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# Estimating the effective population size (Ne) in ectomycorrhizal fungi from genetic data

Anouck Champion

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## To cite this version:

Anouck Champion. Estimating the effective population size (Ne) in ectomycorrhizal fungi from genetic data. Biodiversity and Ecology. 2024. hal-04871084

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# Estimation de la taille efficace ($N_e$) chez les champignons ectomycorhiziens à partir de données génétiques

Estimating the effective population size ($N_e$)
in ectomycorrhizal fungi from genetic data

## Anouck CHAMPION

### Année universitaire 2023-2024

### Mémoire défendu le 18 juin 2024
A l'université de Bordeaux

**Laboratoire :**

UMR BioGeCo, INRAE, Université de Bordeaux
69 route d'Arcachon 33610 Cestas

**Encadrement :**

**Myriam HEUERTZ**

UMR BioGeCo, INRAE, Université de Bordeaux
69 route d'Arcachon 33610 Cestas
&

**Roberta GARGIULO**

Royal Botanic Gardens
Kew, Richmond, Surrey, UK

biogeco

<figure><img src="image_4.png" /></figure>

Royal
Botanic
Gardens Kew
# Introduction

Genetic diversity is the basis for evolutionary change and is critical for species to adapt to changing environments and to have the potential for long-term survival (Hoban et al., 2020). More broadly, genetic diversity is the foundation of ecosystem function and resilience, also making possible the sustainable development of agriculture and managed ecosystems, on which human societies depend (Hoban et al., 2021). However, genetic diversity is declining at an alarming pace because of habitat destruction and fragmentation, over-exploitation and other human activities which significantly reduce population sizes (Hoban et al., 2021, 2023). In conservation and management policies, genetic diversity is acknowledged as one of the three levels of biodiversity, but despite existing genetic tools in conservation genetics, genetic factors are still too often ignored in species recovery plans (Willi et al., 2022). In recent years, however, there has been remarkable progress to integrate genetic conservation concepts in the Convention on Biological Diversity's (CBD) policies, as demonstrated by the Kunming-Montreal Global Biodiversity Framework (KMGBF), adopted in 2022. This framework, via Goal A and Target 4, states that the genetic diversity within and between populations of wild and domesticated species must be maintained and restored in order to safeguard their adaptive potential (CBD, 2022). Several indicators have been developed to assess and monitor genetic diversity in all species, a crucial aspect for achieving the proposed objectives. Among these indicators, three have been proposed by Hoban et al. (2020), the first two being included in the KMGBF. The first and headline indicator is designed to measure the likelihood of long-term population persistence and refers to the number of populations within species with a genetic effective population size ($N_e$) above 500 versus those with $N_e$ below 500 (Hoban et al., 2020).

The effective population size ($N_e$) is a population genetic parameter determining the expected rate of genetic diversity loss due to genetic drift (R. S. Waples, 2022). The "$N_e > 500$" indicator refers to an approximate threshold below which the level of genetic diversity is not sufficient for continual population adaptation, with random allele frequency variations due to genetic drift preventing directional changes due to natural selection (Hoban et al., 2020). In practice, depending on data availability, $N_e$ can be estimated from demographic data (using e.g., sex ratio, variance of reproductive success), genetic data or by approximation from the census size, assuming $N_e / N_c = 0.1$ (Laikre et al., 2021). This ratio is supported by evidence for a large number of taxa (Hoban et al., 2020; Palstra & Fraser, 2012) and is particularly useful when only demographic data are available (Frankham, 1995). Following this rule of thumb, the threshold
of 500 for the effective population size corresponds to a census size of approximately 5000 (Hoban et al., 2023).

In recent years, the use of genetic methods to estimate contemporary effective population size has strongly increased, with the enhanced access to genetic marker technology and the advantage of non-invasive sampling in natural populations (Do et al., 2014). Since the end of the 2000s, single-sample methods (i.e. based on genetic data such as SNPs or microsatellites on individuals sampled at a single time point) have been the most frequently used. Of the single-sample methods, a bias-adjusted version of Hill's method based on linkage disequilibrium is most widely used (R. S. Waples, 2024). Linkage disequilibrium (LD) corresponds to the non-random association of alleles between two loci and arises from physical linkage and recombination in the genome. In addition, genetic drift randomly generates statistical associations between alleles at different loci, increasing LD in a population. Therefore, measuring LD between independently-segregating loci can be used to provide an estimate of *N*<sub>e</sub>, with LD being inversely proportional to *N*<sub>e</sub> (R. K. Waples et al., 2016; R. S. Waples, 2024).

Estimating *N*<sub>e</sub> from genetic markers using the LD-method presents a number of challenges and several possible biases, as reviewed by Waples (2024). Some biases relate to technical limitations, such as missing data, sample size, rare alleles or physical linkage between loci, and are common to all *N*<sub>e</sub> estimations (R. S. Waples, 2024). In addition, other issues may emerge from biological limitations that violate assumptions of the LD-method, i.e. isolated populations with random mating and discrete generations (R. S. Waples, 2024). These include migration, changes in population size (e.g. bottlenecks), age structure or complex mating systems and may affect *N*<sub>e</sub> estimation in non-model species such as ectomycorrhizal fungi, which have biological and genetic peculiarities.

