DOI: 10.5061/dryad.pnvx0k6zm
title: Drift in small populations predicts mate availability and the breakdown of self-incompatibility in a clonal polyploid

description: Mate limitation in small populations can reduce reproductive fitness,
 hinder population growth, and increase extinction risk. Mate limitation is
 exacerbated in self-incompatible (SI) taxa, where shared S-alleles further
 restrict mating. Theory suggests genetic drift as a predictor of
 mate-limitation and the breakdown of SI systems. We tested this prediction
 by evaluating mate availability and S-allele number in populations of a
 tetraploid herb with gametophytic SI (GSI) spanning a range of effective
 population size We performed controlled crosses in 13 populations of
 Argentina anserina to quantify mate availability and S-allele diversity,
 which were compared to simulations of tetraploid populations with GSI. We
 further evaluated mechanisms at the pollen-pistil interface contributing
 to outcross failure and leakiness in self-recognition. Mate availability
 declined in small populations, and closely fit tetraploid GSI
 population-genetic models where maternal plants receive pollen with
 diverse S-alleles generated through tetrasomic inheritance. The failure to
 arrest self-pollen in the style was common in some populations.
 Specifically, leaky SI was more common in small populations with low mate
 availability, where it explained higher seed production in natural
 populations. The restriction of leaky self-recognition to the smallest
 populations is consistent with mate limitation as a pressure driving the
 breakdown of self-incompatibility.
description: <strong><em>Controlled self and outcross
 pollinations</em></strong> We performed
 hand pollinations in 13 populations of <em>A. anserina</em> to
 estimate population level mate availability and self-compatibility index
 (SCI). Crosses were conducted under controlled conditions in the
 greenhouses at Clemson University (Clemson, South Carolina,
 USA). Self-pollinations were carried on an average of
 11.9 maternal lines per population while outcross pollinations were
 carried on an average of 15.3 maternal lines per population. One flower
 per maternal line was self-pollinated to evaluate leakiness in
 self-recognition and the production of seed following self-fertilization.
 Outcross pollinations were performed on 3 to 6 flowers per individual
 using a different paternal donor from the same population chosen at random
 (one donor per flower) to assess mate availability and estimate
 population-level S-allele number in the sample. In total, 901 outcross
 crosses were performed with an average of 4.54 flowers outcrossed per
 maternal line across populations. Flowers of
 <em>A. anserina</em> are open for two days. On the first day
 of anthesis, flowers were emasculated prior to anther dehiscence using a
 jeweler’s mask and forceps. Anthers were stored in 0.7 mL Eppendorf tubes
 left open for 24 hrs. to allow the pollen to mature and dry. The second
 day of anthesis, pollination was carried out using a horse-hair
 paintbrush, and flowers were then labeled using a jewelry tag with their
 respective treatment and pollen donor information. To avoid cross
 contamination, paint brushes were washed with 99% ethanol and allowed to
 dry prior to subsequent pollination with the same brush. 48 hrs. after
 hand pollination, styles were collected using forceps and placed in tubes
 with 70% ethanol. Fruits were collected 3 to 4 weeks after pollination,
 dried on silica gel and maintained at 4°C until cleaning. Seeds were then
 counted and stored at room temperature.
 <strong><em>Calculation of mate availability, number
 of S-alleles, and SCI</em></strong> Mate
 availability was calculated for each maternal line as the number of
 outcross pollinations that successfully set seeds divided by the total
 number of outcross pollinations performed for that maternal individual. An
 average mate availability across maternal lines was used as an estimate of
 population-level mate availability. Since average seed number varied
 across populations, with some populations producing very few seeds per
 fruit (i.e., RL) and others producing fruits with high seed number (i.e.,
 AP), we calculated a population specific cut-off for what we considered a
 “successful” cross (Similar approach used by Pickup & Young,
 2008). We first calculated an average seed number of fruits produced
 through outcrossing and set the cut-off of a ‘successful’ cross as one
 that produced a fruit with 20% of the average seed number value. For
 example, in population CB we performed 59 outcross pollinations (average
 crosses per maternal line= 4.2). Of those, 26 produced 0 seeds and 33
 produced fruits varying from 1 to 31 seeds. The average seed number of the
 fruits producing seeds was 14.81. Any fruit with above 2.96 seeds (14.81 x
 0.2) was considered a successful fruit within that population.
 We additionally estimated the number of S-alleles in the samples
 for each population using diallel mating tables (e.g., Brennan
 <em>et al.</em>, 2002; Busch <em>et al.</em>,
 2010). We selected a maternal line and identified all individuals with
 which it was incompatible. If incompatible with one another, two lines
 were included in a mating group based on the assumption that they shared
 at least one S-allele. Within the mating group, another maternal line was
 selected, and the process was repeated until all members of a mating group
 were identified. We used Paxman’s Estimator (Paxman, 1963) modified for a
 tetraploid N[1-(1-4/N)^m ]= <em>at</em> to determine the
 number of alleles in the population where<em> at</em> is the
 number of S-alleles in the sample, m is the number of individuals in the
 diallel and N is the estimated number of S-alleles in the population.
