- Research article
- Open Access
Heritable determinants of male fertilization success in the nematode Caenorhabditis elegans
© Murray et al; licensee BioMed Central Ltd. 2011
- Received: 7 October 2010
- Accepted: 14 April 2011
- Published: 14 April 2011
Sperm competition is a driving force in the evolution of male sperm characteristics in many species. In the nematode Caenorhabditis elegans, larger male sperm evolve under experimentally increased sperm competition and larger male sperm outcompete smaller hermaphrodite sperm for fertilization within the hermaphrodite reproductive tract. To further elucidate the relative importance of sperm-related traits that contribute to differential reproductive success among males, we quantified within- and among-strain variation in sperm traits (size, rate of production, number transferred, competitive ability) for seven male genetic backgrounds known previously to differ with respect to some sperm traits. We also quantified male mating ability in assays for rates of courtship and successful copulation, and then assessed the roles of these pre- and post-mating traits in first- and second-male fertilization success.
We document significant variation in courtship ability, mating ability, sperm size and sperm production rate. Sperm size and production rate were strong indicators of early fertilization success for males that mated second, but male genetic backgrounds conferring faster sperm production make smaller sperm, despite virgin males of all genetic backgrounds transferring indistinguishable numbers of sperm to mating partners.
We have demonstrated that sperm size and the rate of sperm production represent dominant factors in determining male fertilization success and that C. elegans harbors substantial heritable variation for traits contributing to male reproductive success. C. elegans provides a powerful, tractable system for studying sexual selection and for dissecting the genetic basis and evolution of reproduction-related traits.
- Sperm Competition
- Sperm Production
- Male Reproductive Success
- Mating Trial
- Male Sperm
Anisogamy, the occurrence of different sized gametes in different mating types or sexes, commonly manifests as small male gametes and large female gametes; the small male gametes (sperm) tend to be more numerous than female gametes (oocytes) . When two or more males compete for the fertilization of oocytes in a multiply-mated female, then it is often true that the male that produces the most sperm will procure the greatest fertilization success . This type of sperm competition (a 'fair raffle') can lead to selection for more, and further miniaturized, male gametes as limited resources are allocated to create more individual gametes [2, 3]. However, if multiple sperm actively and directly compete for fertilization rather than being used passively in such a 'lottery,' then the evolution of larger sperm size commonly evolves [4–7] - potentially at the expense of ejaculates containing fewer sperm. Thus, sperm number per ejaculate and sperm size form two important components affecting post-mating fertilization success, with potentially differing fitness optima and developmental constraints that depend on the details of the regime of sperm competition.
Polyandrous mating behavior inducing sperm competition can cause antagonistic co-evolution between the sexes [8–10] and manifest as a suite of traits that includes copulatory plugs [11–13], oocyte stimulation , mate guarding [15, 16] and sperm expulsion by females [13, 17]. Some or all of these traits are common across a wide range of taxa, but their relative importance with respect to sperm competition can be difficult to decipher. Here, we investigate male-male sperm competitive ability in the nematode model organism Caenorhabditis elegans to better understand the relative importance of mating and sperm traits for heritable variation in male reproductive success.
Caenorhabditis elegans is an androdioecious species that consists of males and self-fertilizing hermaphrodites, but evolved from gonochoristic (male/female) ancestors in the relatively recent past [18–20]. Males are rare in nature, but can successfully mate with hermaphrodites when given the chance [reviewed in [21, 22]]. Males also make larger sperm than hermaphrodites, and male sperm are used preferentially over self-sperm for fertilization in a mated hermaphrodite [23, 24]. While perhaps not common for C. elegans in nature, male-male sperm competition likely is an important aspect of mating system evolution in closely related gonochoristic species that retain the ancestral mode of reproduction. With the extensive genetic and developmental tools available for C. elegans, this species provides an exceptionally tractable model system to address general questions about the evolution of sperm traits, as well as more specific issues pertinent to Caenorhabditis mating systems. For example, LaMunyon and Ward  demonstrated how laboratory-induced sexual selection caused the evolution of larger male sperm, and a variety of alternative regimens of experimental evolution have explored the evolution of hermaphrodite sperm production, sex-ratio and outcrossing rate [reviewed in [21, 26, 27]].
