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.