Chris Field

QUANTITATIVE FATTY ACID SIGNATURE ANALYSIS: A NEW METHOD OF ESTIMATING PREDATOR DIETS

Accurate estimates of the diets of predators are required in many areas of ecology, but for many species current methods are imprecise, limited to the last meal, and often biased. The diversity of fatty acids and their patterns in organisms, coupled with the narrow limitations on their biosynthesis, properties of digestion in monogastric animals, and the prevalence of large storage reservoirs of lipid in many predators, led us to propose the use of quantitative fatty acid signature analysis (QFASA) to study predator diets. We present a statistical model that provides quantitative estimates of the proportions of prey species in the diets of individual predators using fatty acid signatures. We conducted simulation studies using a database of 28 prey species (n = 954 individuals) from the Scotian Shelf off eastern Canada to investigate properties of the model and to evaluate the reliability with which prey could be distinguished in the model. We then conducted experiments on grey seals (Halichoerus grypus, n = 25) and harp seals (Phoca groenlandica, n = 5) to assess quantitative characteristics of fatty acid deposition and to develop calibration coefficients for individual fatty acids to account for predator lipid metabolism. We then tested the model and calibration coefficients by estimating the diets of experimentally fed captive grey seals (n = 6, switched from herring to a mackerel/capelin diet) and mink kits (Mustela vison, n = 46, switched from milk to one of three oil-supplemented diets). The diets of all experimentally fed animals were generally well estimated using QFASA and were consistent with qualitative and quantitative expectations, provided that appropriate calibration coefficients were used. In a final case, we compared video data of foraging by individual free- ranging harbor seals (Phoca vitulina, n = 23) fitted with Crittercams and QFASA estimates of the diet of those same seals using a complex ecosystem-wide prey database. Among the 28 prey species in the database, QFASA estimated sandlance to be the dominant prey species in the diet of all seals (averaging 62% of diet), followed primarily by flounders, but also capelin and minor amounts of other species, although there was also considerable individual variability among seals. These estimates were consistent with video data showing sandlance to be the predominant prey, followed by flatfish. We conclude that QFASA provides estimates of diets for individuals at time scales that are relevant to the ecological processes affecting survival, and can be used to study diet variability within individuals over time, which will provide important opportunities rarely possible with other indirect methods. We propose that the QFASA model we have set forth will be applicable to a wide range of predators and ecosystems.

Robust Linear Model Selection by Cross-Validation

Abstract This article gives a robust technique for model selection in regression models, an important aspect of any data analysis involving regression. There is a danger that outliers will have an undue influence on the model chosen and distort any subsequent analysis. We provide a robust algorithm for model selection using Shaos cross-validation methods for choice of variables as a starting point. Because Shaos techniques are based on least squares, they are sensitive to outliers. We develop our robust procedure using the same ideas of cross-validation as Shao but using estimators that are optimal bounded influence for prediction. We demonstrate the effectiveness of our robust procedure in providing protection against outliers both in a simulation study and in a real example. We contrast the results with those obtained by Shaos method, demonstrating a substantial improvement in choosing the correct model in the presence of outliers with little loss of efficiency at the normal model.

Estimation of Single-Generation Sibling Relationships Based on DNA Markers

An algorithm for infering joint sibling relationships for a single generation sample of organisms based on DNA marker data is presented. The technique is based primarily on the exclusion principle, i.e., the process of systematically eliminating hypothetical kinship types between individuals in the basis of DNA incompatibility. The result is an enumeration of all genetically compatible sibling groupings, which is maximal in the sense that no other individual can be added to the sibling group. The technique is computationally feasible for large samples given enough variablility in the DNA markers used. From this, we construct a partition of the individuals into sibling groups based on a score. In addition, we derive some statistical properties of sibling compatibility events as well as various types of error probabilities associated with sibling identification. The techniques are illustrated using fisheries data.

Relationship between neurological and urological status in patients with multiple sclerosis.

The relationship between neurological urinary symptoms and urodynamic findings in patients with multiple sclerosis was examined. The duration of multiple sclerosis was significantly longer in patients with urinary symptoms. The presence of urinary symptoms correlated with the severity of the pyramidal or sensory lesions and the total disability score. Cystometrograms revealed detrusor hyperreflexia in 67 per cent of the patients, areflexia in 21 per cent and a normal detrusor in 12 per cent. Somatic dyssynergia was found in 20 of the 39 patients whose examination revealed clear-cut results. Positive correlation was found between urge incontinence and detrusor hyperreflexia, and between hesitancy and detrusor areflexia but no relationship was found between urological symptoms and sphincter function. Analysis of the neurological lesions in relation to the cystometric findings revealed a positive correlation among pyramidal lesions, detrusor hyperreflexia and detrusor areflexia, and between cerebellar lesions and detrusor areflexia. The correlation between detrusor dysfunction and high total disability score disappeared when patients with high pyramidal scores were excluded. No correlation could be detected between somatic dyssynergia and the various neurological lesions.

