Is equilibrium out of reach or are there some sneaky bouts of sex?

Reproductive systems impact the evolution of genetic diversity at the population level. Yet, we don’t know a lot about organisms that are partially clonal, despite the large component of biodiversity that dabbles in asexual reproduction to varying degrees.
cloning-snoopy
Clonal dynamics are interesting from a purely intellectual level, but are also quite important from an applied perspective as cultivated species, pathogens and invasive species often undergo asexual reproduction. What are the long term impacts on their evolvability?
The conclusions we draw from studies on partially clonal species depends on a

correct understanding of the effects of their reproductive mode on the genetic composition of their populations (Reichel et al. 2016).

Previously, I outlined some of the genetic hallmarks that can hint at clonality (see here and here). One of these signatures is heterozygote excess, in which heterozygosity is theorized to increase with asexual reproduction, though there are not many empirical tests of this hypothesis (but see Halkett et al. 2005, Guillemin et al. 2008, Krueger-Hadfield et al. 2016).
Negative Fis has been previously used to demonstrate exclusive clonality (e.g., Balloux et al. 2003), but other studies have hinted at the impact of temporal dynamics on Fis in natural populations (Stoeckel and Masson 2014). Indeed, in natural populations, both negative and positive Fis values are observed.
Reichel et al. (2016) explore the joint effects of partial clonality, mutation and genetic drift on Fis under increasing rates of clonality in BMC Genetics.
Based on their mathematical models, they argue for a dynamic interpretation of Fis. Negative values cannot alone be used an unequivocal evidence of extremely rare sexual events. likewise, non-negative Fis, including Fis=0, isn’t such a reliable indicator of an absence of clonality.
It will be necessary to provide complementary observations, such as the frequency distribution of multilocus genotypes and population history, with time series data in order to discriminate between different hypotheses on the frequency of clonality when mean Fis deviates from zero and when there is large variation of Fis across loci. In addition, an increase in loci is necessary for partially clonal versus exclusively sexual populations. This might be achieved by moving from population genetics to population genomics.
References
Balloux et al. (2003) The population genetics of clonal and partially clonal diploids. Genetics 164:1635–44.
Halkett et al. (2005) Tackling the population genetics of clonal and partially clonal organisms. TREE 20:194-201.
Guillemin et al. (2008) Genetic variation in wild and cultivated populations of the haploid-diploid red alga Gracilaria chilensis: How farming practices favor asexual reproduction and heterozygosity. Evolution, 62, 1500–1519.
Krueger-Hadfield et al. (2016) Invasion of novel habitats uncouples haplo-diplontic life cycles. Mol Ecol 25: 3801-3816.
Reichel et al. (2016) Rare sex or out of reach equilibrium? The dynamics of FIS in partially clonal organisms. BMC Genetics 17:76.
Stoeckel and Masson (2014) The exact distributions of FIS under partial asexuality in small finite populations with mutation. PLoS One 9:e85228.

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