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There has been a long tradition of the use of population genetic data to infer demographic history (Cavalli-Sforza and Edwards 1967; Thompson 1973; Slatkin 1981). Methods of inference based on moments and likelihood have both been used. The former approach requires equations that give the expected value of statistics as a function of demographic parameters, whereas the latter involves a formula that gives the probability distribution of the observations of interest.

A recent trend in the last 15 years has seen a move towards Bayesian analysis (Wilson and Balding 1998; Beaumont and Rannala 2004), which gives a probability distribution for particular models, their parameter values, and for missing data, conditional on the observed data. Although these advances have broadened the horizons of population geneticists, and allowed molecular genetic data to be used more efficiently, there are some practical difficulties that seem to have held back their wider usage. A general consideration is that a fair amount of programming and analytical effort is necessary to develop each statistical model, which restricts the number of scenarios available, tempting misapplication by researchers.

Other problems include the amount of computational time necessary to carry out the analyses, and the complex nature of the output, which can often be difficult to interpret. Separately, over this period, with the advent of mitochondrial sequence data, demographic inference based on haplotype networks has become popular (Templeton et al. 1995), particularly in human population genetics (Bandelt et al.

1999). The idea is that by visualizing the reconstructed trees and applying a number of sophisticated graph-based analyses it is possible to read the demographic history from the trees. In particular, the nested clade phylogeographic analysis (NCPA) method of Templeton and colleagues (Templeton et al.

1995; Templeton 2004; see Buhay et al. this volume) has been widely used in conservation genetics (e.g.

Gottelli et al. 2004; Ciofi et al. 2006).

An attraction of these methods is that they are essentially non-parametric. However a concern is that there is often no strong correlation of individual gene-trees with demography (Machado and Hey 2003). Conceivably, if demographic history always involved a bottleneck at each vicariance event or range expansion, with limited effects of migration, there might be a closer match between gene-trees and demography (Chikhi and Beaumont 2005).

The circumstances favouring this possibility could be examined, for example with computer simulations, but it does seem a rather restrictive requirement. Extensions to NCPA. 348 j Mark Beaumont that include comparisons of Visual Studio .NET ANSI/AIM Code 39 inferences from different genes could allow for some robustness in the face of genealogical diversity (Templeton 2005). Under the cross-validation criterion of Templeton (2002), for example, inferences are regarded as concordant if more than one locus infers the same historical process involving the same locations.

There has so far been no examination of the performance of this criterion, either empirically (as performed for single loci in Templeton 2004), or via analysis of simulated data sets. Until recently there has been little simulation-based testing of NCPA, even for single loci (Knowles and Maddison 2002). However, with the advent of an automated version (Panchal 2007), it should become more straightforward to assess the procedure.

It is not the purpose of this article to go into any detail about the validity or otherwise of these network-based approaches (see Panchal and Beaumont 2007, for a more extensive discussion), but to point out that in their apparent deliverables they set a bench-mark against which modelbased methods need to be judged. For example a statement that there is evidence of restricted gene flow with long distance dispersal (Templeton et al. 1995) could be restated in terms of the posterior probability of such a model given the data.

Current model-based methods do not yet approach these aims, but, as techniques improve, it is conceivable that they may do so in the future (see Fagundes et al. 2007, for an example). The IM program of Hey and Nielsen (2004), based on the earlier work of Nielsen and Wakeley (2001), is one of the more sophisticated of such models, using MCMC to make inferences about the parameters.

This program has appreciable utility in conservation (e.g. Cassens et al.

2005), allowing six parameters to be inferred in a two-population setting. To be able address the big questions that NCPA claims to answer, it is necessary to go beyond this and rather than make inferences about particular parameters, we need to make inference about particular models, marginal to (i.e.

irrespective of) the parameters within the models..
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