The ongoing biodiversity crisis affects most living organisms, including fungi, driven by widespread and localised habitat degradation, deforestation and pollution (Barron, 2017). However, as ectomycorrhizal fungi (EcMF) spend most of their lives hidden from view (in the form of below-ground vegetative mycelium), their study has long been limited to monitoring abundance and distribution of above-ground sporocarps or to the molecular identification of ectomycorrhizas (van der Linde et al., 2012). Population genetic methods potentially allow for a more accurate assessment of their conservation and threat status. However, the life cycles and life-history traits of EcMF represent serious obstacles for population genetic studies and in
particular for estimating *N*<sub>e</sub>, which has seldom been assessed in these organisms (Dauphin & Peter, 2024; Vincenot & Selosse, 2017). First, there is the difficulty to distinguish individuals, since a mycelial genet (i.e. a genetic individual) can produce several fruit bodies, or no fruit body at all (Vincenot & Selosse, 2017), meaning that fruit bodies are not representative of individuals. This kind of issue has already been explored in clonal plants, for example in the partially clonal orchid *Cypripedium calceolus* (Gargiulo et al., 2023). The authors observed a strong discrepancy between the apparent number of individuals (ramets) and the number of genetic individuals (genets), inferring that ramets are poor estimates of *N*<sub>e</sub> (Gargiulo et al., 2023). Second, while population genetic theory generally assumes fully haploid or diploid organisms with obligate sexuality, most fungi display a complex mating system characterised by a haploid-diploid life cycle, along with frequent asexual multiplication (Bessho & Otto, 2022). Also, some apparently asexual species show high levels of genetic diversity and recombination, suggesting cryptic sexual cycles (Vincenot & Selosse, 2017). Third, EcMF populations are structured depending on how the spores are dispersed (wind, soil mesofauna, mammals) and on the landscape. In areas devoid of barriers, EcMF populations may display extensive gene flow, sometimes over hundreds of kilometres (Vincenot & Selosse, 2017). It seems clear that ectomycorrhizal fungi populations are a long way off the ideal population considered in models, and all the aspects cited above are likely to affect the estimation of *N*<sub>e</sub>.

The main objective of this study was to investigate if life-history traits such as asexual
multiplication (clonality) and a prolonged haploid phase influence significantly the estimation
of *N*<sub>e</sub> in EcMF. Concerning haploidy, *N*<sub>e</sub> in haplo-diploid species is expected to display
dramatically low values when the life cycle is strongly skewed towards the haploid phase, as
haploids undergo stronger genetic drift than diploids (Bessho & Otto, 2022). Partial clonality
also affects *N*<sub>e</sub>, especially when the proportion of clonality is high compared to sexual
reproduction, with low *N*<sub>e</sub> values expected (Balloux et al., 2003; Gargiulo et al., 2023).
Moreover, asexual reproduction increases the variance in sexual reproductive success among
individuals, which is expected to further reduce *N*<sub>e</sub>. This could be particularly pronounced in
the presence of very large clones in the population, which may sexually reproduce more
(Macaya-Sanz et al., 2016). The second objective of this study was to assess the effect of
population structure on *N*<sub>e</sub> estimates in EcMF. Patterns of differentiation and migration can
cause downwardly or upwardly biassed *N*<sub>e</sub> estimations if they are not accounted for (R. S.
Waples, 2024; R. S. Waples & England, 2011). Finally, potential biases associated with the
sampling design were also verified, especially occurrence of missing data, sample sizes, and pseudo-replication in molecular markers. Particular attention was paid to problems arising from the use of large genomic datasets (i.e. with a large number of SNPs), where physical linkage between loci can lead to a downward bias in $N_e$ estimation (R. S. Waples, 2024). Datasets with a large number of SNPs also provide correlated information due to overlapping pairs of the same loci, which introduces pseudoreplication, affecting the precision and accuracy of $N_e$ estimation (R. S. Waples et al., 2022).

In this way, via the analysis of published genetic datasets, this study aimed to address the following questions: (1) What are the factors influencing the accuracy and precision of $N_e$ estimation in ectomycorrhizal fungi? (2) In what directions do these factors bias $N_e$ estimates? (3) What are the best practices to adopt in order to obtain an unbiased estimate of $N_e$?

# Materials and Methods

## Selection of datasets

I carried out a keyword search in NCBI using the following query: mushroom* AND (microsatellites OR SNPs) AND *mycorrhiza*. I deliberately chose general terms, expecting only a few articles on the subject. I also chose the term "mushroom" rather than "fungi" to exclude fungi that do not form fruit bodies ("mushrooms" in the general sense), and because most genetic studies on EcMF are based on sporocarp sampling. A first filter was applied to keep only population genetic studies on EcMFs (removing papers about ericoid or orchid mycorrhiza). Then I limited the search to microsatellite markers and SNPs and kept only the studies that provided the datasets. In addition to this search, other datasets were found via review articles or by contacting authors directly.

## Datasets

Four genetic datasets from ectomycorrhizal fungi were used for this study, from the Ascomycetes and Basidiomycetes groups: *Boletus edulis*, *Suillus brevipes*, *Suillus luteus* and *Tuber melanosporum*. The main characteristics of these datasets are presented in Table 1.

## Data analysis

### Analysis approach

Most analyses were conducted in R 4.3.2 (R Core Team, 2021), using the Rstudio interface or on the Genotoul bioinformatics platform. The workflow common to all datasets
included an initial filtering step addressing missing data and clones, followed by an analysis of genetic structure, and finally an estimation of $N_e$. These steps and the software programmes used are summarised in Figure 1 and the detailed workflow is explained hereafter. Detailed scripts can also be found at: https://github.com/anchampion/Ne_estimation_EcM_fungi.git.