Several traits have identified themselves as being individually important to male fertilization success in C. elegans. As in many animals, mating rate is important , such that males capable of mating often and repeatedly have higher paternity [29, 30]. Similarly, we expect that the number of sperm that a male passes to a hermaphrodite during a single mating event likely will be important for sperm competition success, in addition to the number of matings - as in domestic fowl (Gallus gallus domesticus)  and golden egg bugs (Phyllomorpha laciniata) . However, we know of no direct tests for such an effect in Caenorhabditis. In other systems, the duration of copulation directly affects the number of sperm that a male passes to a female in a given mating bout  and the more sperm he passes, the greater his success in sperm competition . The role of hermaphrodites in attracting (or avoiding) potential mates also likely affects male mating rate and could influence male postcopulatory competitive ability ; as an extreme case, male C. elegans mate more readily with individuals that are motility defective . It is now clear that C. elegans hermaphrodites have lost the ability to produce potent attractive pheromones to attract mates , despite males tending to spend more time on media that has been occupied previously by a hermaphrodite [37–39]. C. elegans males, however, have not lost the ability to detect and seek out females from related species like C. remanei that do release attractive pheromones [36, 40], although C. elegans male mating ability is poorer than that of C. remanei males . Despite the importance of seminal fluid  and male age [42, 43] in other systems, they do not seem to influence sperm competitive ability in C. elegans . Perhaps most-studied in terms of the influence on male sperm competition in C. elegans is the effect of sperm size on paternity: male sperm are larger than hermaphrodite sperm and male sperm are used preferentially for fertilization [23, 44, 45]. Males of two genetically distinct strains of C. elegans make differently-sized sperm, and the larger sperm have greater sperm precedence, although they take longer to make . And yet, we don't know whether there might be a trade-off between the ability of males to transfer sperm that individually are highly competitive (i.e. large sperm) with their ability to transfer many sperm. Moreover, most studies on these issues have focused on strains with the standard N2 genetic background, which are notoriously poor at mating and have small sperm .
In order to capture a deeper understanding of the forces contributing to the evolution of reproductive systems, here we test the relative importance of a range of mating and sperm traits on siring success with a diverse set of distinct genetic backgrounds. Male genotypes were chosen based on known differences in genetic composition, whether or not they produced a copulatory plug, and when possible, male maintenance and mating ability. We hypothesize that genotypes with greatest male reproductive success will map to phenotypes that include large sperm that are produced quickly to be transferred in sperm-dense ejaculates, coupled with high courtship and mating rates and greater sperm precedence.
Culturing and Maintenance
Strains used, their geographic location of origin or mutation and relevant notes*
no plug, 'large-sperm' category
plug, 'large-sperm' category
plug, 'large-sperm' category
plug, 'small-sperm' category
no plug, 'small-sperm' category
no plug, 'small-sperm' category
fog-2(q71) mutation in an N2 genetic background
Populations 50% male + 50% "female"
contains transgene mls12 [myo-2::GFP, pes-10::GFP, F22B7.9::GFP] in an N2 genetic background
N2 background with pharyngeal GFP marker, no plug, 'small-sperm' category
Sperm size measurements
Rate of sperm production
We measured the rate of sperm production in virgin males, modeled after LaMunyon and Ward . L4 male worms were monitored in 15-minute intervals for the molt to adulthood, and if a worm was newly molted we either fixed and stained it with DAPI nucleotide stain immediately or isolated it for 2 hours prior to fixation and staining. We then counted sperm numbers for 16-21 males per strain for each time-point by identifying DAPI-stained spermatid nuclei . DAPI-labeled worms were mounted on a glass slide so that sperm nuclei could be viewed under epifluorescence and counted from digital photographs taken in different focal planes through the specimen.
