Fiedler et al. (2009), reviewed evidence for the utilization of a contingency inference strategy termed pseudocontingencies (PCs). In PCs, the more frequent levels (and, by implication, the less frequent levels) are assumed to be associated. PCs have been obtained using a wide range of task settings and dependent measures. Yet, the readiness with which decision makers rely on PCs is poorly understood. A computer simulation explored two potential sources of subjective validity of PCs. First, PCs are shown to perform above chance level when the task is to infer the sign of moderate to strong population contingencies from a sample of observations. Second, contingency inferences based on PCs and inferences based on cell frequencies are shown to partially agree across samples. Intriguingly, this criterion and convergent validity are by-products of random sampling error, highlighting the inductive nature of contingency inferences.

Obtaining a closed-form sampling distribution for the coalescent with recombination is a challenging problem. In the case of two loci, a new framework based on an asymptotic series has recently been developed to derive closed-form results when the recombination rate is moderate to large. In this paper, an arbitrary number of loci is considered and combinatorial approaches are employed to find closed-form expressions for the first couple of terms in an asymptotic expansion of the multi-locus sampling distribution. These expressions are universal in the sense that their functional form in terms of the marginal one-locus distributions applies to all finite- and infinite-alleles models of mutation.

The exact transient sampling distribution is found for the infinite neutral alleles model with mutation, thus extending the stationary distribution found by Ewens (1972). The first eigenfunction in the sampling distribution depends only on the homozygosity. In a large sample the expected number of allele types is close to the expected number in a stationary distribution and depends little on the initial frequencies or the time of sampling. The expected number of types in a sample for a non-stationary population is tabulated.

The sampling distribution from a population with no mutation is found. The probability that the population is monomorphic given that the sample contains only one type is tabulated, where initially the population has a large number of alleles with equal frequencies.

A study is made of the joint distribution of the allele frequencies in two samples taken time t apart from a stationary population. Of particular interest is the number of allele types in common in two such samples. The distribution of the number of types in common in a population viewed at time t apart is also found and tabulated for different mutation rates and time. The expected frequency of the allele types in common is tabulated.

The distribution of allele frequencies in two divergent populations of common ancestry is shown to be the same as the distribution of frequencies in a single population at two time points 2t apart. A sufficient statistic for the time of divergence is shown to be the paired frequencies of the allele types in common. The expected waiting time until the populations have no allele types in common is tabulated.