<table><caption>**Table 1.** Characteristics of the 4 genetic datasets used in this study. The populations (“Gene pools”) used for the analyses are shown in bold. For *Tuber melanosporum*, the diploid* data correspond to zygotic genotypes, where the first allele corresponds to the maternal one and the second one to the paternal one, deduced from the maternal genotypes.</caption><thead><tr><th>Species name</th><th>Taxonomic group</th><th>Ploidy of samples</th><th>Total sample size</th><th>Total number of markers</th><th>Gene pools (sample size)</th><th>Issues explored</th><th>Reference</th></tr></thead><tbody><tr><td>Boletus edulis Bull.</td><td>Basidiomycota</td><td>Diploid</td><td>134</td><td>7 SSRs</td><td>Cluster 1 (60); Cluster 2 (22); Cluster 3 (43)</td><td>Clonality</td><td>Hoffman et al., 2020</td></tr><tr><td>Suillus brevipes (Peck) Kuntze</td><td>Basidiomycota</td><td>Diploid</td><td>55</td><td>662940 SNPs</td><td>Coastal California (9); Mountain California (16); Wyoming/Colorado (12); Minnesota/Canada (11)</td><td>Genetic structure, Pseudo-replication</td><td>Branco et al., 2017</td></tr><tr><td>Suillus luteus (L.) Roussel</td><td>Basidiomycota</td><td>Diploid</td><td>34</td><td>~ 1.6 M SNPs</td><td>Belgium (34)</td><td>Pseudo-replication</td><td>Bazzicalupo et al., 2020</td></tr><tr><td>Tuber melanosporum Vittad.</td><td>Ascomycota</td><td>Haploid / Diploid*</td><td>154 / 30</td><td>11 SSRs</td><td>Spontaneous "brûlés": haploids (32); diploids* (24)</td><td>Ploidy</td><td>Taschen et al., 2016</td></tr></tbody></table>

<figure><img src="image_5.png" /><figcaption>**Figure 1.** Summary of the workflow used for all datasets. For each step, the method and software programmes used are indicated.</figcaption></figure>
## Missing data correction

Loci with more than 20% of missing data across all individuals were excluded systematically (as in Gargiulo et al. 2024), using the R package *poppr* (Kamvar et al., 2014). This applies especially to SNPs but is not recommended for microsatellite markers, as they are often much less numerous. I also decided to remove individuals with more than 20% missing data across all loci.

## Clone correction

As many species of fungi display high rates of clonality, it was necessary to verify the presence of identical genotypes in the datasets. For SSRs, I assessed the presence of clonal copies as identical Multi-Locus Genotypes (MLGs) using the R package *Rclone* (Arnaud-Haond & Bailleul, 2022). I then merged all MLGs that differed by just one or a few allelic variants (due to genotyping errors or mutations) into Multi Locus Lineages (MLLs). $N_e$ estimation was then conducted after removal of clonal copies, keeping a single ramet per MLG or per MLL. For SNPs, the detection of clones was performed using a kinship matrix computed with KING based on pairwise kinship > 0.354 for ramets belonging to the same genet (Manichaikul et al., 2010). In each pair of individuals with a kinship coefficient above the threshold, one of the two individuals was removed before $N_e$ estimation.

## Genetic structure analysis

I compared genetic structure analysis using a multivariate analysis (DAPC, from the R package *adegenet* (Jombart & Ahmed, 2011) and two Bayesian methods: snmf (R package *LEA* (Frichot & Francois, 2015) and ADMIXTURE (Alexander et al., 2009). If different clusters were detected in the dataset, fixation indices ($F_{ST}$) were calculated between them. When a strong structure was detected in a dataset, I performed $N_e$ estimation on each group separately. It is important to note that analyses of genetic structure are built on the assumption of non-linked markers. Thus, I removed physically linked SNPs with the software programme PLINK2 (Chang et al., 2015), using the “--indep-pairwise” option prior to structure analysis. Parameters were set to 50 and 0.5 for the window size and $r^2$ threshold, respectively.

### $N_e$ estimation

The estimation of the contemporary $N_e$ was performed using the software *NeEstimator* v2 (Do et al., 2014). I used the Linkage Disequilibrium method for a random mating system. The critical values for allele frequencies selected were 0.05, 0.02, 0.01, “no frequency restriction” and “no singleton alleles”. In the Results however, I exclusively considered the
estimates from the “no singleton” threshold, as removing singleton alleles has been proposed
as the best way to avoid bias related to rare alleles (R. S. Waples, 2024).

Bias identification

Life cycle

In many ectomycorrhizal species in the phylum Ascomycota, e.g. truffles (Tuber spp.), the dominant phase of the cycle, or at least, the phase of the fruit body is mainly haploid. In order to assess the effect of haploid datasets on N<sub>e</sub> estimation, I used a genetically homogeneous population (see Table 1) from a dataset for the black truffle, *Tuber melanosporum*, sampled in different locations in the south of France and genotyped with 11 microsatellite markers (Taschen et al., 2016). In addition to the haploid data obtained on the truffles and corresponding to the parental genotypes, “zygotic” data obtained by genotyping reproductive tissue were also collected, aiming to represent the diploid ascospores produced in the truffle. As this diploid stage is ephemeral, a contamination of zygotic genotypes with maternal genotypes, which are predominant in the truffles, might be possible. For these reasons, both haploid and diploid genotypes were analysed, with the aim of identifying the biases inherent in the use of either dataset. As the software used to estimate N<sub>e</sub> only supports diploid data, I had to artificially “diploidise” the haploid datasets. Diploidisation was carried out via two methods, using GenAlEx (Peakall & Smouse, 2012). The first method consisted of duplicating each haploid genotype (n = 32) to generate diploids that were all homozygotes. In the second method, haploid samples were randomly paired to create diploid genotypes (n = 15). The “duplication” method represents an extreme case of total homozygosity (lower range for genotypic diversity), while the “pairing” method represents random mating (maximum genotypic diversity). Therefore, while we cannot directly compare haploid and diploid genotypes, transformed haploid data can still provide us with additional information about the population. Once the 3 types of datasets were generated (hereafter, “zygotes”, “duplicated” and “paired”), 10 genotypes were sampled in each dataset (or 20 for the “duplication” method, in order to sample the same number of alleles as in the “pairing” method), and 10 replicates were made. Then, N<sub>e</sub> was estimated, as well as the allelic richness, expected heterozygosity (H<sub>E</sub>) and inbreeding coefficient (F<sub>IS</sub>), in order to check differences in diversity and heterozygosities between these datasets.