Number of sperm transferred
We quantified the distribution of transferred sperm counts from male ejaculates to test for association with other sperm traits. First, we isolated 10 fog-2 females (strain JK574) as L4s one day in advance of the assay to ensure that they were virgins. The fog-2 (q71) allele that is homozygous in the JK574 strain affects the sperm-oocyte switch of the hermaphrodite ovotestis, such that hermaphrodites are capable of making only oocytes ; hence, we refer to such individuals as "females," which must mate with males to reproduce. Similarly, we also separated males onto plates as L4s from each of the seven experimental strains (AB1, CB4855, CB4856, DR1350, JU440, MY2) and the reference strain (PD4790). The next day, we began the assay by adding individual males to each of the plates containing the 10 females. This female-biased sex ratio ensures that males are unlikely to mate with the same female more than once. We inspected each plate every hour thereafter, and as soon as fertilized eggs were observed, we separated out each female onto an individual plate and discarded the male. If there were no eggs laid by the end of twelve hours, we discarded the plate. The day following the matings, we scored females as either mated or not mated based on the presence or absence of eggs on the plate. We transferred mated females onto new plates daily until they ceased egg production. The resulting progeny were counted when they reached the L4 or young adult stage. For a given mated female, the total progeny count provides our measure of the number of sperm in a single ejaculate. If more than one female was mated by a male, the number of eggs on the initial mating plate was divided evenly between them. Given the highly female-biased sex ratio, generally poor mating-ability of C. elegans males, and frequent monitoring, we assume that a mated female was inseminated only once. The measures for the number of sperm transferred are not downwardly-biased by female fecundity, because females are capable of producing many times more oocytes when mated ad libitum relative to this assay and sperm are highly efficient at achieving fertilization upon insemination . Plates were maintained at 20°C throughout the experiment. We assayed 10 to 21 individuals per strain.
Male mating ability
Following the "9-hour assay" of Wegewitz et al. , we isolated 14 L4 fog-2 "females" (strain JK574) per plate one day prior to the start of the experiment to ensure their virginity. We also isolated multiple L4 males per plate, without hermaphrodites, from each experimental strain (AB1, CB4855, CB4856, DR1350, JU440, MY2) and the reference strain (PD4790) the day before the experiment. To begin the assay, we transferred a single male onto a mating plate with the 14 virgin hermaphrodites. Over the next 9 hours, we inspected the males 14 times (after 10 min, 1 h, 2 h, 4 h, and every 30 min thereafter). At every inspection, we scored the male as: (i) in no contact with any females, (ii) in contact with a female, or (iii) with spicules inserted in copulation. Because males were rarely observed in copula, we analyzed (ii) + (iii) in combination. Following the 9-hour assay, we isolated each female; we then scored them the following day as either mated or not mated, based on the presence of eggs or young larvae on the plate, as our measure of copulatory success that resulted in sperm transfer. We performed this assay on 10 to 13 males per strain. Following our ANOVA analysis of these data, we performed post-hoc comparisons comparing strains with the minimum (Hsu's MCB), rather than all possible pairwise comparisons.
Male-male sperm competition (P1 and P2)
We measured the first- (P1) and second-male sperm precedence (P2) of the six wild isolate C. elegans strains in sperm competition with a reference strain. "Females" from strain JK574 were mated sequentially to two males: a PD4790 reference strain marked phenotypically with the genetically dominant, pharyngially-expressed green fluorescent protein (GFP), and a male from one of six wild isolate strains (Table 1). We changed the mating order of the rival males of different strains as either first or second mates. Excepting the lab-derived allele fog-2 (q71) and transgene mls12 (myo-2::GFP, pes-10::GFP, F22B7.9::GFP), the genetic background of JK574 and PD4790 is identical; both are derived from the canonical strain N2.
Males and females were isolated in the last larval stage and maintained as virgins for 24-30 hours prior to mating trials. Isolated males or females that crawled off the media and onto the sides of plates were either rescued, and included in the study, or died and were excluded. We then placed a single virgin female on a plate for 4 hours with 8 males of a given strain. The males were then removed and replaced with 8 males from a different strain for another 4 hours. Thus, a given female was mated sequentially to one or more males from each of two strains: reference strain PD4790 and a wild isolate strain. In this way, the sperm from different male genotypes is placed in direct competition within the female's reproductive tract. Following both matings, the females were placed on a new plate where they continued to lay eggs. Eggs laid in the mating arena during the 4-hour mate-access periods were discarded. Females were subsequently transferred to a new plate after 18 hours, and then again 24 hours later to time-stamp the progeny as early (first 18 hours after second mating) or late (any eggs laid after that).
