## Parop

The function par is used in order to set the parameters for high level plotting. We save the current setting of plotting in the object op and set the plotting region to contain six plots in two rows and three columns. After plotting, the default setting is restored. Examine the six plots in Fig. 2.2. The first two plots describe the distribution of the phenotype in the two pure inbred strains. Note that the distribution follows the bell shape of the normal distribution. The two distributions...

## The Poisson Distribution

The Poisson distribution is useful in the context of counting the occurrences of rare events. Like the binomial distribution, it takes integer values. As we will see later in this chapter, it can arise as an approximation to the binomial distribution when p is small and n is large. We say that a random variable X has a Poisson distribution with mean value A (written X Poisson(A)) if the probability function of X has the form f (x) e-x , x 0,1, 2, x The expectation and the variance of X are both...

## Info

In general, a Bonferroni-corrected threshold is conservative in the sense that it leads to an actual significance level smaller than the nominal significance level of 5 . Note that the Bonferroni inequality does not use any information regarding the covariances between the different quantities Zs and Zt. It is based solely on the marginal distribution of the individual variables. This is a major advantage, since it leads to a very simple formula. However, this simplicity is a double-edged sword...

## Statistical Power and Confidence Regions

The significance level is the determining factor in the specification of the rejection region of a statistical test. Only the distribution under the null assumption of no signal plays a role in setting the level of the threshold, once the test statistic and the general form of test are decided upon. However, after setting that threshold, one can examine other statistical properties of the resulting test. A central property is statistical power of the test - the probability to reject the null...

## The Multi Marker Process

Whole-genome scans, which involve genotyping a large collection of markers, require a more detailed description of the recombination process. In particular, we need a model for how crossovers relate to each other when moving from one position to another along a chromosome. Crossovers are the genetic mechanism for combining parts of the two homologous chromosomes in the parent during the meiotic process to form the gamete to be transmitted to the child. The result is a mixture of the two...

## The Recombination Fraction

Crossovers between chromosomal segments may occur during meiosis. These crossovers cause the gamete that passes to an offspring to be a mosaic of genetic material originating from the two grandparents. A recombination event between two loci occurs whenever the number of crossovers is odd. In this case, the genetic material at one locus is from one grandparent, whereas the genetic material at the other locus is from the other grandparent. The probability of a recombination is known as the...

## Problems

Consider the representation (2.3) with the conditions that xM xF (to achieve homozygosity) and p 1 2. By observing that the factor multiplying 2 5 is always 1 4 show that (2.3) reduces to the representation of y for recombinant inbreds given in the text, although the value of m is different (how ). 3.2. Demonstrate the generalization of formula (3.1) given below for a randomly mating population of size N. Hints We assume that the population is a constant size of N individuals (2N genes)...

## Correlation and Regression

In most scientific experiments not one but several variables are measured. In particular, we shall be primarily interested in the joint analysis of genotype and phenotype. It is of interest to quantify and assess the relationships between variables. A popular summary statistic for the quantification of pairwise relationships is the covariance. An alternative is the correlation, which is a standardized covariance. Imagine that we are given a sample of n unrelated individuals, who express a...

## Prmax z 1 z 4z v

The function power.marker implements Formula (6.2) > power.marker < - function(z,beta,Delta,xi) + + nu < - Nu(z*sqrt(2*beta*Delta)) + return(1-pnorm(z-xi) + > z < - 3.56 beta < - 0.02 Delta < - 10 1 0.7194996 Compare this to the probability of 0.7044, which was obtained via simulation. The worst case scenario is to have a QTL midway between markers. The formula corresponding to (6.2) is much more complex since it involves conditioning on the values of the process ZiA at both...