Clonality

In order to understand whether the presence of clones in a dataset biassed the N<sub>e</sub>
estimate, I used a dataset from the widespread basidiomycete *Boletus edulis*, where clones had
not been removed (Hoffman et al., 2020). Individuals in this dataset were sampled in many
closeby locations in Germany and genotyped using 7 microsatellite markers. On the original dataset that contained 134 sporocarps, I performed the missing data correction and analysis of genetic structure, which led me to work on a homogeneous population of 60 individuals. Then, as described above, the R package *Rclone* was used to detect MLGs and MLLs. Five treatments were applied on this dataset to assess the impact of clonality on *N*<sub>e</sub>: (1) no correction (n = 60); (2) keeping one ramet/genet for the largest clones (≥ 7 ramets) (n = 41); (3) keeping one ramet/genet for medium and large clones (≥ 3 ramets) (n = 33); (4) keeping one ramet/MLG (n = 31); (5) keeping one ramet/MLL (n = 27). Then, 25 individuals were drawn from each corrected population, and this sampling was replicated 10 times. Finally, *N*<sub>e</sub> was estimated for each replicate.

## Genetic structure

The effect of genetic structure on *N*<sub>e</sub> estimation was tested in different populations of the species *Suillus brevipes*. It is a widespread mushroom species in North America, which develops an obligate symbiotic association with the roots of several species of the *Pinus* genus (Branco et al., 2017). Here I used the dataset from Branco et al. (2017), which contains samples from 7 locations in North America, genotyped with SNPs. A structure analysis had already been carried out by the authors (see Figure 4 in Branco et al., 2017), and I used their results to define the different genetic clusters to consider. Three levels of genetic structure were defined: (i) Local level, containing genetically homogeneous populations (Coastal California, Mountain California, Wyoming + Colorado, Minnesota + Canada); (ii) Regional level, regrouping local clusters by geographic region (California vs Inland); (iii) Global level, regrouping all samples (All). In order to compare these different levels, 12 individuals were sampled in each group, with 10 replicates, and *N*<sub>e</sub> was estimated based on these samples. The “Coastal California” group was not considered for the local scale because it did not contain enough individuals.

## Pseudoreplication

In order to evaluate the potential bias related to the use of large numbers of SNPs, I used two SNP datasets based on whole genome sequencing from the genus *Suillus*, *Suillus brevipes* (Branco et al., 2017) and *Suillus luteus* (Bazzicalupo et al., 2020). The aim was to compare *N*<sub>e</sub> estimates calculated from a “large” number of SNPs (i.e. 20,000) with *N*<sub>e</sub> estimates calculated from a “small” number of SNPs (i.e. 2,000). In *Suillus brevipes*, I used the same dataset as for the genetic structure analysis, with the same populations and standardised samples of 12 individuals (see section above, (Branco et al., 2017)). For *Suillus luteus*, a species sampled in Belgium by Bazzicalupo et al. (2020), only one population was detected by the authors, so all
samples were treated together (n=34). From the original datasets containing around 662K and 1.6M SNPs respectively for *Suillus brevipes* and *Suillus luteus*, random subsets of 20,000 and 2,000 SNPs were produced using VCFtools (Danecek et al., 2011), with 10 replicates. *N*<sub>e</sub> was then estimated for each replicate.

# Results

Following quality filtering for excess of missing data, homogeneous populations were identified in each dataset extracted from the literature (Table 1). It is at the level of these populations that further analyses were carried out, aimed at detecting the presence of bias in *N*<sub>e</sub> estimation.

## Life-history traits

### Life cycle

The effect of haploidy was explored indirectly by using *Tuber melanosporum* samples, and comparing three types of datasets: “zygotes”, “duplicated” and “paired”. The genetic characteristics of each dataset are shown in Table 2.

<table><caption>**Table 2.** Genetic diversity and *N*<sub>e</sub> estimation for the 3 types of datasets studied in the species *Tuber melanosporum*, including allelic richness, expected heterozygosity (*H*<sub>E</sub>), inbreeding coefficient (*F*<sub>IS</sub>), effective population size (*N*<sub>e</sub>) estimation and lower/upper bounds of Jackknife confidence intervals (CI<sub>INF</sub>, CI<sub>SUP</sub>). Values for Number of alleles, *H*<sub>E</sub>, *F*<sub>IS</sub> and *N*<sub>e</sub> are mean values across 10 replicates. Lower and upper bounds of Jackknife confidence intervals (CI<sub>INF</sub>, CI<sub>SUP</sub>) correspond to minimal or maximal values across 10 replicates.</caption><thead><tr><th>Dataset</th><th>Sample size</th><th>Number of replicates</th><th>Number of alleles</th><th>H<sub>E</sub></th><th>F<sub>IS</sub></th><th>N<sub>e</sub></th><th>CI<sub>INF</sub></th><th>CI<sub>SUP</sub></th></tr></thead><tbody><tr><td>zygotes</td><td>10</td><td>10</td><td>27</td><td>0.255</td><td>0.557</td><td><strong>16.22</strong></td><td>0.1</td><td>Inf</td></tr><tr><td>duplicated</td><td>20</td><td>10</td><td>35.6</td><td>0.324</td><td>1</td><td><strong>51.50</strong></td><td>2.7</td><td>Inf</td></tr><tr><td>paired</td><td>10</td><td>10</td><td>36.9</td><td>0.338</td><td>0.032</td><td><strong>3.17</strong></td><td>0.3</td><td>Inf</td></tr></tbody></table>

