Whole genome duplication (WGD) is a dramatic evolutionary event generating many new genes and which may play a role in survival through mass extinctions. Paddlefish and sturgeon are sister lineages that both show genomic evidence for ancient WGD. Until now this has been interpreted as two independent WGD events due to a preponderance of duplicate genes with independent histories. Here we show that although there is indeed a plurality of apparently independent gene duplications, these derive from a shared genome duplication event occurring well over 200 million years ago, likely close to the Permian-Triassic mass extinction period. This was followed by a prolonged process of reversion to stable diploid inheritance (rediploidization), that may have promoted survival during the Triassic-Jurassic mass extinction. We show that the sharing of this WGD is masked by the fact that paddlefish and sturgeon lineage divergence occurred before rediploidization had proceeded even half-way. Thus, for most genes the resolution to diploidy was lineage-specific. Because genes are only truly duplicated once diploid inheritance is established, the paddlefish and sturgeon genomes are thus a mosaic of shared and non-shared gene duplications resulting from a shared genome duplication event.

How can we best learn the history of a protein’s evolution? Ideally, a model of sequence evolution should capture both the process that generates genetic variation and the functional constraints determining which changes are fixed. However, in practical terms the most suitable approach may simply be the one that combines the convenience of easily available input data with the ability to return useful parameter estimates. For example, we might be interested in a measure of the strength of selection (typically obtained using a codon model) or an ancestral structure (obtained using structural modeling based on inferred amino acid sequence and side chain configuration). But what if data in the relevant state-space are not readily available? We show that it is possible to obtain accurate estimates of the outputs of interest using an established method for handling missing data. Encoding observed characters in an alignment as ambiguous representations of characters in a larger state-space allows the application of models with the desired features to data that lack the resolution that is normally required. This strategy is viable because the evolutionary path taken through the observed space contains information about states that were likely visited in the “unseen” state-space. To illustrate this, we consider two examples with amino acid sequences as input. We show that $$\omega$$, a parameter describing the relative strength of selection on nonsynonymous and synonymous changes, can be estimated in an unbiased manner using an adapted version of a standard 61-state codon model. Using simulated and empirical data, we find that ancestral amino acid side chain configuration can be inferred by applying a 55-state empirical model to 20-state amino acid data. Where feasible, combining inputs from both ambiguity-coded and fully resolved data improves accuracy. Adding structural information to as few as 12.5% of the sequences in an amino acid alignment results in remarkable ancestral reconstruction performance compared to a benchmark that considers the full rotamer state information. These examples show that our methods permit the recovery of evolutionary information from sequences where it has previously been inaccessible. [Ancestral reconstruction; natural selection; protein structure; state-spaces; substitution models.]

In this paper we present some results of an interactive source/receiver computer program written for a personal computer. The program has been used to simulate simple acoustical environments and to study limitations of the sound intensity method. The program is also useful for showing students how source position, strength, and phase angle determine the acoustic field in a multi-source environment. The user can select interactively the characteristics of the sources, including sources on lines and sources on surfaces such as planes and spheres. Receivers may be selected individually by specifying their Cartesian coordinates; receivers may also be generated automatically to lie on certain simple surfaces such as planes, spheres or rectangular paralle-lopipeds. A pair of such receiver surfaces, separated by a fixed distance, can be generated automatically to study the sound intensity method. Examples of the above described features will be presented.

How can we best learn the history of a protein’s evolution? Ideally, a model of sequence evolution should capture both the process that generates genetic variation and the functional constraints determining which changes are fixed. However, in practical terms the most suitable approach may simply be the one that combines the convenience of easily available input data with the ability to return useful parameter estimates. For example, we might be interested in a measure of the strength of selection (typically obtained using a codon model) or an ancestral structure (obtained using structural modelling based on inferred amino acid sequence and side chain configuration).But what if data in the relevant state-space are not readily available? We show that it is possible to obtain accurate estimates of the outputs of interest using an established method for handling missing data. Encoding observed characters in an alignment as ambiguous representations of characters in a larger state-space allows the application of models with the desired features to data that lack the resolution that is normally required. This strategy is viable because the evolutionary path taken through the observed space contains information about states that were likely visited in the “unseen” state-space. To illustrate this, we consider two examples with amino acid sequences as input.We show that ω, a parameter describing the relative strength of selection on non-synonymous and synonymous changes, can be estimated in an unbiased manner using an adapted version of a standard 61-state codon model. Using simulated and empirical data, we find that ancestral amino acid side chain configuration can be inferred by applying a 55-state empirical model to 20-state amino acid data. Where feasible, combining inputs from both ambiguity-coded and fully resolved data improves accuracy. Adding structural information to as few as 12.5% of the sequences in an amino acid alignment results in remarkable ancestral reconstruction performance compared to a benchmark that considers the full rotamer state information. These examples show that our methods permit the recovery of evolutionary information from sequences where it has previously been inaccessible.