Approximate entropy of network parameters

We study the notion of approximate entropy within the framework of network theory. Approximate entropy is an uncertainty measure originally proposed in the context of dynamical systems and time series. We first define a purely structural entropy obtained by computing the approximate entropy of the so-called slide sequence. This is a surrogate of the degree sequence and it is suggested by the frequency partition of a graph. We examine this quantity for standard scale-free and Erdös-Rényi networks. By using classical results of Pincus, we show that our entropy measure often converges with network size to a certain binary Shannon entropy. As a second step, with specific attention to networks generated by dynamical processes, we investigate approximate entropy of horizontal visibility graphs. Visibility graphs allow us to naturally associate with a network the notion of temporal correlations, therefore providing the measure a dynamical garment. We show that approximate entropy distinguishes visibility graphs generated by processes with different complexity. The result probes to a greater extent these networks for the study of dynamical systems. Applications to certain biological data arising in cancer genomics are finally considered in the light of both approaches.

Estimating the relative roles of top-down and bottom-up forces on insect herbivore populations: A classic study revisited

Although most ecologists agree that both top-down and bottom-up forces (predation and resource limitation, respectively) act in concert to influence populations of herbivores, it has proven difficult to estimate the relative contributions of such forces in terrestrial systems. Using a combination of time–series analysis of population counts recorded over 16 years and experimental data, we present the first estimates of the relative roles of top-down and bottom-up forces on the population dynamics of two terrestrial insect herbivores on the English oak (Quercus robur). Data suggest that temporal variation in winter moth, Operophtera brumata, density is dominated by time-lagged effects of pupal predators. By comparison, spatial variation in O. brumata density is dominated by host–plant quality. Overall, top-down forces explain 34.2% of population variance, bottom-up forces explain 17.2% of population variance, and 48.6% remains unexplained. In contrast, populations of the green oak tortrix, Tortrix viridana, appear dominated by bottom-up forces. Resource limitation, expressed as intraspecific competition among larvae for oak leaves, explains 29.4% of population variance. Host quality effects explain an additional 5.7% of population variance. We detected no major top-down effects on T. viridana populations. An unknown factor causing a linear decline in T. viridana populations over the 16-year study period accounts for most of the remaining unexplained variance. We discuss the observed differences between the insect species and the utility of time–series analysis as a tool in assessing the relative importance of top-down and bottom-up forces on herbivore populations.

Frequency of HLA allele-specific peptide motifs in HIV-1 proteins correlates with the allele’s association with relative rates of disease progression after HIV-1 infection

An HLA allele-specific cytotoxic T lymphocyte response is thought to influence the rate of disease progression in HIV-1-infected individuals. In a prior study of 139 HIV-1-infected homosexual men, we identified HLA class I alleles and observed an association of specific alleles with different relative hazards for progression to AIDS. Seeking an explanation for this association, we searched HIV-1 protein sequences to determine the number of peptides matching motifs defined by combinations of specific amino acids reported to bind 16 class I alleles. Analyzing complete sequences of 12 clade B HIV isolates, we determined the number of allele motifs that were conserved (occurring in all 12 isolates) and nonconserved (occurring in only one isolate), as well as the average number of allele motifs per isolate. We found significant correlations with an allele’s association with disease progression for counts of conserved motifs in gag (R = 0.73; P = 0.002), pol (R = 0.58, P = 0.024), gp120 (R = 0.78, P = 0.00056), and total viral protein sequences (R = 0.67, P = 0.0058) and also for counts of nonconserved motifs in gag (R = 0.62, P = 0.013), pol (R = 0.74, P = 0.0017), gp41 (R = 0.52, P = 0.046), and total viral protein (R = 0.71, P = 0.0033). We also found significant correlations for the average number of motifs per isolate for gag, pol, gp120, and total viral protein. This study provides a plausible functional explanation for the observed association of different HLA alleles with variable rates of disease progression.

Echolocation detections and digital video surveys provide reliable estimates of the relative density of harbour porpoises

Acknowledgements We would like to thank Erik Rexstad and Rob Williams for useful reviews of this manuscript. The collection of visual and acoustic data was funded by the UK Department of Energy & Climate Change, the Scottish Government, Collaborative Offshore Wind Research into the Environment (COWRIE) and Oil & Gas UK. Digital aerial surveys were funded by Moray Offshore Renewables Ltd and additional funding for analysis of the combined datasets was provided by Marine Scotland. Collaboration between the University of Aberdeen and Marine Scotland was supported by MarCRF. We thank colleagues at the University of Aberdeen, Moray First Marine, NERI, Hi-Def Aerial Surveying Ltd and Ravenair for essential support in the field, particularly Tim Barton, Bill Ruck, Rasmus Nielson and Dave Rutter. Thanks also to Andy Webb, David Borchers, Len Thomas, Kelly McLeod, David L. Miller, Dinara Sadykova and Thomas Cornulier for advice on survey design and statistical approache. Data Accessibility Data are available from the Dryad Digital Repository: http://dx.doi.org/10.5061/dryad.cf04g