A total of 111 females were mated to males. Eight females died before they had laid all of their eggs and were excluded from the dataset. Of the remaining 103, 14 showed complete sperm precedence for one strain indicating that one male genotype failed to mate successfully during the trial, and also were excluded (9 indicated no sperm transferred during the second mating, and 5 indicated no sperm transferred during the first mating). In all cases, reference strain PD4790 was the strain that failed to mate successfully, which corroborates the relatively poor male mating ability of the N2 genetic background [29, 30]. Paternity (P1 or P2, early or late) was assigned on the basis of GFP phenotype, with adult progeny scored as either GFP (sired by reference PD4790 males) or non-GFP (sired by one of the six wild isolate males). There were between 14 and 16 successful sperm competition assays per strain combination.
Integrating Male Reproductive Traits
Summary of male reproductive traits.
courtship ability a*
mating ability b*
number of transferred sperm c
spermatid size d*
sperm production rate e*
P2 fertility f
male maintenance g
Heritable variation in male sperm traits
Male mating ability
Competitive ability of male sperm
Integrating Traits Contributing to Male Reproductive Success
Summary of the leading four eigenvectors from a Principal Components (PC) Analysis of male reproduction traits
courtship ability a
mating ability b
number of transferred sperm c
spermatid size d
sperm production rate e
Our assays of pre- and post-mating traits demonstrate heritable natural variation for male mating ability, sperm size, rate of sperm production and sperm precedence in C. elegans. The number of sperm transferred in a single ejaculate by virgin males, however, does not vary significantly among male genetic backgrounds. We confirm that sperm size is an important indicator of fertilization success in male-male sperm competition and that large sperm come at a cost because they take longer to produce  - indeed, we demonstrate that heritable differences in the rate of sperm production is the strongest correlate of second-male sperm precedence.
The factors contributing to sperm precedence and male reproductive success
The C. elegans literature shows that, in mated hermaphrodites, male sperm outcompete self-sperm [23, 24] and the larger size of male sperm likely contributes to their superior competitive ability . Following sperm transfer to a hermaphrodite, a C. elegans male's amoeboid sperm must crawl up one of two gonad arms to reach the spermathecae (the sites of fertilization), where they can compete with the accumulated self-sperm for access to oocytes. Mature oocytes pass through the spermathecae where they are fertilized, and then into the uterus before exiting the animal through the vulva. During this process, sperm can be carried with the egg as it moves away from the site of fertilization. Sperm in the spermathecae of mated hermaphrodites are significantly larger than sperm in the uterus, indicating that smaller sperm are more likely to be displaced or less likely to re-migrate to the spermathecae following displacement . Displaced sperm risk being expelled to the external environment when an egg is laid. Almost all of a hermaphrodite's relatively small self-sperm can be lost during egg-laying if a hermaphrodite receives enough male sperm . Thus, being able to crawl faster back into the spermathecae or being able to adhere better to the reproductive tract likely are beneficial sperm traits; both have been observed in vitro as characteristic of larger sperm . These characteristics must be critical components of sexual selection by male-male sperm competition in nature for gonochoristic relatives of C. elegans.
In a direct test of inter-male sperm competitive ability, we saw that genetically distinct strains with larger sperm had greater early paternity when mated second (high P2-early). This indicates that when the male with larger sperm is mated second to a fog-2 female, the portion of male sperm that is larger than the reference strain's sperm gets used for fertilization immediately and preferentially over the pre-existing male's smaller competitor sperm. Unexpectedly, we saw no increase in paternity when strains with larger sperm mated first in our double-mating assay (no P1 advantage). We suspect that the following scenario might explain this pattern. C. elegans lay ~9 eggs per hour at peak levels of oogenesis when they have high sperm availability , which corresponds well to the 20 - 40 fewer progeny of a given genotype over the 4 hr period that it is mated first relative to second in our sperm precedence assay, implying that our assay "missed" the first 20 - 40 progeny sired by the first male assayed. When a large-sperm male inseminates a female, she receives sperm that are variable with respect to size. If this large-sperm male is mated first, then the largest sperm will be used immediately (during the mating trial period; such eggs were discarded in our assay) and will have already fertilized oocytes by the time the smaller reference-strain sperm enter the reproductive tract. This would result in a situation where all sperm that remain in the reproductive tract after the mating trials will be of similar size and, therefore, of similar competitive ability. This overlap in the sperm size distribution could explain the pattern of 50% first-male paternity in our assay, even for strains that have larger sperm on average than males of the reference strain.
