# Validation of Automated Chromosome Recovery in the Reconstruction of Ancestral Gene Order
## 8 Conclusions  
As a simple contribution of this work, the fixed proportion of gray shadings on the heat map could have wider applications beyond visualizing ancestral chromosome clustering. We have already used it here in comparing co-occurrence measures, for comparing analyses of real versus simulated data, for comparisons among the four ancestors and for showing parallels between replications of the simulation. There are other possibilities, even within our particular application to reconstruction. For example, were we to use 200 contigs or 400 contigs instead of 250, the improved heat maps could avoid the effect of the contig number on the overall impression, since the average brightness or darkness would not change.  
In clustering the contigs using complete-linkage, we hoped to ensure that all the contigs in a cluster are related at least at some minimal level. A disadvantage might be a slight tendency for clusters to be broken up by some fortuitous link early in the execution of the algorithm due to the nature of greedy algorithms. We have not found superior results with other clustering methods such as average-linkage or \(k\)-means.  
In estimating the number of genes in gene families in ancestral genomes, \(N(i,j)\), we did not explore the possibility of iterating the successive estimation of \(N(i,j)\) and \(a,b,c,d\). Adopting this approach might decrease the overall noise in the heat map.  
One interesting aspect of our reconstruction of the ancestral genomes is that Ancestors 2, 3 and 4 all displayed seven clusters despite the whole genome duplication between Ancestor 1 and Ancestor 2, both in the real data and the simulations. An explanation in terms of selective pressures towards a seven-chromosome state may have some credibility, though a methodological artifact seems more likely; the two subgenomes created by whole genome duplication would be very similar, meaning that co-occurrence patterns of contigs containing runs of homologous genes would be parallel, and separate chromosomes would not emerge from the clustering. This could be an objective of future study.  
To what extent would our methods be applicable to sets of genomes even more distantly related than the monocot orders? On the one hand, the reconstructed contigs would be shorter, the co-occurrence frequencies lesser and the clustering less clear. On the other hand, the intermediate ancestors should be more distinct, meaning that we might better distinguish the evolutionary development of the extant genomes.  
Conceptualization, Q.X., L.J., J.H.L.-M., D.S.; methodology, Q.X., L.J., D.S.; software, Q.X., L.J.; writing, Q.X., L.J., D.S.; funding acquisition, D.S., L.J. All authors have read and agreed to the published version of the manuscript.  
This research was funded by Discovery grants to L.J. and D.S. from the Natural Sciences and Engineering Research Council of Canada. [PERSON] holds the Canada Research Chair in Mathematical Genomics.  
Figure 5: Heat maps for Ancestor 1 from four different simulations showing the clusters of contigs making up ancestral chromosomes from the longest 250 contigs, using complete-linkage on chromosomal co-occurrence correlations.