where f(t |Θ) is the probability density of the coalescent time. Assuming free recombination between loci, the full likelihood is a product of each locus likelihood. In order to determine the likelihood we must determine the density f(t |Θ) for coalescent of two samples in the IM model. Wang and Hey (2009) find the time to the MRCA by explicitly integrating over all possible sample paths in the...

Recent statistical and computational analyses have shown that a genealogical most recent common ancestor (MRCA) may have lived in the recent past [Chang, J.T., 1999. Recent common ancestors of all present-day individuals. Adv. Appl. Probab. 31, 1002-1026. 1027-1038; Rohde, D.L.T., Olson, S., Chang, J.T., 2004. Modelling the recent common ancestry of all living humans. Nature 431, 562-566]. Howe...

Chemical differences between mid-ocean ridge basalts (MORBs) and ocean island basalts (OIBs) provide critical evidence that the Earth's mantle is compositionally heterogeneous. MORBs generally exhibit a relatively low and narrow range of (3)He/(4)He ratios on a global scale, whereas OIBs display larger variability in both time and space. The primordial origin of (3)He in OIBs has motivated hypo...

We demonstrate broadband frequency comb generation in the mid-infrared (MIR) from 2.3 to 3.5 μm in a Si(3)N(4) microresonator. We engineer the dispersion of the structure in the MIR using a Sellmeier equation we derive from experimental measurements performed on Si(3)N(4) films from the UV to the IR. We use deposition-anneal cycling to decrease absorption losses due to vibrational transitions i...

The number of segregating sites in a sample of DNA sequences and the age of the most recent common ancestor (MRCA) of the sequences in the sample are positively correlated. The value of the former can be used to estimate the value of the latter. Using the coalescent approach, we derive in this paper the joint probability distribution of the number of segregating sites and the age of the MRCA of...