Behavioral Ecology Vol. 13 No. 4: 561-570
© 2002 International Society for Behavioral Ecology
Maintenance of androdioecy in the freshwater shrimp Eulimnadia texana: sexual encounter rates and outcrossing success
a New Mexico State University, Las Cruces, NM 88003-8001, USA b Department of Biology, The University of Akron, Akron, OH 44325-3908, USA
Address correspondence to S.C. Weeks. E-mail: scweeks{at}uakron.edu . V.G. Hollenbeck is now at the Department of Forest Science, Oregon State University, Corvallis, OR 97331-5752, USA.
Received 2 May 2001; revised 30 November 2001; accepted 11 December 2001.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMETHODSRESULTSDISCUSSIONREFERENCES |
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The clam shrimp Eulimnadia texana has a rare mating system known as androdioecy, in which males and hermaphrodites cooccur but there are no pure females. In this species, reproduction takes place by outcrossing between males and hermaphrodites, or by selfing within a hermaphrodite; this system provides a unique opportunity to examine the adaptive significance of out-crossing and selfing in animals. Our study examined mating behavior in hermaphrodites and males from two populations to understand the propensity of these shrimp to mate and to estimate a parameter of a model developed by Otto et al. (American Naturalist 141:329-337), which predicts the conditions for stability of the mixed mating system in E. texana. Here we present evidence that mating frequency is environmentally sensitive, with greater numbers of encounters and matings per male when males are rare and in younger males. However, the effects of shrimp density, relative male frequency, and shrimp age interact in a complex way to determine male mating success. Overall, mating frequency was determined by a combination of encounter rates between the sexes and the proportion of encounters resulting in mating. The mating rates were then used to estimate one of four parameters of the Otto et al. model, and these estimates were combined with previous estimates of the other three parameters to examine the fit of the predicted to the observed sex ratios in the two populations.
Key words: androdioecy, branchiopod crustaceans, evolution of breeding systems, inbreeding, mating success, mating tactics, mixed mating system, self-fertilization.
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONREFERENCES |
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In self-compatible hermaphrodites, questions arise as to when individuals should outcross (mate with an unrelated individual) or self-fertilize (Charlesworth and Charlesworth, 1987
; Lande and Schemske,
1985). Outcrossing incurs a two-fold cost compared to selfing (the
fusion of gametes from the same individual) because gametes contain only half
the genetic material of the parent (cost of meiosis;
Williams, 1975). The genetic
cost of meiosis can be recovered with selfing because all of the zygote's
genetic material is from the same individual
(Fisher, 1941;
Maynard Smith, 1977;
Naglyaki, 1976). However,
despite the twofold cost, outcrossing is still prevalent in the majority of
eukaryotic organisms (Bell,
1982). Many of the hypotheses put forth to explain the
predominance of outcrossing can be lumped into adaptive variation hypotheses
based on the premise that outcrossing leads to greater variation in progeny,
which is advantageous in variable environments
(Bell, 1982;
Johnson et al., 1997;
Wells, 1979).
Most theoretical models of mating systems predict evolutionary equilibria
of complete selfing or complete outcrossing populations
(Fisher, 1941;
Holsinger et al., 1984;
Lande and Schemske, 1985;
Naglyaki, 1976;
Wells, 1979). Yet other models
predict that mixed mating systems (i.e., those with both outcrossing and
selfing modes of reproduction) can be maintained
(Charlesworth, 1980;
Charlesworth et al., 1991;
Holsinger et al., 1984;
Lande et al., 1994;
Latta and Ritland, 1994;
Lloyd, 1979;
Maynard Smith, 1977). Mixed
mating systems provide excellent opportunities to address questions regarding
selfing and outcrossing in a single system.