We observed that all P1 (early and late) and late P2 values for wild isolate-sired offspring did not differ from equal paternity (50%; Figure 6). Even given the model proposed above, it is unexpected that we do not observe higher paternity for second mated males (regardless of sperm size) in the late progeny, assuming an equal number of sperm are transferred by the two genotypes and that the first male's sperm is partially exhausted from fertilization during the mating trial itself. One pre-copulatory explanation for this finding is that the females might not facilitate mating as readily with second males. This idea is supported by the report that C. elegans hermaphrodites are less likely to mate if their reproductive tracts contain self-sperm , which likely extends to the case of male sperm being present in the reproductive tract. Males mate more easily with older hermaphrodites , that also will have fewer self-sperm in their reproductive tract, but the < 4-hour difference in age of females between mating trials is probably too small of a difference to reflect this age effect. Possible post-copulatory explanations include second-male sperm being flushed at a higher rate from the reproductive tract by egg passage, or, a higher rate of ejaculate ejection of second-male sperm - as observed in hermaphrodite-male sperm competition, such that hermaphrodites are more likely to eject male sperm when self-sperm are present . Sperm age, however, is unlikely to have been an important factor, because previous work indicates that sperm age does not affect competitive ability in male-hermaphrodite sperm competition , and sperm in our experiment competed over several days but differed in age by only a matter of hours. In addition, this type of temporal variation of sperm use patterns has been seen in other systems .
Some studies have measured C. elegans male reproductive success by the ability of males to persist within androdioecious populations . Although not statistically significant, given only 6 strains that could be included in correlation, Teotonio et al.'s  male maintenance ability metric showed the highest magnitude correlations with P2-late and with sperm size (Additional File 2), suggesting that these traits are worth further investigation for a role in the maintenance of males within C. elegans populations. Some of the male genotypes we assayed produce a mating plug [12, 53]. Mating plugs affect re-mating rates in some taxa , but did not appear to affect P2 in this experiment. Our experimental design was such that the non-plugging reference strain PD4790 is the only strain that must mate following a mating plug deposit. It is formally possible that mating plugs retard re-mating ability more for some male genetic backgrounds, but that the reference strain (PD4790) males are largely unaffected by mating plugs. In this study, we focused mostly on sperm traits, but we expect that differences in other mating traits, such as time spent in copula or the incidence of sperm ejection by females, might also exhibit heritable variation contributing to differences in male reproductive success. Note that if females discriminate among male genetic backgrounds to cause differential sperm ejection, we would have expected significant differences among male genotypes in the assay of sperm transferred per ejaculate. Because we observed no such differences, it is unlikely that such a mechanism of female choice operated with the strains used in this study. An in-depth analysis of heritable variation in mating behaviors will help to fully dissect the relative importance of pre-mating, copulatory, and post-mating contributions to male reproductive success.
Because we use a reference strain to compare sperm precedence among wild isolates, we are unable to identify any non-transitive effects. Similarly, identical fog-2 female genotypes provide the arena for all sperm competition, so we cannot test for an effect of female genetic background on fertilization success. However, further investigation using sperm-depleted hermaphrodites from different strains or introgression of fog-2 (q71) into a variety of genetic backgrounds could provide valuable insight into variation in hermaphrodite and female mating traits. Indeed, Wegewitz et al.  showed recently that males are better at mating with strain CB4856 hermaphrodites than with hermaphrodites of the lab-adapted strain N2. In addition, CB4856 hermaphrodites have lower self-fecundity than do N2 hermaphrodites. They thus concluded that males are maintained more easily in populations of CB4856 both because the males are better at obtaining copulations and the hermaphrodites are worse at avoiding copulations than N2. Isogenic populations of strain CB4856 indeed retain males more readily than several other wild isolate and lab-adapted strains [29, 54, 55].
Mating rate also could positively affect the rate of sperm production, either as a consequence of selection or as a physiological byproduct. Alternatively, males with a high re-mating rate might transfer fewer sperm at each subsequent mating if the rate of sperm production is not modulated. Either of these scenarios would impact the resulting size distribution of sperm that a male produces, because larger, more-competitive sperm take longer to make.
It should be noted that mated C. elegans hermaphrodites have a decreased lifespan compared to non-mated hermaphrodites . In our sperm precedence assay, individual female worms were exposed to a total of 16 male worms. This biased operational sex ratio, with corresponding male-induced harm to females, might have contributed to the mortality of 8 females prior to laying all of their eggs.
