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.

Controlled self and outcross pollinations

We performed hand pollinations in 13 populations of A. anserina 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 A. anserina 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.

Calculation of mate availability, number of S-alleles, and SCI

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 et al., 2002; Busch et al., 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 ]= at to determine the number of alleles in the population where at 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. at ranged from 1-11 and m ranged 14-19 among populations. However, N was unestimable for at < 4 (six of 13 populations) and when estimable, N and at were 1:1. Therefore, we only report at.

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 et al., 2010; Cisternas‐Fuentes et al., 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.

Models of self-incompatibility          

To compare the empirical relationships among N_E, 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 (N) with tetraploid genotypes at a single locus determining gametophytic incompatibility. To approximate populations near equilibrium (Wright 1939), fully heterozygous genotypes (S₁S₂S₃S₄) were initially generated by randomly sampling k equally frequent alleles without replacement. To generate progeny each generation, N 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 et al., 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 A. anserina is an ancient allopolyploid (Christenhusz & Leitch, 2023), chromosomal segregation is typically a mosaic of tetrasomic inheritance, disomic inheritance, and varying frequencies of each (Stift et al., 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 et al., 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 et al., 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 et al., 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 (N) 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 N=250, since mate availability saturates at high values in larger populations (Vekemans et al., 1998). At each value of N and k, 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.

Pollen-pistil dynamics

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).

Characterizing leaky self-incompatibility

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.