One form of mixed mating is androdioecy, an unusual system in which males
and hermaphrodites co-occur, but there are no true females
(Charlesworth, 1984). Many
structurally androdioecious organisms have been found to be functionally
dioecious: the hermaphrodites of these organisms function only as females
(Charlesworth, 1984;
Wolf et al., 1997). There have
been only a few documented cases of functional androdioecy (or near
androdioecy) in plants, including Datisca glomerata
(Liston et al., 1990),
Mercurialis annua (Pannell,
1997), Saxifraga cernua
(Molau and Prentice, 1992),
and Phillyrea augustifolia
(Lepart and Dommee, 1992). The
few animals exhibiting androdioecy include the nematode Caenorhabditis
elegans (Wood, 1988), the
barnacle Balanus galeatus (Gomez,
1975), the vertebrate killifish, Rivulus marmoratus
(Lubinski et al., 1995), and
several branchiopod crustaceans (Sassaman,
1995; Sassaman and Weeks,
1993).
One such androdioecious branchiopod is the clam shrimp Eulimnadia
texana (Sassaman and Weeks,
1993; Zucker et al.,
1997). Biparental reproduction occurs via outcrossing only between
males and hermaphrodites; uniparental reproduction consists of selfing within
a hermaphrodite. Hermaphrodites are of two types: monogenic and amphigenic.
These terms refer to the genotypes for sex determination, which are
hypothesized to be under the control of a single genetic locus with two
alleles (Sassaman and Weeks,
1993). Monogenics are homozygous dominant for the sex-determining
gene, and amphigenics are heterozygous. The homozygous recessive condition
produces males (Sassaman and Weeks,
1993).
Various studies of androdioecious plants have addressed the stability of
this breeding system. Fritsch and Rieseberg
(1992) used outcrossing rates
(determined via polymorphic DNA markers) to compare predicted and actual male
frequencies in two populations of D. glomerata. They concluded that
high pollen production by males (three times that of hermaphrodites) coupled
with the high outcrossing rates in hermaphrodites appear to be sufficient to
allow androdioecy to persist in this species. In M. annua, it has
been hypothesized that a balance between selection for reproductive assurance
(i.e., ability to produce offspring without a mate) during colonization and
selection favoring more males in established populations allows for the
maintenance of androdioecy (Pannell,
1997). Lepart and Dommee
(1992) suggested that
androcioecy in P. angustifolia is an intermediate state between
hermaphroditism and dioecy. The ability of hermaphrodites to self-fertilize
could be an adaptation for colonizing new habitats with few founders
(Lepart and Dommee, 1992).
Because of the unusual mating system of E. texana (e.g., two
hermaphroditic types and hermaphrodites unable to fertilize one another), Otto
et al. (1993) specifically
developed a population genetics model for this species. The model describes
conditions under which males can be maintained in the population given
discrete generations and describes a life history that consists of mating,
offspring production, and viability selection
(Otto et al., 1993). Males can
be maintained if the costs of sex (the reduction in gene copies due to
meiosis) and reduced male longevity are offset by the costs of selfing
(inbreeding depression and sperm limitation) and high relative male mating
success. Specifically, the model predicts a stable polymorphism (maintenance
of monogenics, amphigenics, and males) whenever the following inequality is
true:
 | (1) |
The parameter 
is a measure of relative male mating success and is
defined by the fact that u is the proportion of eggs that a
hermaphrodite fertilizes with male sperm. Although u must lie
strictly between 0 and 1 for all u, need not. In the extreme
case where all eggs are fertilized by male sperm if at least one male is
present, then = 1/u, which is >>1 when males are rare
(reflecting the fact that relative male mating success is enormous in this
case). The variable is a function that includes several components of
male mating success: the number of encounters with hermaphrodites experienced
by an average male during its reproductive lifetime; the probability of
outcrossing per encounter; and the proportion of eggs fertilized using male
sperm given that mating has occurred. In general, may depend on the
frequency of males in the population, although would be constant for
all u if encounters are rare and if they were governed by a Brownian
motion process.
