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Biological Mechanisms for Bayesian Inference

Final Report Summary - BMBISAMJOHNSON (Biological Mechanisms for Bayesian Inference)

The work we have carried out during the two years of the grant falls into the following four sub-projects:

- Robust short-term memory without synaptic learning:

Long-term memories are stored in the brain through gradual modifications to the strengths of the synapses linking neurons. However, many cognitive processes occur on time-scales of seconds or less, too quickly for this mechanism of “synaptic learning” to be at their basis – such as sensory memory, working memory, and even high-level functions like inference. We have shown that a mechanism we call “cluster reverberation”, which relies on many small groups of neurons which mainly receive signals from each other, can support short-term memory with the characteristics required for the cognitive functions mentioned above (Johnson et al., PLOS ONE 8(1), e50276, 2013). We have yet to test the predictions of the theory in vitro. However, several observations from neurobiology and psychology emerge naturally from cluster reverberation. Furthermore, we have suggested a mechanism whereby the appropriate neural network structures can grow via known processes of synaptic plasticity during brain development, and how cluster reverberation might support our capacity to carry out optimal inference from uncertain sensory information.

- Factors determining nestedness in complex networks:

Many real-world networks exhibit a property called “nestedness”, originally described by ecologists. The nestedness of plant-pollinator networks, for instance, entails that two species of insect competing for the same resources can also be mutually beneficial by pollinating the same set of plants, thereby reducing the net extent of their competition. It is thought that this mechanism might also be useful for financial institutions. We investigated mathematically how other network structural features affect nestedness, and found that it is enhanced by “disassortativity”, a property whereby nodes with many connections tend to attach to nodes with particularly few (Johnson et al, PLOS ONE 8(9), e74025, 2013). In an earlier work we showed that most complex networks become disassortative because of simple natural processes (Johnson et al., Physical Review Letters 104, 108702, 2010). This means that nestedness need not have been built into systems through design or selection, but is likely the inescapable product of chance.

- Bias in Respondent Driven Sampling:

Respondent Driven Sampling is a method widely used in public health studies to gauge the prevalence of a disease among hard-to-reach individuals. For instance, if one wishes to sample a population of drug users to asses the proportion with AIDS, one locates a few “seed” users and asks them to bring along friends whom they have taken drugs with. Because people with more friends are more likely to come in, one must ask subjects how many such contacts they have in order to apply a statistical correction to the result. In an investigation led by Dr Harriet Mills at Imperial College London, we found that such subjects show clear signs of rounding up or down to the nearest 10, 100 or other round numbers in their answers, suggesting a certain error. We then showed that errors of this kind can have important consequences for the final estimate of disease prevalence if contagion depends on one's number of friends. For instance, one might measure a reduction in prevalence after an intervention when in fact it increased – or vice-versa. We suggested that in order to improve results, one must make more effort to ascertain the exact number of contacts of subjects, particularly of those with relatively few contacts (Mills et al., Drug and Alcohol Dependence 142, p. 120, 2014).

- Trophic coherence determines food-web stability:

In the eraly seventies, Sir Robert May showed mathematically that the larger and more interconnected a dynamical system, the harder it should be to stabilise (all else being equal and connections placed at random). This was puzzling for ecologists, who had long observed highly biodiverse ecosystems, such as rainforests and coral reefs, to be particularly stable (in the sense that species' populations are less likely to suffer runaway fluctuations, potentially causing cascades of extinctions). This problem has become known as May's Paradox, and the “diversity-stability debate” rages on to this day. We have identified a network property we call “trophic coherence”, exhibited by many networks but particularly visible in food webs, which may be the key to this issue (Johnson et al. arXiv:1404.7728; PNAS, under review). Trophic coherence accounts statistically for most of the variance in stability in a large dataset of food webs, and a simple model we have proposed to capture the feature significantly outperforms existing food-web models in a variety of ways. Most notably, the model predicts that, if networks are sufficiently coherent, stability can indeed increase with size and complexity. This not only suggests a solution to the paradox, but may be important for diagnosing the vulnerability of an ecosystem: if loss of a few species would reduce stability instead of increasing it, relatively small damage could be amplified into extensive biodiversity collapse (a “tipping point"). The importance of this result is likely to go beyond ecology, since neural, genetic, metabolic and many other networks exhibit trophic coherence to some degree. For instance, it may be relevant for finance, where the view that diversification reduces systemic risk still prevails. We are currently working on these and other issues stemming from the initial results.