THE VARIABILITY AMONG POPULATIONS OF COHO SALMON IN THE MAXIMUM REPRODUCTIVE RATE AND DEPENSATION

Estimating parameters for population-dynamics models is a critical component in assessing extinction probabilities of populations. For many individual populations, key parameters will be poorly defined, and meta-analysis would provide a basis for estimating the parameters. Here, we introduce meta-analytical techniques to estimate the maximum reproductive rate, carrying capacity, and depensation in coho salmon on the west coast of North America. We used both nonlinear mixed-effects models and Bayesian techniques to estimate several population-dynamics models, including the Beverton-Holt and hockey-stick models, for 14 spawner–recruitment time series. The Beverton-Holt and hockey-stick mixed-effects models yielded equivalent fits to the data but gave very different estimates of α (the maximum rate at which female spawners can produce female smolts at low population sizes). The mean α for the Beverton-Holt mixed-effect model was 71.5 (1 se = 1.2) female smolts per spawning female, whereas the hockey-stick estimate was 53.0 (1 se = 1.14). We found little evidence for a general effect of depensation in coho salmon, unless fewer than one female per kilometer of river returned to spawn. Corresponding Editor: L. B. Crowder

The Multivariate g-and-h Distribution

In this article we consider a generalization of the univariate g-and-h distribution to the multivariate situation with the aim of providing a flexible family of multivariate distributions that incorporate skewness and kurtosis. The approach is to modify the underlying random variables and their quantiles, directly giving rise to a family of distributions in which the quantiles rather than the densities are the foci of attention. Using the ideas of multivariate quantiles, we show how to fit multivariate data to our multivariate g-and-h distribution. This provides a more flexible family than the skew-normal and skew-elliptical distributions when quantiles are of principal interest. Unlike those families, the distribution of quadratic forms from the multivariate g-and-h distribution depends on the underlying skewness. We illustrate our methods on Australian athletes data, as well as on some wind speed data from the northwest Pacific.

Estimation of rates-across-sites distributions in phylogenetic substitution models

Previous work has shown that it is often essential to account for the variation in rates at different sites in phylogenetic models in order to avoid phylogenetic artifacts such as long branch attraction. In most current models, the gamma distribution is used for the rates-across-sites distributions and is implemented as an equal-probability discrete gamma. In this article, we introduce discrete distribution estimates with large numbers of equally spaced rate categories allowing us to investigate the appropriateness of the gamma model. With large numbers of rate categories, these discrete estimates are flexible enough to approximate the shape of almost any distribution. Likelihood ratio statistical tests and a nonparametric bootstrap confidence-bound estimation procedure based on the discrete estimates are presented that can be used to test the fit of a parametric family. We applied the methodology to several different protein data sets, and found that although the gamma model often provides a good parametric model for this type of data, rate estimates from an equal-probability discrete gamma model with a small number of categories will tend to underestimate the largest rates. In cases when the gamma model assumption is in doubt, rate estimates coming from the discrete rate distribution estimate with a large number of rate categories provide a robust alternative to gamma estimates. An alternative implementation of the gamma distribution is proposed that, for equal numbers of rate categories, is computationally more efficient during optimization than the standard gamma implementation and can provide more accurate estimates of site rates.

Small-Sample Confidence Intervals

In this article we present a technique for constructing oneor two-sided confidence intervals, which are second-order correct in terms of coverage, for either parametric or nonparametric problems. The construction is valid in the presence of nuisance parameters. The situation we consider is this: there are p parameters and we want a confidence interval for some function of them, possibly one of the parameters itself. The p parameters are estimated by M-estimates, which means they are obtained as a solution of a system of equations. Maximum likelihood estimates are included as a special case. The essential intermediate result, given in Equation (3.4), says that the estimated parameter of interest, 0, can be written as a mean, up to order op(l/ V/ ). The representation (3.4) is attained when 0 = 0(a) is a smooth function of the parameters q and aj is the solution of a well-behaved system of equations. We avoid the use of pivots and strive to obtain accurate coverage. Confidence intervals are constructed from a series of tests for the natural parameter of a one-parameter exponential family. We use the Lugannani and Rice (1980) tail area approximation to calculate bootstrap P values for the test statistic.

Tail areas of linear combinations of chi-squares and non-central chi-squares

This paper uses a uniform saddlepoint approximation to obtain extreme tail areas for a linear combination of independent chi-square random variables. The approximation uses a transformation of the tail area coming from the Fourier inversion of the characteristic function. The transformation yields a quadratic in the exponent. A Taylors expansion of the Jacobian leads to the approximation. The approximation is shown to be easy to compute and very accurate in the extreme tails.

Patterns of ecological specialization among microbial populations in the Red Sea and diverse oligotrophic marine environments

Large swaths of the nutrient-poor surface ocean are dominated numerically by cyanobacteria (Prochlorococcus), cyanobacterial viruses (cyanophage), and alphaproteobacteria (SAR11). How these groups thrive in the diverse physicochemical environments of different oceanic regions remains poorly understood. Comparative metagenomics can reveal adaptive responses linked to ecosystem-specific selective pressures. The Red Sea is well-suited for studying adaptation of pelagic-microbes, with salinities, temperatures, and light levels at the extreme end for the surface ocean, and low nutrient concentrations, yet no metagenomic studies have been done there. The Red Sea (high salinity, high light, low N and P) compares favorably with the Mediterranean Sea (high salinity, low P), Sargasso Sea (low P), and North Pacific Subtropical Gyre (high light, low N). We quantified the relative abundance of genetic functions among Prochlorococcus, cyanophage, and SAR11 from these four regions. Gene frequencies indicate selection for phosphorus acquisition (Mediterranean/Sargasso), DNA repair and high-light responses (Red Sea/Pacific Prochlorococcus), and osmolyte C1 oxidation (Red Sea/Mediterranean SAR11). The unexpected connection between salinity-dependent osmolyte production and SAR11 C1 metabolism represents a potentially major coevolutionary adaptation and biogeochemical flux. Among Prochlorococcus and cyanophage, genes enriched in specific environments had ecotype distributions similar to nonenriched genes, suggesting that inter-ecotype gene transfer is not a major source of environment-specific adaptation. Clustering of metagenomes using gene frequencies shows similarities in populations (Red Sea with Pacific, Mediterranean with Sargasso) that belie their geographic distances. Taken together, the genetic functions enriched in specific environments indicate competitive strategies for maintaining carrying capacity in the face of physical stressors and low nutrient availability.