Bayesian approach reveals confounding effects of population size and seasonality on outcrossing rates in a fragmented subalpine conifer

We showed that P. cembra in the Tatra Mts. is characterized by the mixed mating system. The average outcrossing rate of 72 % is comparable to results for populations from the Eastern Carpathians (Politov and Krutovskii 1994; Politov et al. 2008), while slightly lower than outcrossing rates found for populations in the Alps (81 %; Lewandowski and Burczyk 2000; Salzer and Gugerli 2012). Furthermore, using the newly developed method, we detected confounding effects of population size and seasonal variation on outcrossing rates. In concordance with the expectations, small populations were characterized by lower outcrossing rate. However, we found no association between DBH of a mother and the outcrossing rate. Also, our study demonstrated that biparental inbreeding is a significant component of mating system. Interestingly, biparental inbreeding was found in both small and large populations. Finally, we inferred that pollen dispersal follows a heavy-tailed distribution, enabling long-distance pollen dispersal.

Density-dependent mating system is well documented in the literature on plant mating systems. Most often, low stand density significantly increases the proportion of selfed progeny (Rajora et al. 2002; Robledo-Arnuncio et al. 2004; Mimura and Aitken 2007). Comparing core and peripheral populations in the Swiss Alps, Salzer and Gugerli (2012) found sharp differences in selfing rates (9 % vs. 35 %), indicating that pollen availability must be negatively associated with population size in P. cembra. Other reports for P. cembra seem to be in agreement with this statement (Lewandowski and Burczyk 2000; Politov et al. 2008). In our case, significant differences in outcrossing rates found between small and large populations in the Tatras are in line with these conclusions. According to the reproductive assurance hypothesis (Lloyd 1979), when outcross pollen is unavailable, selfing allows to continue seed production. In our case, small subpopulations of P. cembra in the Tatras can experience outcross pollen limitation because sporadic mature trees are scattered in the forest so that inter-individual distances (even between nearest neighbors) are longer, and due to the presence of the other species, harder to traverse (Milleron et al. 2012) as compared with large, dense subpopulations (especially Morskie Oko).

The average outcrossing rate found in this study translates into the expected inbreeding level F = (1 – 0.72)/(1 + 0.72) = 0.16. In the Ukrainian Carpathians, Politov et al. (2008) found a good correspondence between outcrossing rates and inbreeding levels estimated at embryonic stage. However, low outcrossing rates do not necessarily lead to high inbreeding at the adult stage. In Abies balsamea, the population at the highest elevation revealed the lowest outcrossing rate measured at the seed stage (Neal and Adams 1985). However, the adult population showed an excess of heterozygotes, suggesting that selection favors heterozygotes in this marginal environment. The results for P. cembra fully support this prediction (Salzer and Gugerli 2012) in respect to populations in the Swiss Alps. In the case of the Tatras, a related study revealed that the population of mature individuals is only slightly inbred, with the overall average F = 0.051 (Dzialuk et al. 2014). Using the equilibrium equation (Ritland 1990), we can estimate the relative fitness of selfed individuals to be as low as w = 2tF/((1 – t)(1 – F)) = 0.283. Hence, it seems reasonable to expect that inbred individuals will be outcompeted by non-inbred ones during the seedling development, as often observed in pine species (Savolainen and Hedrick 1995; Koelewijn et al. 1999; Bower and Aitken 2007). On the other hand, the evolutionary theory predicts that recurrent selfing accompanied by intensive selection against inbred individuals can lead to genetic purging (Crnokrak and Barrett 2002). In such conditions, a number of deleterious alleles is significantly reduced, opening possibility for increased self-fertilization and inbreeding without negative consequences for fitness. An experimental study on Scots pine provided good support for this theory (Kärkkäinen et al. 1996). In our case, small and isolated populations of P. cembra seem to be particularly prone to genetic purging, assuming they will continue to experience outcross pollen limitation.