 <em>at</em> ranged from 1-11 and m ranged 14-19 among
 populations. However, N was unestimable for <em>at
 </em>&lt; 4 (six of 13 populations) and when estimable, N and
 <em>at</em> were 1:1. Therefore, we only report
 <em>at</em>. Using only maternal lines that
 had both self and outcross treatments (Average of 10 maternal lines per
 population, SE= 0.82), we calculated an index of self-compatibility (SCI;
 Zapata & Arroyo, 1978; Ruhsam <em>et al.</em>, 2010;
 Cisternas‐Fuentes <em>et al.</em>, 2022), as the ratio of
 seeds produced by self-pollination to those produced from outcross
 pollination to each maternal line. These values were averaged across
 maternal lines to obtain a population-level index of self-compatibility.
 An SCI value of 0 can be interpreted as fully self-incompatible while an
 SCI value of 1 is fully self-compatible. Our goal was to generate
 population-level SCI values. Because only one flower was self-fertilized
 per maternal line, we caution against interpreting individual-level SCI
 values. <strong><em>Models of
 self-incompatibility</em></strong>          
 To compare the empirical relationships among
 N<sub>E</sub>, S-allele number, and mate availability with
 theoretical predictions, we conducted forward population genetic
 simulations of tetraploid GSI systems. In a simulation, a single
 population with discrete, non-overlapping generations contained a constant
 number of individuals (<em>N</em>) with tetraploid genotypes
 at a single locus determining gametophytic incompatibility. To approximate
 populations near equilibrium (Wright 1939), fully heterozygous genotypes
 (S<sub>1</sub>S<sub>2</sub>S<sub>3</sub>S<sub>4</sub>) were initially generated by randomly sampling <em>k</em> equally frequent alleles without replacement. To generate progeny each generation, <em>N</em> style parents were randomly sampled. Pollen parents were sampled randomly from all other plants in the population and compatibility between the style parent and the pollen genotype was determined. Diploid pollen genotypes were generated assuming tetrasomic inheritance without double reduction (Bever & Felber, 1992). Pollen genotypes sharing at least one S-allele with the style parent were incompatible, causing additional random sampling of pollen genotypes until a compatible pollen genotype fertilized an ovule. All progenies were produced by this scheme of sexual reproduction mediated by self-incompatibility. Inclusion of clonal reproduction was not considered given a lack of empirical data on its prevalence, yet this would depress effective population size considerably. Simulations were run for 100 generations, at which point S-allele number stabilized given strong natural selection in these systems (Busch & Schoen, 2008). Simulations were conducted in R. Tetraploid inheritance varies on a continuum between two simple extremes: tetrasomic and disomic inheritance (Stift <em>et al.</em>, 2008). Our model is based on tetrasomic inheritance, where all chromosomes pair randomly, and all possible allele combinations are generated at equal frequency in gametes. If this assumption were violated, the simplest alternative would assume disomic inheritance, where two sets of homologous chromosomes independently pair during meiosis – which involves two separate S-loci to be considered. We lack an empirical grounding to justify the more complex model of chromosomal inheritance. Even though there is some evidence that <em>A. anserina</em> is an ancient allopolyploid (Christenhusz & Leitch, 2023), chromosomal segregation is typically a mosaic of tetrasomic inheritance, disomic inheritance, and varying frequencies of each (Stift <em>et al.</em>, 2008). It is not yet known whether mate availability would differ in otherwise identical populations with tetrasomic or disomic inheritance, though this is a question that deserves careful attention. Finally, the model assumes there is no double reduction – which happens when there is a recombination event causing alleles on sister chromatids to migrate into the same gamete. This process generates homozygotes, which would yield a much wider array of possible genotypes within populations, which would likely increase the variance in mate limitation. Nevertheless, we have made our modeling decisions because the majority of population-genetic models of tetraploid populations also assume tetrasomic inheritance and no double reduction (e.g. Stift <em>et al.</em>, 2008; Layman & Busch, 2018, and references therein). We evaluated two distinct models that differed in the number of pollen genotypes received by styles during mating. For a given pair of mates, styles received either a single pollen genotype (Model 1) or all six of the pollen genotypes produced during tetrasomic inheritance by the pollen parent (Model 2). Model 1 was constructed for comparison with historical models of self-incompatibility in diploid populations (Wright, 1939; Vekemans <em>et al.</em>, 1998). Mate-availabilities in these simulations of tetraploid populations were always below those in otherwise identical diploid populations, as expected given the two-fold increase in the number of S-alleles expressed by pollen grains (Table 3 in Vekemans <em>et al.