Conclusions and Perspective

Here and in the previous publications,32'36'37 we describe a rather general class of models, which are based on the classical concept of a birth-and-death process and seem to be applicable to the genome evolution process. Similar, although not identical and apparently less general, modeling approaches have been considered by others.16,31'46 Even earlier, evolution of gene families has been modeled within the distinct mathematical framework of multiplicative processes.47

The utility of birth-and-death type models in evolutionary genomics in itself is not a trivial matter and stems from fundamental features of genome evolution which, in part, have been presciendy envisaged by classic geneticists and, in part, became apparent after the advent of genomics. As captured in the tide of Ohno's famous book,18 although foreseen even in the early days of genetics,17'48 gene duplication probably is the principal mechanism of genome evolution. Of course, genomes cannot grow ad infinitum and, through most of the evolutionary history, the number of genes within a given phylogenetic lineage probably remains roughly constant. Hence duplication is intrinsically coupled to gene loss. The results of comparative genomics further show that many genes in each lineage cannot be obviously linked to other genes through duplication. Without necessarily specifying the biological mechanisms (these could involve rapid change after duplication, gene acquisition via horizontal transfer, and possibly, birth of genes from noncoding sequences), it is reasonable to view these unique genes as resulting from innovation. For genomes to maintain equilibrium, the combined rates of duplication and innovation over the entire ensemble of gene families should equal the rate of gene loss, at least when averaged over long time spans. Furthermore, the observed distribution of family sizes, which asymptotically tends to a power law, dictates a much more specific connection between the gene birth and death rates, namely, the second order balance (4).

The incentive to examine these models in detail stems from at least three rather fundamental questions: (i) are the above elementary evolutionary mechanisms sufficient to account for the empirically observed characteristics of genomes, (ii) what is the contribution of natural selection to the general quantifiable features of genomes, such as the size distribution of gene families, and (iii) how similar or how different are the models describing evolution of phyloge-netically distant genomes, such as those of prokaryotes and eukaryotes. The analysis of BDIMs starts to provide some answers, although it is premature to consider these final in any sense. The critical observation made in the course of BDIM analysis was that different versions of these models could be readily distinguished on the basis of goodness of fit to the empirical data. This being the case, we found that the simplest possible model in which all paralogs are considered independent does not explain the data well. Thus, turning to the first of the above questions, we have to conclude the "something else" is required to model genome evolution, on top of the three elementary processes. This "something" is dependence or "interaction" between gene family members which results in self-accelerating family growth. In order to account for the observed stationary distribution of family sizes, it is sufficient to introduce a very weak dependence as embodied in the linear BDIM. However, when we switched from the deterministic to the stochastic version of BDIMs which provide for the possibility of analysis of the dynamics of the systems evolution, we found that evolution under the linear BDIM was much too slow to account for the emergence of the large families of paralogs found in all genomes during the time of life's evolution. Only higher order BDIMs, with degrees between 2 and 3, i.e., with "strong interactions" between family members were found to provide for sufficiendy fast evolution to be compatible with the real biological timescale.

Obviously, these findings beg the question: what is the nature of the mysterious "interactions" between paralogs? This brings us to the second of the above major problems. BDIMs do not explicidy include the notion of selection. However, the simplest interpretation of the interactions implied by the higher order BDIMs seems to be that these reflect adaptive evolution of gene families driven by positive selection. Should that be the case, we are justified to conclude that very weak selection would suffice to explain the stationary distribution of family sizes, but much stronger selective pressure is needed to account for the dynamics of genome evolution. However, the interpretation of BDIM degree as a manifestation of selection is, at this point, no more than a guess. One of the further developments of genome evolution modeling involves introducing selection explicidy and determining whether the resulting more sophisticated models will be equivalent to the higher order BDIMs explored here.

BDIMs worked well in describing evolution of all analyzed genomes, from the smallest prokaryotic ones to the most complex genomes of plants and animals. However, the parameters of the resulting models, i.e., the duplication, deletion, and innovation rates differed significantly, suggesting some tantalizing answers to the third of the questions posed above. In particular, we found that the innovation rates in prokaryotes were an order of magnitude greater than those in eukaryotes.32 An optimistic interpretation of this difference is that the relatively high innovation rates detected for prokaryotes reflect rampant horizontal gene transfer, an increasingly recognized defining feature in the evolution of bacteria and archaea.49"51 Should that be the case, we might be justified to conclude that BDIMs are telling us something new regarding the extent of this phenomenon. However, it would be premature to rule out the pessimistic explanation, i.e., that the observed differences are due to some cryptic modeling artifacts. The issue definitely deserves further investigation, through refined modeling approaches and analysis of additional comparative-genomic data.

In conclusion, it makes sense to ask the $64K question: do the models discussed in this chapter (and similar ones) reveal something new about biology? So far we seem to have only rather equivocal answers. Earlier in this section, we discuss some interesting hints on new aspects of the role of selection in genome evolution and on distinct regimes of evolution in different domains of life. Realistically, however, the principal conclusions seem to be quite general and mosdy methodological. Indeed, it was observed in these and related analyses that important aspects of genome evolution can be realistically modeled with simple, straightforward approaches. Perhaps more importandy, the work summarized here makes the next step by showing (to paraphrase Einstein's famous aphorism) that models of genome evolution should be as simple as possible but not simpler and that we seem to be able to identify the minimal required level of complexity. Future developments will show whether or not a path exists from these general findings to new biology.


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