It should be stressed that the reported selfing rates can be underestimated, because our estimates did not account for seed abortion, which is highly correlated with self-fertilization (Koski 1971; Savolainen et al. 1992; Kärkkäinen et al. 1999). The total probability of survival of a seed can be expressed as P(B) = sw_s + (1 − s)w_t, where s is the actual self-fertilization rate, w_s and w_t is the proportion of progeny survived after selfing and outcrossing, respectively. After Ritland (1990), let w = w_s/w_t. Then, the (posterior) probability for a seed to be after self-fertilization, given that it survived, is equal \( P\left(A\Big|B\right)=\frac{sw}{1-s\left(1-w\right)} \). In fact, P(A|B) is equivalent to the effective self-fertilization rate \( \widehat{s} \) typically estimated based on genotypes of viable progeny. Consequently, the true selfing rate in small and large populations in the Tatras adjusted for seed abortion, i.e., estimated as \( s=\frac{\widehat{s}}{\widehat{s}+w\left(1-\widehat{s}\right)} \), can be as high as 0.788 and 0.313, respectively. Interestingly, these estimates are in a good agreement with equivalent estimates for peripheral and core populations in the Alps (Salzer and Gugerli 2012; see the Appendix). According to the mass action model (Holsinger 1991), where the frequency of self-fertilization is the proportion of self pollen in the total pollen received by a given tree, in small populations only 21 % of the pollen pool of a given tree is not produced by that tree. For comparison, in large populations the outcross pollen is expected to prevail (69 % of the total). It thus seems that pollen limitation is among the main threats in small subpopulations of P. cembra.

Knowledge about pollen dispersal in P. cembra is extremely scarce. Using a parentage assignment approach, Salzer (2011) revealed that within a marginal stand of P. cembra in the Alps, effective pollen dispersal distance was, depending on the conditions, <200 m or about 315 m on average (maximum distance of 659 m). Our own analysis revealed that the total pollen dispersal follows a heavy-tailed dispersal kernel, confirming great potential of P. cembra to long-distance pollen dispersal. The mean dispersal of about 1 km inferred in this study was threefold higher than previously found. However, estimates reported by Salzer (2011) did not account for pollen immigration, which reached about 40 % from at least 1 km. Thus, the total effective pollen dispersal in the Alps could be higher. Using the cumulative probability distribution (CDF) for the exponential-power kernel (Fig. 2) estimated in this study, we can infer that in the Tatras about 69 % pollen travels up to 1 km, while 31 % would be immigrating from at least 1 km. Thus, our results are in line with the findings based on the direct approach by Salzer (2011). They also correspond well with general knowledge that species with saccate pollen are characterized by great pollen dispersal potential (Schwendemann et al. 2007). In the case of P. cembra, the potential can be further increased by suitable environmental conditions, such as high wind speed. Nonetheless, at a regional scale, the specific configuration of P. cembra populations would eventually determine the potential for long-distance dispersal. More detailed, parentage-based study would be helpful to compare small and large populations in this respect.

An important component of plant mating system is mating between relatives, leading to biparental inbreeding (e.g., Degen et al. 2004; Hirao 2010; Fenster et al. 2003). Interestingly, except for our study, no strong signatures of biparental inbreeding in P. cembra have been shown (Lewandowski and Burczyk 2000; Politov et al. 2008). The between-locus correlation of selfing (r_s) can be interpreted as roughly equal to the proportion of inbreeding due to selfing, while (1 − r_s) as a proportion of inbreeding due to mating between relatives (Ritland 2002). Consequently, small subpopulations in the Tatras showed a lower proportion of mating between relatives as compared with large ones. However, a lower proportion of consanguineous mating is somewhat counterintuitive, because typically one can expect that biparental inbreeding tends to increase as a number of mates decreases (Morgante et al. 1991; Takayama and Isoagi 2005). One possible scenario can be proposed taking into account the result that pollen dispersal was large. In this case, because short distances are under-represented in small subpopulations (due to lower density), it seems very likely that most outcross pollen travels long distances, favoring gene flow between unrelated individuals. Similar observations were previously made for isolated trees of Picea glauca (O’Connel et al. 2007). On the contrary, in large and denser subpopulations, where short and intermediate distances are well represented, mating between close neighbors can occur relatively frequently (see Fig. 2). However, in such conditions, biparental inbreeding can evolve only if relatives tend to be spatially closer than at random (Fenster et al. 2003). In the case of P. cembra, seeds are typically dispersed by birds (N. caryocatactes; Tomback et al. 1993) and squirrels (Sciurus vulgaris). Given that seeds of P. cembra have no structures facilitating dispersal, such a mechanism allows efficient colonization of new habitats. Birds typically bury several seeds together (Tomback et al. 1993), enabling the development of a family structure. In fact, strong spatial genetic structure was found in populations of P. cembra in the Swiss Alps (Salzer 2011), providing some support for this prediction. However, we cannot be sure that strong spatial genetic structure is also present in the study populations, where clumps of individuals due to seed caching seem to be relatively rare.