The “zygote” dataset displayed a lower number of alleles and lower expected heterozygosity in comparison with the pseudo-diploid datasets (“duplicated” and “paired”). Concerning the inbreeding coefficient, it was relatively high in this “zygote” dataset (*F*<sub>IS</sub> = 0.557), reflecting a deficit in heterozygotes compared to the Hardy-Weinberg equilibrium. In the case of the transformed datasets, the results were very mixed, with *F*<sub>IS</sub> = 1 in the “duplicated” data, against a *F*<sub>IS</sub> almost at equilibrium in the “paired” data.
265

The $N_e$ estimations for these datasets were overall low, with $N_e = 16.22$ in the zygotes and $N_e = 3.17$ in the “paired”, and a slightly higher average for the “duplicated” dataset with $N_e = 51.50$. Confidence intervals (Jackknife CIs), ranged between near-zero and infinity.

## Clonality

270

To explore the effect of clonality on $N_e$ estimations, Figure 2 shows the estimated values of $N_e$ depending on the 5 conditions of clone correction in *Boletus edulis*.

<figure><img src="image_6.png" /><figcaption>**Figure 2.** $N_e$ estimations for a single population of *Boletus edulis* (10 replicates / condition, n=25): (1) no correction; (2) one ramet/genet for the largest clones ($\ge$ 7 ramets); (3) one ramet/genet for medium and large clones ($\ge$ 3 ramets); (4) 1 ramet per MLG; (5) 1 ramet per MLL). Significant differences are indicated with letters (Tukey test).</figcaption></figure>

275

There was a clear increase in $N_e$ estimation, as the level of clonal correction increased. Even if adjacent correction classes were not significantly different, estimates made on datasets containing important proportions of clones appeared to be systematically underestimated. In fact, this is particularly obvious when comparing the treatments “No correction” and “1 ramet/MLL”, with mean values of $N_e = 2.63$ and $N_e = 12.29$, respectively. This downward bias was also observed when less strict correction methods were applied, such as keeping 1 ramet per genet or removing clones that have more than 3 ramets per genet.
## Population structure

As for all datasets, the genetic structure of populations in *Suillus brevipes* was assessed, resulting in the identification of four genetic clusters, of which only three were considered for reasons of sample size : Mountain California, Wyoming/Colorado and Minnesota/Canada (see Table 1). In addition to estimating *N*<sub>e</sub> in these local populations, this operation was also carried out at higher geographic scales. It is the comparison between *N*<sub>e</sub> estimates at these different scales that interests us here (Figure 3).

<figure><img src="image_7.png" /><figcaption>**Figure 3.** Population structure was assessed via a PCA by the authors. On the map, for each group or subgroup, “Ne” corresponds to the mean *N*<sub>e</sub> estimate over 10 replicates of 2000 SNPs, with n = 12, except for Minnesota + Canada (n = 11). Figures modified from Branco et al. (2017).</figcaption></figure>

At the local level, very variable values of *N*<sub>e</sub> were observed depending on the population considered, ranging from 2.82 for the “Wyoming + Colorado” population, to 67.22 in the “Mountain California” population. Then, at the regional scale, when mixing several clusters together, the local *N*<sub>e</sub> information seemed to show a downward bias, as regional estimates were lower than local estimates contained in these groups. The same process occurs at the global scale of the study, with *N*<sub>e</sub> = 12.65.

## Data features

### Pseudo-replication

The effect of the number of SNPs used for the estimation of *N*<sub>e</sub> is shown in Figure 4, for the species *Suillus brevipes* and *Suillus luteus*. In almost all cases, the *N*<sub>e</sub> estimate was lower when using the larger number of SNPs. Only two populations (California and Mountain
California) of the *Suillus brevipes* dataset displayed no significant difference between *N*<sub>e</sub> estimates from 2K versus 20K SNPs datasets.

<figure><img src="image_8.png" /><figcaption>**Figure 4.** *N*<sub>e</sub> estimations for *Suillus brevipes* populations (left) and for a *Suillus luteus* population (right), using subsets of 20,000 SNPs vs 2,000 SNPs with 10 replicates. Sample sizes are n = 12 for *Suillus brevipes*, (except for Minnesota + Canada (n = 11)), n = 34 for *Suillus luteus*. Wilcoxon tests for paired samples : *, p < 0.05 ; **, p < 0.01 ; ***, p < 0.001; n.s, non significant.</figcaption></figure>

