Spectral analysis of phylogenetic data

The spectral analysis of sequence and distance data is a new approach to phylogenetic analysis. For two-state character sequences, the character values at a given site split the set of taxa into two subsets, a bipartition of the taxa set. The vector which counts the relative numbers of each of these bipartitions over all sites is called a sequence spectrum. Applying a transformation called a Hadamard conjugation, the sequence spectrum is transformed to the conjugate spectrum. This conjugation corrects for unobserved changes in the data, independently from the choice of phylogenetic tree. For any given phylogenetic tree with edge weights (probabilities of state change), we define a corresponding tree spectrum. The selection of a weighted phylogenetic tree from the given sequence data is made by matching the conjugate spectrum with a tree spectrum. We develop an optimality selection procedure using a least squares best fit, to find the phylogenetic tree whose tree spectrum most closely matches the conjugate spectrum. An inferred sequence spectrum can be derived from the selected tree spectrum using the inverse Hadamard conjugation to allow a comparison with the original sequence spectrum. A possible adaptation for the analysis of four-state character sequences with unequal frequencies is considered. A corresponding spectral analysis for distance data is also introduced. These analyses are illustrated with biological examples for both distance and sequence data. Spectral analysis using the Fast Hadamard transform allows optimal trees to be found for at least 20 taxa and perhaps for up to 30 taxa. The development presented here is self contained, although some mathematical proofs available elsewhere have been omitted. The analysis of sequence data is based on methods reported earlier, but the terminology and the application to distance data are new.     

Optimal neural population coding of an auditory spatial cue

A sound, depending on the position of its source, can take more time to reach one ear than the other. This interaural (between the ears) time difference (ITD) provides a major cue for determining the source location. Many auditory neurons are sensitive to ITDs, but the means by which such neurons represent ITD is a contentious issue. Recent studies question whether the classical general model (the Jeffress model) applies across species. Here we show that ITD coding strategies of different species can be explained by a unifying principle: that the ITDs an animal naturally encounters should be coded with maximal accuracy. Using statistical techniques and a stochastic neural model, we demonstrate that the optimal coding strategy for ITD depends critically on head size and sound frequency. For small head sizes and/or low-frequency sounds, the optimal coding strategy tends towards two distinct sub-populations tuned to ITDs outside the range created by the head. This is consistent with recent observations in small mammals. For large head sizes and/or high frequencies, the optimal strategy is a homogeneous distribution of ITD tunings within the range created by the head. This is consistent with observations in the barn owl. For humans, the optimal strategy to code ITDs from an acoustically measured distribution depends on frequency; above 400 Hz a homogeneous distribution is optimal, and below 400 Hz distinct sub-populations are optimal.     

A single population of olfactory sensory neurons mediates an innate avoidance behaviour in Drosophila

All animals exhibit innate behaviours in response to specific sensory stimuli that are likely to result from the activation of developmentally programmed neural circuits. Here we observe that Drosophila exhibit robust avoidance to odours released by stressed flies. Gas chromatography and mass spectrometry identifies one component of this 'Drosophila stress odorant (dSO)' as CO2. CO2 elicits avoidance behaviour, at levels as low as 0.1%. We used two-photon imaging with the Ca2+-sensitive fluorescent protein G-CaMP to map the primary sensory neurons governing avoidance to CO2. CO2 activates only a single glomerulus in the antennal lobe, the V glomerulus; moreover, this glomerulus is not activated by any of 26 other odorants tested. Inhibition of synaptic transmission in sensory neurons that innervate the V glomerulus, using a temperature-sensitive Shibire gene (Shi(ts)), blocks the avoidance response to CO2. Inhibition of synaptic release in the vast majority of other olfactory receptor neurons has no effect on this behaviour. These data demonstrate that the activation of a single population of sensory neurons innervating one glomerulus is responsible for an innate avoidance behaviour in Drosophila.