When an encounter does not result in sperm transfer, or when sperm transfer
does not lead to fertilization of an entire clutch of eggs, a proportion,
ß, of the remaining eggs are self-fertilized by the hermaphrodite
(Otto et al., 1993). The
selfed offspring may suffer inbreeding depression, 
[= 1 - (fitness of
selfed offspring/fitness of outcrossed offspring)]. The model also
incorporates the often-observed difference in viability between males and
hermaphrodites (Sassaman and Weeks,
1993; Strenth,
1977) by reducing male fitness to (1 - 
) relative to
hermaphrodites. Equation 1 states that male relative mating success and
relative viability [(1 - )] must be high enough to overcome the
twofold cost of outcrossing, which can be offset by high inbreeding depression
(1 - ) or inability of the hermaphrodite to fertilize many of her own
eggs (low values of ß) in order for the mixed mating system to persist
(Otto et al., 1993).
The objectives of this study were to (1) understand the likelihood of
outcrossing in E. texana and how mating frequencies might be modified
by environmental conditions and (2) quantify relative male mating success
[ in the Otto et al.
(1993) model]. An operational
definition of is that it is a product of encounter rates between males
and hermaphrodites, the proportion of these encounters that result in sperm
transfer from the male to the hermaphrodite, and the proportion of eggs then
successfully sired by the male's sperm. To make this operational definition a
relative value, encounters need to be summed across the time between
receptivity periods for the hermaphrodites (i.e., the time in which a male can
mate with multiple hermaphrodites before an average hermaphrodite is again
available for mating). The current study examined the first two of the above
three components of (encounter rates and the proportion of encounters
resulting in sperm transfer); the third component (proportion of eggs then
successfully sired by the male's sperm) has been estimated elsewhere
(Weeks et al., 2000b). The
current estimates of were collected from two populations of E.
texana that differ in their evolutionary histories. The results suggest
that does depend on environmental characters such as shrimp age,
relative male frequency, and shrimp density. Therefore, a reliable test of the
fit of the Otto et al. (1993)
model to natural sex ratios will not be forthcoming until the model is
reformulated to incorporate an environmentally sensitive , and the
parameters of the Otto et al.
(1993) model are estimated
from natural populations.
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METHODS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONREFERENCES |
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Study organism
Eulimnadia texana is a freshwater clam shrimp in the crustacean subclass Branchiopoda and the order Spinicaudata (Spears and Abele, 2000
).
Although its higher taxonomy remains controversial, E. texana has
been placed in the family Limnadiidae with two other genera and 15 congeners
(Sassaman, 1995). Clam shrimp
derive their common name from the bivalve-shaped carapace that covers the
shrimp. Sexual dimorphism is evident. In males, the first two pairs of
thoracic appendages are hooked and serve as claspers during mating. In gravid
hermaphrodites, fertilized eggs are seen through the transparent carapace as a
dorsal mass in the fold of the carapace. When not gravid, eggs lining the
ovotestes are readily seen through the carapace.
Eulimnadia texana is a small clam shrimp, reaching only 8 mm in
carapace length. This shrimp inhabits ephemeral habitats such as natural
playas and human-made cattle tanks in the southwestern United States.
Reproduction can take place by outcrossing between a male and a hermaphrodite
or by selfing within a hermaphrodite. Fertilization between hermaphrodites
does not occur because hermaphrodites lack the claspers necessary for
outcrossing between two individuals
(Sassaman and Weeks, 1993).
