Parameters most influenced by c and the consequent accuracy of inferences based on these parameters
The index R (clonal richness) is widely used to assess the level of clonality within natural populations, especially in correlation with environmental drivers, to decipher the impacts of ecological features on PC (McMahon et al., 2017). Using entire populations, we empirically formalised the mathematical relationship between c and the genotypic richness indices R and β (Figures 1 and S1). The relationship with R is not linear (as sometimes seemingly assumed in the literature) but follows\(R=\sqrt{1-c^{2}}\pm\varepsilon\) (with \(\varepsilon\) being a small, positive, almost zero random error depending on the strength of genetic drift). Clonal evenness, represented by Pareto \(\beta,\) is also not a linear function of c . Instead, Pareto \(\beta\)follows a custom sigmoid curve with three domains (ranging from c\(\in\) [0, 0.15], [0.15, 0.9] and [0.9, 1]), with the first and last showing a strong decrease in Pareto \(\beta\) with increasingc. In contrast, in the smooth linear domain ranging fromc ~0.15 to c ~0.9, the relationship is almost horizontal, suggesting limited changes in genotypic evenness in populations with balanced amounts of sexual and clonal events.
In contrast, and in agreement with previous findings (Balloux et al., 2003; De Meeûs et al., 2006), the genetic parameters are, on average, largely unaffected below extreme rates of clonality (c <0.95). However, the variance inF IS and \({\overset{\overline{}}{r}}_{d}\) hints at PC and should theoretically allow estimation of its extent under a high prevalence of clonality (c ≥0.95; Figures and S1). Clonality acts by releasing the coercive effects of sexuality that constrain and channel the evolutionary trajectories of genotype frequencies towards Hardy-Weinberg proportions, which in turn increases the range of possible values for the genetic indices. This effect results in a broader distribution of genetic indices with a larger variance and unusual shapes, despite nearly unaffected mean values. The effect of clonality on the composition of natural populations is thus expected to be much more pronounced in terms of the genotypic structure, which strongly influences the nature of the targets of natural selection, the vectors of migration and the long-term retention of polymorphism, than for the genetic composition of populations.
Logically, genetic parameters reach their equilibrium value with lower temporal variation and faster than genotypic indices, even at small population sizes (N ≤1000 in our simulations). Although they are poorly informative regarding c below extreme values, accounting for genetic indices may limit the risk of misinterpretation when estimating c not at equilibrium.
As a consequence, genotypic and genetic parameters appear to be complementary in terms of the estimation of c , with the former being helpful at equilibrium and for all values of c(<0.95) and the latter being more accurate for estimating the incidence of clonality in populations not at equilibrium or discriminating among extreme values of c , which often implies a longer time needed to reach equilibrium (Reichel et al., 2016).
Unfortunately, these relationships cannot provide reliable information for detecting PC or estimating c due to the pervasive effect of sampling on these parameters, which has proven particularly worrying and raises questions regarding many conclusions reached thus far in the literature as to the importance of sexual reproduction in a diverse range of partially clonal species.