Understanding sperm size inC. elegans
In the broader context of the genus, four explanations seem plausible for the small size of C. elegans sperm compared to obligately outcrossing species. First, tiny self-sperm might result from selection for rapid spermatogenesis in hermaphrodites because they cannot fertilize oocytes until sperm production is complete [27, 57, 58]. C. elegans hermaphrodite self-sperm are very small and have been proposed to be near the lower limit for sperm size given the constraints of sperm mobility . This also is consistent with the minimal investment in male gametes by hermaphrodites that is expected from models of resource allocation in selfing organisms [59, 60]. Second, the relatively small size of male C. elegans sperm compared to related gonochoristic species might be a byproduct of selection for small sperm in hermaphrodites via genetic correlation or pleiotropy. Third, male sperm size might have experienced relaxed selection on size when selfing hermaphroditism evolved, resulting in the evolution of smaller size. Developmental and/or mutational biases in the origin or evolution of sperm size also could generate small hermaphrodite and male sperm in the absence of strong countervailing selection . Finally, selection may have favored decreased size of male sperm following the origin of selfing hermaphroditism, because male sperm no longer competed against other male sperm with any regularity and only had to be bigger than hermaphrodite sperm to ensure male fertilization success. At present, we cannot assess the relative likelihood of these alternatives.
The evolution of mating traits in C. elegans and its relatives
Because C. elegans hermaphrodites mate so rarely, there is little reason for them to invest in large, competitive self-sperm. It might also be true that it is advantageous for hermaphrodites to outcross (masked recessive deleterious alleles, increased genetic variation, and other benefits of sex) with males when possible by allowing male sperm to win fertilization every time they mate. For example, some forms of stressful laboratory environments select for the maintenance of males in C. elegans [reviewed in [21, 26]]. However, C. elegans lab and field data suggest that recombinant genotypes might not generally experience a selective advantage [62, 63], which could indicate that selection for fast sperm production in hermaphrodites is a stronger selective force on sperm size and competitive ability than are benefits of outcrossing sex . Indeed, changes in traits associated with outcrossing in C. elegans have been likened to the "selfing syndrome" described in plants . Some of the traits related to this syndrome in hermaphrodites include a lack of mate searching behavior , their inability to produce potent pheromones to attract mates , and hermaphrodites' lack of mating facilitation behavior (particularly if they have self-sperm in their reproductive tract) . In addition, hermaphrodites decrease cross-fertilization rates by ejecting male sperm post-mating [17, 66]. C. elegans males are also less efficient at mating than their gonochoristic counterparts , and many wild strains (31%) have lost a functional version of a gene responsible for the ability to produce a copulatory plug after mating [12, 53]. However, males of C. elegans are able to transfer sperm into different heterospecific partners  and are also attracted to the pheromones released by heterospecific females  which suggests that C. elegans' selfing syndrome manifests more strongly for hermaphrodite/female traits than for male traits.
Male-hermaphrodite sperm competition is likely the more important form of sperm competition in C. elegans because males are rare in nature [63, 68] and are unlikely to encounter one another's sperm. Interestingly, C. briggsae (also androdioecious) exhibits similarly reduced male sperm size with even tinier hermaphrodite sperm . However, male-male sperm competition surely is an important force in breeding system evolution in closely related gonochoristic species: males of outcrossing species have much larger sperm . Here we have shown that C. elegans provides a tractable model to better understand the evolution of sperm competition patterns in Caenorhabditis species in general, which can shift toward direct tests as experimental tools are developed in other species, such as C. remanei . It is critical to determine whether the relative importance of the various pre- and post-mating traits differs between species as a function of the intensity of male-male competition.
Increased sperm size under sperm competition has been favored in a variety of taxa, despite the high variability in sperm form and function [6, 7]. However, other traits also correlate with sperm size, such as fertilization priority [e.g., ] and preferential sperm storage [e.g., ], which complicates our understanding of the relative importance of sperm size and its general role in competitive ability. This study demonstrates that for C. elegans nematodes, it appears that sperm size and their rate of production represent dominant factors in deciding the success of male reproduction.
We thank M. Bueno de Mesquita for laboratory assistance and H. Teotonio for making male maintenance data available to us. Support for this project was facilitated by funding from the Natural Sciences and Engineering Research Council of Canada with a Discovery Grant to ADC.
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