Eulimnadia texana typically survive for 12-17 days
(Marcus and Weeks, 1997;
Weeks et al., 1997), although
hermaphrodites typically live 25-50% longer than males
(Knoll, 1995;
Zucker et al., 2001). One or
two clutches of eggs are produced daily once hermaphrodites reach sexual
maturity, and eggs are continually produced until the hermaphrodites
reproductively senesce at 14-21 days of age
(Weeks et al., 1997). Because
there is no sperm storage in hermaphrodites, a hermaphrodite must mate with a
male every day if all the clutches are to be outcrossed
(Weeks et al., 2000b). Eggs
remain in the brood chamber for 10-20 h
(Weeks et al., 1997) and are
then buried in a small burrow in the pond bottom made by the hermaphrodite
(Zucker et al., 2002). There
is a period of about 3 h after the hermaphrodite buries the clutch of eggs
before the next clutch is extruded into the brood chamber
(Zucker et al., 2002). Eggs
usually do not hatch until a period of desiccation has passed.
In natural populations, male frequencies are highly variable and range from
0 to 42% (Sassaman, 1995).
Densities are also variable: MacKay et al.
(1990) reported densities of
E. texana in a desert tank of 250/m3, and Medland
(1989) found branchiopod
densities to be 3000-7000 individuals/m3 in similar tanks, although
densities for individual species were not reported. In natural conditions,
E. texana exhibits a patchy distribution, concentrating around the
rim and often the top of a pool (Hollenbeck, personal observations). In
addition, small or drying pools often contain a nearly continuous layer of
clam shrimp over the surface (Hollenbeck, personal observations;
Pennak, 1989).
Study populations
Two populations of E. texana were used in this study: WAL is a
population inhabiting a cattle tank (25.3 m x 26.2 m x 1 m deep
when filled) constructed in the 1950s (Sherbrooke WC, personal communication)
located 4 km north of Portal Road (Road 533) near Portal, Arizona, USA. It
receives an average of 49 cm of rain annually, with approximately 60% falling
during the monsoon season from June through September
(Marcus and Weeks, 1997). JT4
is a population from an older, natural depression (Havstad K, personal
communication; 32 m x 18.5 m x 0.3 m deep when filled), also used
by cattle, located 5.8 km north of the entrance to the USDA Jornada
Experimental Range on Jornada Road near Las Cruces, Doña Ana County,
New Mexico, USA. Rainfall for JT4 averages 24 cm annually. As with WAL,
approximately 60% falls from June through September via convection storms
(Marcus and Weeks, 1997).
Recent studies indicate that WAL has greater genetic diversity than JT4
(Weeks and Zucker, 1999;
Weeks et al., 1999).
Rearing conditions
We collected samples of the top 2 cm of soil from various locations within
each population and stored the samples in the lab for less than 1 year. On day
0 of an experimental observation period, a small amount of soil from a
population was filtered through a 270-µm sieve with dechlorinated tap water
into 30 cm x 14 cm (5 cm water depth) plastic storage tanks. The
filtering removed eggs of Triops sp., which, if allowed to hatch,
prey on clam shrimp. Tanks were kept under constant incandescent light to
maintain temperatures of 28-30°C. Many eggs hatch between 17 and 24 h
after hydration, although some continue to hatch for up to 72 h. To ensure
that all shrimp used in the experiment were approximately the same age, water
with larvae was poured into a 35 cm x 22 cm (5 cm water depth) plastic
rearing tank after 24 h, separating larvae from any unhatched eggs in the
soil. Approximately 0.5 l of water from the alternate population was filtered
through a 63-µm sieve (small enough to remove any E. texana
larvae) and added to each rearing tank. This allowed both populations access
to food items (e.g., microorganisms) and minerals that may be present in the
soil of one population but not the other. Larvae were supplemented with 0.25 g
dry yeast in solution and 0.02 g TetraMin Baby "E" fish food upon
transfer to rearing tanks and again 24 h later. Subsequently, clam shrimp were
fed finely ground TetraMin fish flakes as needed until day 6, and frog tadpole
food (Carolina Biological) as needed thereafter. We added dechlorinated tap
water periodically to replace evaporated water. On day 6 or 7, we removed clam
shrimp from their original rearing tanks and transferred them to fresh rearing
tanks with new dechlorinated tap water to minimize algal growth. At this
point, heat lamps were turned off and tanks were kept on a 15 h:9 h light:dark
cycle at approximately 24°C.