It is also interesting to look at the range of confidence intervals according to the number of SNP markers used, for both species (Table 3). No clear trend emerged for the populations of the species *Suillus brevipes*. However, if we look only at the populations that showed a significant difference between the two estimates (Figure 4), the confidence interval was narrower for the estimate carried out on the larger number of SNPs (20K), except for the “Wyoming/Colorado” population. The same phenomenon was observed in the *Suillus luteus* population, where the *N*<sub>e</sub> estimate based on the sample of 20K SNPs is associated with a reduced confidence interval (1.7-4.8 vs. 433.5-Inf for the estimate based on the sample of 2K SNPs), not even containing the average value of *N*<sub>e</sub>.
<table><caption>**Table 3.** *N*<sub>e</sub> estimations and Jackknife confidence intervals for all populations studied in the species *Suillus brevipes* and *Suillus luteus*, with 2 conditions for the number of SNPs used. *N*<sub>e</sub> estimation value is a mean value across 10 replicates. Lower and upper bounds of Jackknife confidence intervals (CI<sub>INF</sub>, CI<sub>SUP</sub>) correspond to minimal or maximal values across 10 replicates.</caption><thead><tr><th>Species</th><th>Population</th><th>Number of SNPs</th><th>N<sub>e</sub></th><th>CI<sub>INF</sub></th><th>CI<sub>SUP</sub></th></tr></thead><tbody><tr><td rowspan="10">Suillus brevipes</td><td rowspan="2">All</td><td>2K</td><td>12.71</td><td>3.2</td><td>102.8</td></tr><tr><td>20K</td><td>4.32</td><td>0.8</td><td>3</td></tr><tr><td rowspan="2">California</td><td>2K</td><td>35.3</td><td>17.6</td><td>188</td></tr><tr><td>20K</td><td>33.4</td><td>3.1</td><td>Inf</td></tr><tr><td rowspan="2">Inland</td><td>2K</td><td>6.83</td><td>2.5</td><td>21.6</td></tr><tr><td>20K</td><td>3.22</td><td>1</td><td>3.7</td></tr><tr><td rowspan="2">Mount. Cal.</td><td>2K</td><td>64.85</td><td>13.8</td><td>Inf</td></tr><tr><td>20K</td><td>55.07</td><td>2.5</td><td>14.3</td></tr><tr><td rowspan="2">Min / Canada</td><td>2K</td><td>32.63</td><td>12.8</td><td>817.7</td></tr><tr><td>20K</td><td>17.88</td><td>1.4</td><td>6.5</td></tr><tr><td rowspan="2">Wyoming / Col</td><td>2K</td><td>2.78</td><td>1</td><td>50.8</td></tr><tr><td>20K</td><td>2.38</td><td>1</td><td>695.5</td></tr><tr><td rowspan="2">Suillus luteus</td><td rowspan="2">Belgium</td><td>2K</td><td>3872.09</td><td>433.5</td><td>Inf</td></tr><tr><td>20K</td><td>721.9</td><td>1.7</td><td>4.8</td></tr></tbody></table>

# Discussion

## Life-history traits

### Life cycle

Based on the conclusions of Bessho & Otto (2022), I first expected lower *N*<sub>e</sub> estimates in haploids than in diploids, as haploids undergo a stronger drift than diploids. Unfortunately, this potential bias cannot be verified, due to the impossibility of directly comparing haploid and diploid datasets. In the dataset extracted from the publication of Taschen et al. (2016), I took advantage of the presence of both haploid and diploid genotypes from the same population of *Tuber melanosporum* to better understand the effects of haploidy on *N*<sub>e</sub> estimation.

Within the three studied datasets, the “zygotic” one displays unexpectedly low values of allelic richness and *H*<sub>E</sub>, and a high *F*<sub>IS</sub>. This situation can be explained by a phenomenon called allele dropout. As mentioned in the Methods, a contamination was suspected in this dataset, with the fungal material not corresponding to true zygotes, but to maternal tissue containing diploid spores, therefore the paternal contributions were expected to have a lower tissue representation inducing a possible dropout of paternal alleles. In other words, because of this imbalance, the paternal alleles were likely overlooked, interpreting as homozygous loci that
were in fact heterozygous, which led to the appearance of a heterozygote deficiency (high $F_{IS}$) and the non-detection of certain alleles. On the contrary, for the two pseudo-diploid datasets, the results for allelic and genotypic diversity were rather expected. In the “duplicated” dataset, $F_{IS} = 1$ illustrates well a completely homozygous population, while the equilibrium $F_{IS}$ value of the “paired” dataset reflects a situation of random mating. Therefore, even if allelic dropout affected the zygotic dataset, we can still rely on the two extreme populations represented by the “duplicated” and the “paired” datasets, and assume that the “true” population lies somewhere in between. In this case, we expect very low values of $N_e$ in the first case (total homozygosity being interpreted by the LD-method as a strong drift signal), whereas the “paired” dataset would represent the highest possible $N_e$ values for this population.

Unfortunately, the results of $N_e$ estimations are very difficult to understand and interpret for many reasons. First, the different values are not really comparable, given that the “duplicated” populations had a larger sample size ($n = 20$), which may be sufficient to explain the higher value of $N_e$ compared to the other two. But beyond that, the main point to consider is the huge range of confidence intervals (Jackknife CIs), often between nearly zero and infinity, which means that almost all values of $N_e$ are possible. According to Do et al. (2014), this kind of values depicts a situation where the sampling error is larger than the signal due to drift. Finally, we must consider that when point $N_e$ estimates are infinite, there is no evidence for variation in the genetic characteristics caused by a finite number of parents. In our case, this result could be due to a too small sample size ($n = 10$), especially for the “zygotes” and “paired” datasets. It would therefore be necessary to repeat this type of analysis on other, larger haploid datasets to see if the two approaches can really give us indications on effective population size. Also, another way of working with haplodiploid species such as EcMF would be to study separately haploid and diploid levels, but also considering the whole population (by grouping haploids and diploids), as suggested by Stoeckel et al. (2021), but such approaches are also associated with technical constraints. One way of overcoming these constraints would be to build simulations and carry out analyses on the simulated data in order to gain a better understanding of the situation.

More generally, even when diploid data are available for haplo-diploid species, we need to ask whether the LD-method is really appropriate for this kind of species or not. This was studied by Wang (2016) who used simulations to compare single-sample methods, and found that LD estimators greatly underestimated $N_e$ when applied to haplodiploid species. Other methods could be used, e.g. the sibship frequency method, with assumptions which are more
appropriate for our study system (haplo-diploid species, non-random mating, high robustness to allele dropout) and having a wide application scope (Wang, 2016).

