Exact moment calculations for genetic models with migration, mutation, and drift

Using properties of moment stationarity we develop exact expressions for the mean and covariance of allele frequencies at a single locus for a set of populations subject to drift, mutation, and migration. Some general results can be obtained even for arbitrary mutation and migration matrices, for example: (1) Under quite general conditions, the mean vector depends only on mutation rates, not on migration rates or the number of populations. (2) Allele frequencies covary among all pairs of populations connected by migration. As a result, the drift, mutation, migration process is not ergodic when any finite number of populations is exchanging genes. in addition, we provide closed form expressions for the mean and covariance of allele frequencies in Wright's finite-island model of migration under several simple models of mutation, and we show that the correlation in allele frequencies among populations can be very large for realistic rates of mutation unless an enormous number of populations are exchanging genes. As a result, the traditional diffusion approximation provides a poor approximation of the stationary distribution of allele frequencies among populations. Finally, we discuss some implications of our results for measures of population structure based on Wright's F-statistics.

Dynamic Smile Analysis : Changes with Age

Introduction: The objective of this study was to define age-related changes in the human smile. The areas of interest were: upper lip length at smile and repose, upper lip thickness at smile and repose, maxillary incisal display at smile, interlabial gap height at smile, smile index, percent buccal corridors, intercommissural width at rest, smile height, and smile arc. A secondary objective was to study the perioral changes from rest to smile and compare them on the basis of age. Materials and Method: Video equipment was used to capture video for 261 subjects. Two frames for each subject were selected; one frame representing the lips and rest and the second representing the widest smile. After excluding 40 subjects the data for the remaining 221 subjects was analyzed. Results: There was a decrease of 1.5 to 2 mm in the maxillary incisor display during smile, with increase in age. Smile index significantly increased with increase in age. Most (78%) subjects displayed an average smile height. No subjects in the 50 and over age group displayed a high smile while no subjects in the 15-19 year old age group presented with a low smile. All the dynamic measures indicated there was a pattern of decreasing change from rest to smile especially evident after the 30-39 year old age group. Conclusions: This study helps to establish age related dynamic norms. As the person ages the smile gets narrower vertically and wider transversely. The dynamic measures indicate that the muscles' ability to create a smile decreases with increasing age.

Capital Accumulation in the Presence of Informal Credit Contracts: Does the Incentive Mechanism Work Better than Credit Rationing Under Asymmetric Information?

Credit markets with asymmetric information often prefer credit rationing as a profit maximizing device. This paper asks whether the presence of informal credit markets reduces the cost of credit rationing, that is, whether it can alleviate the impact of asymmetric information based on the available information. We used a dynamic general equilibrium model with heterogenous agents to assess this. Using Indian credit market data our study shows that the presence of informal credit market can reduce the cost of credit rationing by separating high risk firms from the low risk firms in the informal market. But even after this improvement, the steady state capital accumulation is still much lower as compared to incentive based market clearing rates. Through self revelation of each firm's type, based on the incentive mechanism, banks can diversify their risk by achieving a separating equilibrium in the loan market. The incentive mechanism helps banks to increase capital accumulation in the long run by charging lower rates and lending relatively higher amount to the less risky firms. Another important finding of this study is that self-revelation leads to very significant welfare improvement, as measured by consumptiuon equivalence.