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I've been reading paper on ancient horse genome (Recalibrating Equus evolution using the genome sequence of an early Middle Pleistocene horse) and in abstract authors mention term continuous selection:

We also find evidence for continuous selection on the immune system and olfaction throughout horse evolution

Can someone please explain what it means? What is continuous selection? Is it selection without interruptions, but what are those interruptions?

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As far as I know this is not a precisely defined technical term, and there's not a huge amount of additional detail in the paper. Here's the sentence from the paper that seems to correspond to the highlighted phrase in the abstract:

Finally, we identified loci potentially selected in modern horses (Supplementary Figs 11.1–11.2), focusing on regions showing unusual densities of derived mutations (Supplementary Information, section 11.1) ... Functional clustering analyses revealed significant enrichment for immunity-related and olfactory receptor genes (Supplementary Table 11.4), two categories also enriched for non-synonymous single nucleotide polymorphisms (SNPs) (Supplementary Information, section 5.2d).

And from the supplementary information:

We used quartet alignments including the donkey as out-group, one ancient horse and two modern horses in order to scan for genomic regions where the two modern horses shared unusual accumulation of derived alleles. Those could represent regions where alleles reached fixation faster than the rest of the genome, as a result of recurrent positive selection along the modern horse lineage or more recent selective sweeps, possibly in relation to their domestication. ... Comparing genomic scans performed with our ancient genomes enabled us to dissect selection regimes at two time periods predating the tMRCA of modern horses.

As far as I can tell without spending much time reading the paper and supplementary methods much more carefully, the authors are comparing sets of genes that differ between between two ancient horses and the modern horse in order to determine what changes occurred during different time periods e.g. between ancient horse 1 and ancient horse 2 or between ancient horse 2 and modern horses), and are concluding that in fact changes occurred approximately equally in all periods ("continuously") rather than early vs. late.

enter image description here

In this picture DK is the donkey (out-group), TC21 and CGG10022 are two different ancient horses, and M1 and M2 are modern horses.

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Continuous selection is not a term; it would not be bolded in a textbook.

When studying the history of a genome/lineage, you could have two very broad hypotheses about a given trait:

1) The trait was not present in a lineage, then appeared fairly suddenly (at least on a long time scale, it could still be hundreds, thousands, or millions of generations), and since then did not change much.

2) The trait was not present in a lineage, then the trait appeared in part of that lineage, and since then, the trait has continued to change substantially among different descendants of that lineage.

You could find evidence towards (1) if, for example, you observe a trait that is fairly constant among a diverse modern taxon but you don't see a similar trait in the cousins of that taxon.

You could find evidence towards (2) if you see a lot of diversity even among recently speciated members of a taxon.

The statement in the article is just saying in plain English, rather than using a scientific terminology, that they see evidence towards (2).

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I don't think it means anything more than repeated occurrence of the selection of the prefered traits.

A trait vital for survival will always be exposed to stronger evolutionary pressure. Even if the trait is good there will always be room for improvement.

It can be seen in contrast with the introduction of a radical improvement with the introduction of a new genetic mutation. This will probably happen only once until the entire gene pool is updated.

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