</em>, 1998). Model 2 was constructed to better approximate realistic transfers of multiple pollen grains by pollinators in natural populations. Since Model 2 provides more chances for styles to encounter a potentially compatible pollen genotype, mate-availability was expected to correspondingly increase. The empirical relationship between mate-availability and S-allele number was compared with simulations to identify the best-fitting model. Population size (<em>N</em>) in simulations ranged from 25 to 250, and the number of S-alleles in simulations ranged from the minimum allowed to maintain sexual reproduction in a tetraploid GSI system (k=5) to 40 (Lawrence, 2000). Simulations were conducted in populations smaller than <em>N</em>=250, since mate availability saturates at high values in larger populations (Vekemans <em>et al.</em>, 1998). At each value of <em>N</em> and <em>k</em>, 100 replicate populations were simulated, where the number of S-alleles and the average proportion of crosses that produced seed (i.e. mate availability) were saved. <strong><em>Pollen-pistil dynamics</em></strong> We excised styles from the controlled self and outcrossed flowers without damaging ovules 24hrs after hand-pollinations. Preliminary data collection showed that style collection 24 and 48hrs after pollination were similar for pollen tube growth. Styles were stored in 70% EtOH until they were treated with decolorized aniline blue (DAB) following methods described in Cisternas-Fuentes et al. (2023). Five stained styles per flower were observed under a Zeiss AXIOlab 5 microscope using UV fluorescence to visualize pollen grains adhered to the stigma and pollen tubes in styles. We counted the number of pollen grains deposited in the stigma, the number of pollen grains that germinated, pollen tubes reaching 1/3 the length of the style, pollen tubes reaching 2/3 of the styles, and pollen tubes extending the entire length of the style for each of the 5 styles per flower. We scored 130 flowers obtained from the self-crosses across 13 populations (mean of 10/population). We scored 289 flowers from outcross pollinations across 8 of the populations spanning the range in effective population size (mean of 36.13/population). <strong><em>Characterizing leaky self-incompatibility</em></strong> We generated indices of leaky SI at the population level by calculating the average proportion of germinated pollen grains that grew pollen tubes surpassing the location of self-recognition from self-pollinations. Cisternas-Fuentes et al. (2023) showed that self-pollen tubes were arrested primarily in the upper ⅓ of the style and then further suppressed between ½ and ⅔ the length of the style. Therefore, we calculated the ratio of pollen tubes counted at ⅓ the length of the style divided by the number of grains that germinated on the style, and then the number of tubes reaching 2/3 the length of the style divided by the number of germinated grains. Higher values for both indices were interpreted as higher leakiness in self-recognition.
description: # Drift in small populations predicts mate availability and the breakdown
 of self-incompatibility in a clonal polyploid
 [https://doi.org/10.5061/dryad.pnvx0k6zm](https://doi.org/10.5061/dryad.pnvx0k6zm) ## Description of the data and file structure **Drift in small populations predicts mate availability and the breakdown of self-incompatibility in a clonal polyploid** Cisternas-Fuentes, Anita; Forehand, Cameron; Morris, Kate; Busch, Jeremiah W.; Koski, Matthew H. We performed controlled crosses in 13 populations of *Argentina anserina* to quantify mate availability and S-allele diversity, which were compared to simulations of tetraploid populations with GSI. We further evaluated mechanisms at the pollen-pistil interface contributing to outcross failure and leakiness in self-recognition. ### Files and variables #### File: leakiness\_data\_input.xlsx **Description:** Pollen-pistil data and seed number for the self-pollinations performed ##### Variables * Description of the variables in the file; NA values are not available values or not available information. #### File: mate\_availability\_data.xlsx **Description:** Proportion of mate availability by maternal lines ##### Variables * Maternal lines, proportion of successful crosses and total number of outcross pollination performed by maternal lines #### File: pop\_level\_average\_data.xlsx **Description:** Population averages for mate availability, s-allele diversity, mate availability and leakiness of self-incompatibility. ##### Variables * Description of the variables in the file #### File: SCI\_data.xlsx **Description:** Self-compatibility index by maternal lines ##### Variables * Maternal line, population, SCI #### File: model1.R **Description:** Mate availability of simulated GSI tetraploid populations across a range of population sizes and S-allele numbers when a single diploid S-allele pollen genotype is received by a maternal plant in a given mating event #### File: model2.R **Description:**  Mate availability of simulated GSI tetraploid populations across a range of population sizes and S-allele numbers when all potential S-allele pollen genotypes is received by a maternal plant in a given mating event. #### File: success\_vs\_unsuccess\_fruits.xlsx **Description:** Pollen-pistil data comparison for successful and unsuccessful pollinations ##### Variables * Description of the variables in the file; NA values are not available values or not available information. #### File: seed\_data\_outcrossing.xlsx **Description:** Seed number for all outcross pollinations performed ##### Variables * Cross identification, population, maternal line, paternal line, date cross pollination was performed, identification for the slide prepare for the pollen-pistil data and seed number. #### File: nonlinMods\_success\_leakiness.R **Description:** Analysis of sucess and unsucess fruits, leakiness and population-level averages.