Introduction
The maintenance of genetic diversity is a central objective in the conservation and use of plant genetic resources. In germplasm banks, breeding populations, seed collections, and conservation stands, diversity determines the adaptive potential of populations as well as their future value for breeding and restoration. As such, coancestry-based measures are commonly used to quantify the genetic representativeness of managed populations (Cockerham Reference Cockerham1969; Vencovsky and Crossa Reference Vencovsky and Crossa1999; Sebbenn Reference Sebbenn, Higa and Silva2006; Vencovsky et al. Reference Vencovsky, Chaves and Crossa2012).
Two parameters are frequently used for this purpose. Variance effective number was developed from the variance of allele frequency under genetic drift (Kimura and Crow, Reference Kimura and Crow1963; Cockerham Reference Cockerham1969), while status number was later proposed as a coancestry-based measure of retained diversity (Lindgren et al. Reference Lindgren, Jefferson and Gea1996, Reference Lindgren, Gea and Jefferson1997). Although both parameters are intended to describe the same general property, they are often presented as if they were distinct. The objective of this short communication is to show that, under the same assumptions, they are algebraically identical.
Experimental
Consider a group of 
$N$ diploid individuals. Let 
$f$ be the average coancestry between different individuals, 
$F$ the average inbreeding coefficient, and 
${{\Theta }}$ the average group coancestry including self-coancestry.
For an ideal random-mating population with no inbreeding and no relatedness, the variance of allele frequency is
\begin{equation*}\qquad\qquad\qquad\qquad\qquad V\left( p \right) = \frac{{p\left( {1 - p} \right)}}{{2N}}{ }\end{equation*}When individuals are related and/or inbred, the variance becomes (Cockerham Reference Cockerham1969):
\begin{equation*}\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad V(p) = p(1 - p)\left[ f+{\frac{{1 + F - 2f}}{{2N}}} \right].\end{equation*} The variance effective number, 
${N_{eV}}$, is obtained by equating this expression to the variance expected for an ideal population with a size of 
${N_{eV}}$ (Kimura and Crow, Reference Kimura and Crow1963; Cockerham Reference Cockerham1969):
\begin{equation*}\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad \frac{{p(1 - p)}}{{2{N_{ev}}}} = p(1 - p)\left[ {f + \frac{{1 + F - 2f}}{{2N}}} \right].\end{equation*}Thus,
\begin{equation*}\qquad\qquad\qquad\qquad\qquad\qquad\qquad {N_{ev}} = \frac{N}{{1 + F + 2(N - 1)f}}.\end{equation*}Now consider the status number, defined as (Lindgren et al. Reference Lindgren, Jefferson and Gea1996, Reference Lindgren, Gea and Jefferson1997):
\begin{equation*}{N_s} = \frac{1}{{2\Theta }}.\end{equation*} The average group coancestry can be written as the mean of all pairwise coancestries, including self-coancestry. In a group of 
$N$ individuals, there are 
$N\left( {N - 1} \right)$ off-diagonal terms with an average 
$f$, and 
$N$ diagonal terms. The coancestry of an individual with itself is
\begin{equation*}\frac{{1 + F}}{2}.\end{equation*}Therefore,
\begin{equation*}\Theta = \frac{{N(N - 1)f + N\left( {\frac{{1 + F}}{2}} \right)}}{{{N^2}}},\end{equation*}which simplifies to
\begin{equation*}\Theta = \frac{{2(N - 1)f + 1 + F}}{{2N}}.\end{equation*}Substituting this into the expression for status number gives
\begin{equation*}{N_s} = \frac{1}{{2\Theta }} = \frac{N}{{1 + F + 2(N - 1)f}}.\end{equation*}Therefore,
\begin{equation*}{N_s} = {N_{eV}}.\end{equation*} As an example, let 
$N = 10$, 
$f = 0.05$, and 
$F = 0.10$. Then,
\begin{equation*}{N_{eV}} = \frac{{10}}{{1 + 0.10 + 2(9)(0.05)}} = \frac{{10}}{{2.00}} = 5.\end{equation*}Also,
\begin{equation*}\Theta = \frac{{2(9)(0.05) + 1 + 0.10}}{{2(10)}} = \frac{{2.00}}{{20}} = 0.10\end{equation*}and
\begin{equation*}{N_s} = \frac{1}{{2(0.10)}} = 5,\end{equation*}confirming the identity.
Discussion
The present derivation shows that the variance effective number and status number provide the same value when expressed within the same coancestry framework (Tambarussi Reference Tambarussi2013, p. 87). The difference between them is terminological, not conceptual.
This clarification is relevant in plant genetic resources research because both parameters are used to evaluate retained diversity in germplasm collections, breeding populations, and conservation materials (Lindgren et al. Reference Lindgren, Jefferson and Gea1996, Reference Lindgren, Gea and Jefferson1997; Vencovsky and Crossa Reference Vencovsky and Crossa1999; Vencovsky et al. Reference Vencovsky, Chaves and Crossa2012). Treating them as distinct creates unnecessary confusion and hinders comparison among studies.
The result also highlights the unifying role of group coancestry in the interpretation of diversity measures. Once average group coancestry is expressed as a function of pairwise coancestry and inbreeding, the equivalence between status number and variance effective size follows directly. In this context, both parameters can be used interchangeably, provided that notation and assumptions are clearly stated.
Acknowledgements
The author is sincerely grateful to Professor Dr Roland Vencovsky for his encouragement and for inspiring his interest in effective population size. This paper is dedicated to his memory and recognizes his outstanding contributions to genetics and plant breeding. Evandro V. Tambarussi is supported by the CNPq research fellowship grant no. 303789/2022-0.
Competing interests
The author declares no conflict of interest.
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