Temporal variation in outcrossing rates is often found in natural conifer populations (e.g., Shea 1987; Cheliak et al. 1985; El-Kassaby et al. 1993). It is due to various reasons, with environmental variation being most often indicated. However, seasonality in outcrossing rates inferred in our study might be also caused by the masting behaviour of the species (Ulber et al. 2004). In fact, the significantly lower outcrossing rate in 2009 coincided with the large number of seeds collected in that year, relative to the other years (see M&M). Although we are rather skeptical about a definitely causal linkage between these two characteristics, this might be reasonable to expect that higher fecundity leads to lower outcrossing rate (Shea 1987). Nonetheless, similarly as in O’Connel et al. (2006), we failed to show that a tree size, used as a proxy for fecundity, is associated with outcrossing rates. Therefore, further studies are needed to confirm the role of both male fecundity and masting behavior in shaping mating system parameters of P. cembra.

Usually, P. cembra in the Tatras occupies hardly accessible locations. In consequence, our study was based on a limited number of mother trees and localities. Despite that inferences on mating system parameters were in concordance with predictions, we need to stress that a small number of sampled mother trees may preclude very strong conclusions, especially regarding conservation strategies for the species. A special caution should be paid in the case of pollen dispersal inferences. In order to achieve sufficient statistical power, the parameters of pollen dispersal kernel were estimated based on the entire sample, without any respect of temporal or spatial variation of the dispersal, which might be present in our case. Thus, the estimated dispersal kernel represents rather the average across different population types and different seasons. On the other hand, the indirect approach (KINDIST) used in this study requires correlation of paternity to be a continuous and significant function of a distance between mother trees (Robledo-Arnuncio et al. 2006, 2007). Moreover, the latter is assumed to result entirely from pollen dispersal and not population genetic structure (Austerlitz and Smouse 2001). The absence of correlation between genetic and geographic distance found in the Tatras (Dzialuk et al. 2014) suggests that the observed pollen structure was indeed a result of limited pollen dispersal. Nonetheless, due to discontinuous sampling (see Fig. 2), the estimation procedure might suffer from the bias, which cannot be assessed based on the existing data.

As a threatened species, P. cembra in the Tatras is under strict protection. However, in situ conservation has been questioned as an efficient and satisfactory means to preserve gene pools. Our results show that gene flow through pollen should be generally sufficient to counterbalance genetic drift. In fact, studying genetic structure of P. cembra in the Tatras, we detected very weak genetic differentiation (Dzialuk et al. 2014), suggesting that gene exchange between subpopulations is probably high. On the other hand, based on mating system parameters, we argued that small and isolated subpopulations of P. cembra both in the Alps and Carpathians can experience severe local pollen limitation, which can dramatically lower seed production (Salzer and Gugerli 2012) and fitness of individuals due to inbreeding. In particular, seed yield can be reduced (Salzer and Gugerli 2012), lowering (variance) effective population size. However, because tree species seem to be generally “resistant” to the impact of fragmentation on the genetic diversity (O’Connel et al. 2006; Kramer et al. 2008), the question of whether high adult genetic homogeneity in the Tatras (Dzialuk et al. 2014) will be preserved in future generations remains open. To answer this, we need to know if potentially high pollen-mediated gene flow can preclude erosion of the gene pool in small populations. Therefore, the next-generation genetic structure remains a pending issue for future studies.