uk.One sentence summary: A computer tournament helps to explain why social learning is common in nature and why human beings happen to be so good at it. NIH Public Access Author ManuscriptScience. Author manuscript; available in PMC 2010 November 22. Published in final edited form as:Science. 2010 April 9; 328(5975): 208-213. doi:10.1126/science.1184719. NIH-PA Author ManuscriptNIH-PA Author Manuscript NIH-PA Author Manuscript across the animal kingdom (4). Yet it remains something of a mystery why it pays individuals to copy others, and how best to do this.At first sight, social learning appears advantageous because it allows individuals to avoid the costs, in terms of effort and risk, of trial-and-error learning. However, social learning can also cost time and effort, and theoretical work reveals that it can be error prone, leading individuals to acquire inappropriate or outdated information in nonuniform and changing environments (5-11). Current theory suggests that to avoid these errors individuals should be selective in when and how they use social learning, so as to balance its advantages against the risks inherent in its indiscriminate use (9). Accordingly, natural selection is expected to have favoured social learning strategies, psychological mechanisms that specify when individuals copy, and from whom they learn (12-13).These issues lie at the interface of multiple academic fields,...

Evolutionary invasion analysis is a powerful technique for modelling in evolutionary biology. The general approach is to derive an expression for the growth rate of a mutant allele encoding some novel phenotype, and then to use this expression to predict long-term evolutionary outcomes. Mathematically, such 'invasion fitness' expressions are most often derived using standard linear stability analyses from dynamical systems theory. Interestingly, there is a mathematically equivalent approach to such stability analyses that is often employed in mathematical epidemiology, and that is based on so-called 'next-generation' matrices. Although this next-generation matrix approach has sometimes also been used in evolutionary invasion analyses, it is not yet common in this area despite the fact that it can sometimes greatly simplify calculations. The aim of this article is to bring the approach to a wider evolutionary audience in two ways. First, we review the next-generation matrix approach and provide a novel, and easily intuited, interpretation of how this approach relates to more standard techniques. Second, we illustrate next-generation methods in evolutionary invasion analysis through a series of informative examples. Although focusing primarily on evolutionary invasion analysis, we provide several insights that apply to biological modelling in general.

Characterising the longevity of immunological memory requires establishing the rules underlying the renewal and death of peripheral T cells. However, we lack knowledge of the population structure and how self-renewal and de novo influx contribute to the maintenance of memory compartments. Here, we characterise the kinetics and structure of murine CD4 T cell memory subsets by measuring the rates of influx of new cells and using detailed timecourses of DNA labelling that also distinguish the behaviour of recently divided and quiescent cells. We find that both effector and central memory CD4 T cells comprise subpopulations with highly divergent rates of turnover, and show that inflows of new cells sourced from the naive pool strongly impact estimates of memory cell lifetimes and division rates. We also demonstrate that the maintenance of CD4 T cell memory subsets in healthy mice is unexpectedly and strikingly reliant on this replenishment.DOI: http://dx.doi.org/10.7554/eLife.23013.001

Recent work on the evolution of behaviour is set in a structured population, providing a systematic way to describe gene flow and behavioural interactions. To obtain analytical results one needs a structure with considerable regularity. Our results apply to such "homogeneous" structures (e.g., lattices, cycles, and island models). This regularity has been formally described by a "nodetransitivity" condition but in mathematics, such internal symmetry is powerfully described by the theory of mathematical groups.Here, this theory provides elegant direct arguments for a more general version of a number of existing results. Our main result is that in large "group-structured" populations, primary fitness effects on others play no role in the evolution of the behaviour. The competitive effects of such a trait cancel the primary effects, and the inclusive fitness effect is given by the direct effect of the actor on its own fitness. This result is conditional on a number of assumptions such as (1) whether generations overlap, (2) whether offspring dispersal is symmetric, (3) whether the trait affects fecundity or survival, and (4) whether the underlying group is abelian.We formulate a number of results of this type in finite and infinite populations for both Moran and Wright-Fisher demographies. K E Y W O R D S :Allele frequency, group theory, homogeneous, population structure, relatedness, selection.A standard approach for the study of the selective effects of a social trait is provided by Hamilton's (1964) inclusive fitness effect, measured as the sum of the fitness effects of a behavioural deviation, each effect weighted by the relatedness of the actor to the recipient. It is well understood that this sum must include "all" effects, the "primary" effects that follow a direct interaction, for example on fecundity, as well as the resulting "secondary" competitive effects, for example, on mortality arising from changes in fecundity. At some level, this was well understood right from the beginning, but we suspect that the significance of the secondary effects was underestimated until more systematic studies of structured populations were undertaken. Wilson et al. (1992) in a Monte Carlo study of a large two-dimensional lattice population with limited dispersal, made the surprising discovery that an allele for altruistic behaviour to a neighbor declined in frequency no matter how great was the benefit b. As there was significant relatedness R between neighbors, this seemed to contradict Hamilton's (1964) rule that this allele should increase in frequency whenever Rb > c where c is the cost of the altruistic act. This observation led to the an analysis of Taylor (1992aTaylor ( , 1992b showing that in both an infinite island model and a onedimensional lattice model the conferred benefit b of the altruistic act would be exactly cancelled by secondary competitive effects removing b completely from the inclusive fitness effect of the action. This effect was generalized by Queller's (1994) concept of "economic neighborhood," whi...