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This is why we mentioned the deterministic evolution of linkage disequilibrium.
On the other hand, in the HAPimLDL method we used a probabilistic modelling of the temporal evolution of linkage disequilibrium.
Recent work has shown that the evolution of linkage to mating type occurs independently in various species of Microbotryum (Abbate and Hood 2010; Petit et al. 2012).
Therefore, the modelling of the evolution of linkage disequilibrium was a deterministic process; it was complete at time 0 and remained complete during the following generations.
The second method, HAPimLDL, was a maximum likelihood approach [ 12] and it used probabilistic modelling of the temporal evolution of linkage disequilibrium based on a Wright-Fisher model.
These two methods differed in the way they modelled the evolution of linkage disequilibrium between a QTL and its flanking markers, through the probability of bearing the favourable QTL allele given the marker observations.
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In most cases, this reflects retention of an ancestral association; however, some instances of repeated evolution of physical linkage between pairs or groups of genes have been described.
In the case of BIUFF, the organizational and management changes perhaps slowed the evolution of UIG linkages.
But these studies remain highly static and cannot account for the evolution of the linkages between maritime transport and urban development.
These equations are part of the standard population genetic toolkit and as shown above are straightforward to derive from Equation 2 (for a thorough treatment of multilocus systems including equations for the time evolution of the linkages, see Barton and Turelli 1991; Kirkpatrick et al. 2002; Neher and Shraiman 2011).
Westneat, M. W. Evolution of levers and linkages in the feeding mechanisms of fishes.
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