How small are small mutation rates?

We consider evolutionary game dynamics in a finite population of size N. When mutations are rare, the population is monomorphic most of the time. Occasionally a mutation arises. It can either reach fixation or go extinct. The evolutionary dynamics of the process under small mutation rates can be approximated by an embedded Markov chain on the pure states. Here we analyze how small the mutation rate should be to make the embedded Markov chain a good approximation by calculating the difference between the real stationary distribution and the approximated one. While for a coexistence game, where the best reply to any strategy is the opposite strategy, it is necessary that the mutation rate μ is less than N ^−1/2exp[−N] to ensure that the approximation is good, for all other games, it is sufficient if the mutation rate is smaller than (N ln N)⁻¹. Our results also hold for a wide class of imitation processes under arbitrary selection intensity.     

Testimation in Regression Parameter Estimation

Testimation is considered in the problem of estimation of regression parameters. The first stage sample is used to test a (null) hypothesis that specifies initial (preassumed) values for some of the regression parameters. Linear combination of the preassumed values and the ordinary least square (OLS) estimates is considered as the estimate if the data agree with the hypothesis. Otherwise, a second sample is taken and parameters are estimated only by using OLS, based on the combined sample. The procedure protects against type II error and against taking larger samples when inference can be made from a smaller sample.     

Efficient protoplast regeneration ofBacillus thuringiensis andAgrobacterium tumefaciens

Summary Treatment ofBacillus thuringiensis andAgrobacterium tumefaciens taken from the early growth phase (8 h) with lysozyme at 1 mg/ml gave 90–99% protoplast formation and 10–12% protoplast regeneration on the minimal medium in absence of plasma expander (Bovine serum albumin). Enhanced fusion frequency was obtained when protoplasts from 8 h grown cells were used for fusion experiments.     

Dermatophytoses in Poona,India observations on incidence,clinical features,environmental factors and causal agents studied during 1958 to 1963 at Sassoon hospitals,Poona

Incidence of dermatophytoses in patients attending the Department of Dermatology, Sassoon Hospitals, Poona carried out over a period of six years from 1958–1963 is presented. Every year ten to fourteen per cent of skin infections were of mycotic origin.T. rubrum was the commonest causal pathogen in 65.30 per cent of the positive cases. Infections of the scalp which were thought to be rare were found in 12.97 per cent of the cases of dermatophytoses.T. violaceum andT. tonsurans var.sulfureum were the main causal organisms of ringworm of the scalp. Observations on the influence of climatic conditions on the incidence, personal habits and causal agents are also presented.This work represents a portion of the thesis of A.A.P. submitted for the degree of Doctor of Philosophy, University of Poona, India. The work was aided by a research grant from Indian Council of Medical Research, New Delhi.