## Clonality

In this example based on the species *Boletus edulis*, the effect of clones on $N_e$ estimation is clear. When identical genotypes (i.e. clones) are present in a population, genotype frequencies strongly depart from expectations of random mating, and instead reflect a situation of strong inbreeding. This is interpreted as a signal of drift by the LD-method, and this signal is even stronger when clones are numerous. The hypothesis of a downward bias in $N_e$ estimation due to clones (Balloux et al., 2003; Gargiulo et al., 2023) is confirmed here. A particular effect of large clones was also expected, because genets reproducing more would generate a strong variance in reproductive success, which would also lower $N_e$ (Macaya-Sanz et al., 2016). However, this effect has not been highlighted here. In fact, there was no significant difference between $N_e$ estimates for non corrected data and data without large clones (first level of correction). It should also be remembered that the definition of ‘large clones’ was defined here according to the dataset studied, with an arbitrarily chosen threshold (≥ 7 ramets / genet). This does not sound ideal for considering large clones, but it turns out that the best way of doing it, i.e. inferring the rate of clonal reproduction (c) from genotype frequencies is not straightforward (Stoeckel et al., 2021). Thus, no clear recommendation can be made regarding the treatment of large clones, we can only suggest keeping 1 ramet per MLL to avoid a downward bias in $N_e$ estimation.

More broadly, it is important to notice that removing clones from a dataset for analyses remains a temporary solution, allowing us to use the LD-method in clonal species, but at last, it does not give access to the true value of $N_e$. In fact, this value is expected to be higher than the one of the clone-corrected datasets, as $N_e$ increases with the rate of clonality in haplodiploid partially clonal populations, because clonality limits the effect of genetic drift (Stoeckel et al., 2021). Instead of inferring the rate of clonal reproduction, an alternative would be to rely on the Pareto $\beta$ index to assess rates of clonality and proportion of haploids, which would make it possible to study the combined effects of these two life-history traits in EcMF (Stoeckel et al., 2021).

## Population structure

In view of the results for *Suillus brevipes*, it seems appropriate to validate the hypothesis that a downward bias in $N_e$ estimation arises when sampling and analysing different gene pools together. Whenever estimates are made by combining several gene pools, the estimates are
lower than some estimates of the populations contained in this group. Such a bias is to be
expected, given that the LD-method assumes a closed population (R. S. Waples & England,
2011). This downward bias is surely due to the emergence of linkage disequilibrium when we
consider together descendants of genetically differentiated parents (Neel et al., 2013). In other
words, some alleles never occur together in the same individuals, because they come from
parents belonging to different populations, and vice-versa. This linkage disequilibrium is
considered as a signal of genetic drift by the LD-method and leads to an underestimation of N<sub>e</sub>
(Neel et al., 2013). This mixture of individuals from different gene pools (which have possibly
very different allele frequencies), is known as the two-locus Wahlund effect, in reference to the
(one-locus) Wahlund effect that depicts the observed deficit in heterozygotes arising when
different gene pools are mixed (R. S. Waples & England, 2011).

On the other hand, another bias was expected: in case of strong migration (with
migration rate > 0.1) an upward bias can appear because this gene flow will expand the number
of potential parents, making the population appear to have a low level of genetic drift. In this
case, N<sub>e</sub> would be overestimated, as this low drift would induce a low LD (R. S. Waples, 2024;
R. S. Waples & England, 2011). This bias has not been observed for the *Suillus brevipes*
populations studied here. However, as some populations of ectomycorrhizal fungi may show
extensive gene flow, sometimes over large distances (Vincenot & Selosse, 2017), it would be
interesting to find out what rates of migration exist in various species, to see if this bias can be
observed.

These several biases should alert us on the importance of taking into account the genetic
structure of populations, in order to work on the scale of genetically homogeneous populations.
This is especially important in continuously distributed populations, which may involve EcMF
populations. If the geographic scale of sampling is not in accordance with the breeding area (or
“breeding window”), it can dramatically affect estimates of N<sub>e</sub> when using the LD-method
(Neel et al., 2013; Nunney, 2016). Considering individuals from the same gene pool is therefore
the basis of any protocol aimed at estimating effective population size with a linkage
disequilibrium based method.

Data features

Pseudo-replication

As expected and described by Waples (2024), there is a recurrent downward bias on N<sub>e</sub>
estimation when many markers are used. In this case, the assumption of loci independence no
longer holds, and SNPs are very likely to be physically linked. In the LD-method, this linkage
can be interpreted as a signal of drift, leading to a downward bias in $N_e$ estimation (R. S. Waples, 2024). This phenomenon is observed for most populations of *Suillus brevipes* and also for *Suillus luteus* and leads to the conclusion that it is not advisable to use too many markers to estimate $N_e$ with the LD-method.

We also expected an effect on precision and accuracy of $N_e$ estimations, because datasets with a large number of SNPs would provide correlated information due to overlapping pairs of the same loci. This pseudoreplication can affect the precision and accuracy of $N_e$ estimation, with expected confidence intervals much narrower than they would be if all the pairwise comparisons were independent (R. S. Waples et al., 2022). Here, this effect is not so obvious as it can be observed in the population of *Suillus luteus*, and some populations of *Suillus brevipes*, while other populations of the latter species display the opposite pattern, i.e. wider confidence intervals for datasets with 20,000 SNPs (see Table 3).

