The asymptotic distribution of canonical correlations and vectors in higher-order cointegrated models

The study of the large-sample distribution of the canonical correlations and variates in cointegrated models is extended from the first-order autoregression model to autoregression of any (finite) order. The cointegrated process considered here is nonstationary in some dimensions and stationary in some other directions, but the first difference (the “error-correction form”) is stationary. The asymptotic distribution of the canonical correlations between the first differences and the predictor variables as well as the corresponding canonical variables is obtained under the assumption that the process is Gaussian. The method of analysis is similar to that used for the first-order process.

Patterns of variance in stage-structured populations: Evolutionary predictions and ecological implications

Variability in population growth rate is thought to have negative consequences for organism fitness. Theory for matrix population models predicts that variance in population growth rate should be the sum of the variance in each matrix entry times the squared sensitivity term for that matrix entry. I analyzed the stage-specific demography of 30 field populations from 17 published studies for pattern between the variance of a demographic term and its contribution to population growth. There were no instances in which a matrix entry both was highly variable and had a large effect on population growth rate; instead, correlations between estimates of temporal variance in a term and contribution to population growth (sensitivity or elasticity) were overwhelmingly negative. In addition, survivorship or growth sensitivities or elasticities always exceeded those of fecundity, implying that the former two terms always contributed more to population growth rate. These results suggest that variable life history stages tend to contribute relatively little to population growth rates because natural selection may alter life histories to minimize stages with both high sensitivity and high variation.

Age-specific inbreeding depression and components of genetic variance in relation to the evolution of senescence.

Two major theories of the evolution of senescence (mutation accumulation and antagonistic pleiotropy) make different predictions about the relationships between age, inbreeding effects, and the magnitude of genetic variance components of life-history components. We show that, under mutation accumulation, inbreeding decline and three major components of genetic variance are expected to increase with age in randomly mating populations. Under the simplest version of the antagonistic pleiotropy model, no changes in the severity of inbreeding decline, dominance variance, or the genetic variance of chromosomal homozygotes are expected, but additive genetic variance may increase with age. Age-specific survival rates and mating success were measured on virgin males, using lines extracted from a population of Drosophila melanogaster. For both traits, inbreeding decline and several components of genetic variance increase with age. The results are consistent with the mutation accumulation model, but can only be explained by antagonistic pleiotropy if there is a general tendency for an increase with age in the size of allelic effects on these life-history traits.

Folding protein models with a simple hydrophobic energy function: The fundamental importance of monomer inside/outside segregation

The present study explores a “hydrophobic” energy function for folding simulations of the protein lattice model. The contribution of each monomer to conformational energy is the product of its “hydrophobicity” and the number of contacts it makes, i.e., E(h⃗, c⃗) = −Σi=1N cihi = −(h⃗.c⃗) is the negative scalar product between two vectors in N-dimensional cartesian space: h⃗ = (h1, … , hN), which represents monomer hydrophobicities and is sequence-dependent; and c⃗ = (c1, … , cN), which represents the number of contacts made by each monomer and is conformation-dependent. A simple theoretical analysis shows that restrictions are imposed concomitantly on both sequences and native structures if the stability criterion for protein-like behavior is to be satisfied. Given a conformation with vector c⃗, the best sequence is a vector h⃗ on the direction upon which the projection of c⃗ − c̄⃗ is maximal, where c̄⃗ is the diagonal vector with components equal to c̄, the average number of contacts per monomer in the unfolded state. Best native conformations are suggested to be not maximally compact, as assumed in many studies, but the ones with largest variance of contacts among its monomers, i.e., with monomers tending to occupy completely buried or completely exposed positions. This inside/outside segregation is reflected on an apolar/polar distribution on the corresponding sequence. Monte Carlo simulations in two dimensions corroborate this general scheme. Sequences targeted to conformations with large contact variances folded cooperatively with thermodynamics of a two-state transition. Sequences targeted to maximally compact conformations, which have lower contact variance, were either found to have degenerate ground state or to fold with much lower cooperativity.

Social transmission of reproductive behavior increases frequency of inherited disorders in a young-expanding population

The observation of high frequencies of certain inherited disorders in the population of Saguenay–Lac Saint Jean can be explained in terms of the variance and the correlation of effective family size (EFS) from one generation to the next. We have shown this effect by using the branching process approach with real demographic data. When variance of EFS is included in the model, despite its profound effect on mutant allele frequency, any mutant introduced in the population never reaches the known carrier frequencies (between 0.035 and 0.05). It is only when the EFS correlation between generations is introduced into the model that we can explain the rise of the mutant alleles. This correlation is described by a c parameter that reflects the dependency of children’s EFS on their parents’ EFS. The c parameter can be considered to reflect social transmission of demographic behavior. We show that such social transmission dramatically reduces the effective population size. This could explain particular distributions in allele frequencies and unusually high frequency of certain inherited disorders in some human populations.

Localization of atherosclerosis susceptibility loci to chromosomes 4 and 6 using the Ldlr knockout mouse model

Atherosclerosis is a complex disease resulting from the interaction of multiple genes. We have used the Ldlr knockout mouse model in an interspecific genetic cross to map atherosclerosis susceptibility loci. A total of 174 (MOLF/Ei × B6.129S7-Ldlrtm1Her) × C57BL/6J-Ldlrtm1Her backcross mice, homozygous for the Ldlr null allele, were fed a Western-type diet for 3 months and then killed for quantification of aortic lesions. A genome scan was carried out by using DNA pools and microsatellite markers spaced at ≈18-centimorgan intervals. Quantitative trait locus analysis of individual backcross mice confirmed linkages to chromosomes 4 (Athsq1, logarithm of odds = 6.2) and 6 (Athsq2, logarithm of odds = 6.7). Athsq1 affected lesions in females only whereas Athsq2 affected both sexes. Among females, the loci accounted for ≈50% of the total variance of lesion area. The susceptible allele at Athsq1 was derived from the MOLF/Ei genome whereas the susceptible allele at Athsq2 was derived from C57BL/6J. Inheritance of susceptible alleles at both loci conferred a 2-fold difference in lesion area, suggesting an additive effect of Athsq1 and Athsq2. No associations were observed between the quantitative trait loci and levels of plasma total cholesterol, high density lipoprotein cholesterol, non-high density lipoprotein cholesterol, insulin, or body weight. We provide strong evidence for complex inheritance of atherosclerosis in mice with elevated plasma low density lipoprotein cholesterol and show a major influence of nonlipoprotein-related factors on disease susceptibility. Athsq1 and Athsq2 represent candidate susceptibility loci for human atherosclerosis, most likely residing on chromosomes 1p36–32 and 12p13–12, respectively.

A modified gambler's ruin model of polyethylene chains in the amorphous region.

Polyethylene chains in the amorphous region between two crystalline lamellae M unit apart are modeled as random walks with one-step memory on a cubic lattice between two absorbing boundaries. These walks avoid the two preceding steps, though they are not true self-avoiding walks. Systems of difference equations are introduced to calculate the statistics of the restricted random walks. They yield that the fraction of loops is (2M - 2)/(2M + 1), the fraction of ties 3/(2M + 1), the average length of loops 2M - 0.5, the average length of ties 2/3M2 + 2/3M - 4/3, the average length of walks equals 3M - 3, the variance of the loop length 16/15M3 + O(M2), the variance of the tie length 28/45M4 + O(M3), and the variance of the walk length 2M3 + O(M2).