## Recommendations

Ectomycorrhizal fungi have biological characteristics that often contradict the assumptions of the LD-method for $N_e$ estimation, in particular because of their partially clonal reproduction, their haplo-diploid life cycle or the genetic structure present in their populations. The resulting biases can, however, be mitigated by applying certain corrections to the data. First, it is paramount to consider working at the population level, in other words, at the scale of a genetically homogeneous group of individuals. Then, to avoid the effect of clonality on $N_e$ estimation, all clones present in the genetic dataset should be removed prior to this estimation. These two corrections limit the appearance of additional LD that would suggest a greater drift than actually occurs, and thus limit the downward bias in $N_e$ estimation. On the contrary, how to handle haploid data has not been clarified here, and it appears that the use of the LD-method is not appropriate for haplo-diploid species. This aspect will have to be dealt with in greater depth, as it concerns many species of ectomycorrhizal fungi.

From a more practical point of view, several characteristics of the data must be verified in order to obtain robust estimates of $N_e$. The largest possible sample sizes should be used, as too small sample sizes make it impossible to estimate $N_e$, all the more so in large populations (R. S. Waples, 2024). Missing data are also to be accounted for to avoid supplementary biases, by removing loci with more than 20% of missing data across all individuals (Gargiulo et al., 2024), as well as individuals with more than 20% of missing data across all loci. Following on from previous publications on plants (Gargiulo et al., 2024) or modelling studies (R. S. Waples et al., 2022), the present study has highlighted the risks of using large datasets (i.e. containing
20,000 SNPs or more), and confirms the need to work with a reduced number of markers (around 2,000 SNPs).

Finally, these recommendations apply to *N*<sub>e</sub> estimations in NeEstimator, but other software programmes (e.g. CurrentNe, GONE) might produce different results. It should also be noted that other types of *N*<sub>e</sub> can be estimated (not only contemporary but also historical *N*<sub>e</sub>), which may give other perspectives on the genetic conservation status of ectomycorrhizal species studied here. In fact, if we come back to our headline indicator, “*N*<sub>e</sub> > 500”, and if we rely on the estimates obtained here, almost all populations are below the threshold. Further study of these populations is needed to determine whether these results reflect a real threat to EcMF genetic diversity or an underestimation of *N*<sub>e</sub> due to the method used.

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## Contributions

All data processed came from previously published articles, and were either retrieved via the publications (supplementary material made available by the authors) or by contacting the authors directly. The data analysis workflow was drawn up following discussions with Roberta Gargiulo and Myriam Heuertz, the internship supervisors, drawing in particular on their previous work (Gargiulo et al. 2024). I carried out the majority of data filtering, genetic and statistical analyses, with help from the two supervisors, in particular for the use of certain packages in R and VCF data processing in the computing cluster. I am grateful to the genotoul bioinformatics platform Toulouse Occitanie (Bioinfo Genotoul, https://doi.org/10.15454/1.5572369328961167E12) for providing computing and storage resources. Finally, proofreading and comments by the two internship supervisors helped improve the report.

## Acknowledgement

I would like to thank UMR BioGeCo for hosting me for this Master 2 internship, in the very pleasant site of Pierroton. My thanks also go to Labex CEBA for funding this internship. I would like to extend my warmest thanks to my two supervisors, Myriam Heuertz and Roberta Gargiulo, for their excellent supervision and invaluable help throughout this internship. Working together over the last 6 months has really allowed me to develop my knowledge in population genetics and my skills in genetic data analysis, and I would like to thank them for all the enriching discussions we have had together, which I hope will continue.

I would also like to thank all the people in the E4E team and more generally within the BioGeCo unit who have given me advice and taken an interest in my subject. The quality of this internship would not have been the same without the friendly presence of many people, especially the other M2 students and PhD students: Marie-Gabrielle, Thomas, Tom, Rayan, Greg, Adélaïde, Julien, Thomas, Victor,... Thank you for all the lunchtimes spent together and the moments of relaxation, digestive walks and board games.
# Summary

Genetic diversity is the basis for evolutionary change, and high genetic diversity confers greater adaptive capacity and long-term survival to populations. However, the genetic diversity of many species is under severe threat due to human activities, particularly through the destruction and fragmentation of natural habitats. The 2022 Kunming-Montreal Global Biodiversity Framework includes a genetic indicator based on effective population size, *N*<sub>e</sub>, to assess the genetic conservation status in all species. Although this indicator can be computed from genetic or proxy data, uncertainties remain regarding best practices for *N*<sub>e</sub> estimation in species with complex life history traits (e.g., clonality, long lifespan) such as ectomycorrhizal fungi. The aim of this internship was to understand the factors influencing *N*<sub>e</sub> estimation in ectomycorrhizal fungi, and to obtain reference *N*<sub>e</sub> estimates in these organisms using genetic data extracted from the literature. The effects of haploidy and clonality on *N*<sub>e</sub> estimation were assessed, as well as the influence of population genetic structure when estimating *N*<sub>e</sub>. Biases associated with sampling design were also investigated, particularly in terms of missing data, sample size, number of molecular markers and their non-independence (i.e. pseudo-replication). Through the analysis of four datasets covering the genera *Boletus*, *Suillus* and *Tuber*, several biases were identified which allows to propose several recommendations for an unbiased estimation of *N*<sub>e</sub> in ectomycorrhizal fungi using the software programme NeEstimator. While no clear recommendation can be made for the analyse of haploid data, working at the level of homogeneous populations as well as removing clones from the datasets help limit downward biases. It is also shown that using small subsets of SNPs prevents biases related to pseudoreplication when estimating *N*<sub>e</sub>. The estimates obtained here will need to be developed further in order to use effective population size as an indicator of genetic diversity in ectomycorrhizal fungi.