Mating behavior
We observed mating behavior of groups of E. texana under various
demographic conditions. A completely randomized design with a 24
factorial arrangement of treatments was used, resulting in 16 treatment
combinations. The factors included (1) population, (2) age of shrimp, (3)
density of shrimp within an observation cup, and (4) male frequency
(percentage of males in a treatment population). Each factor was set at two
distinct levels: (1) population: JT4 and WAL; (2) age: young (5-7 days) and
old (9-11 days); (3) density: high (24 individuals/observation cup) and low
(12 individuals/observation cup); and (4) male frequency: high (42%) and low
(14-17%).
We established treatments 24 h before sampling. Shrimp were removed from rearing tanks, sexed, and placed in 500-mL (9 cm diam) clear plastic cups with 0.02 g finely ground TetraMin fish flakes and dechlorinated tap water to a depth of 6 cm. On the day of an observation, shrimp were marked with different colors of Testor's enamel paint for individual identification.
An observation consisted of three 20-min periods, interrupted by 10-min
rest periods to avoid observer fatigue. We used scan sampling
(Altmann, 1974) to determine
the number of encounters that took place and the number of those encounters
resulting in outcrossing within the cumulative 60-min observation. An
"encounter" was defined as clasping of a hermaphrodite by a male
for at least 3 s. This disqualified random bumping and male—male
interactions as encounters. "Mating" was defined as an encounter
that continued uninterrupted for at least 5 min. Knoll
(1995) found that if an
encounter lasted longer than 1 min, subsequent copulation and movement of eggs
into the brood chamber occurred (mean = 27 min; range = 2-120 min; N
= 95 out of 95 observations). Therefore, a 5-min encounter has a high
probability of resulting in mating. Scanning was continuous, and the amount of
time spent on each individual lasted only a few seconds. Therefore, sampling
approached a continuous, simultaneous sample on all males
(Altmann, 1974). The order in
which males were scanned was randomly chosen and retained throughout the
20-min observation. Scanning rounds continued until every male was observed an
equal number of times in a particular 20-min period. We observed each male in
an observation cup in turn, and any new encounters were noted. If a male was
seen engaged in an encounter, the identities of the male and hermaphrodite, as
well as the time, were recorded. If the encounter continued throughout the
next 5 min, it was noted as an encounter that resulted in mating. Encounters
that began during the last 4 min of an observation period were followed for a
full 5 min to determine their outcomes. During the second and third 20-min
observation periods, encounters that were noted as resulting in mating at the
end of the previous period were considered to be continuous throughout the
rest period and were not counted as new encounters. If more than one male
clasped a hermaphrodite simultaneously, we recorded each encounter. However,
if all males remained clasped for 5 min (rarely), we counted only one
encounter as resulting in sperm transfer. At the end of the 60-min observation
period, we tallied the total number of encounters and the total number of
those likely resulting in sperm transfer. Each treatment combination was
replicated eight times for a total of 128 observations.
Statistical analyses
We estimated mating frequency by dividing the numbers of encounters per
tank in a 1-h period in which a male clasped a hermaphrodite for 
5 min
(see above) by the total number of males in that tank. These data were
analyzed in a factorial, four-way ANOVA, with population, shrimp age, density,
and male frequency as the four main effects (all considered fixed effects).
The data were square-root transformed to normalize residuals.
Analysis of encounter rates was the same as for mating frequency, except the statistic was numbers of encounters per tank divided by numbers of males per tank (i.e., the number of encounters per male per hour). These data also required square-root transformation to normalize residuals.
To determine the effect of the four treatments on the proportion of
successful encounters (i.e., the number of successful encounters divided by
the number of encounters), we used a four-way weighted analysis of variance
(treatment proportions weighted by the number of encounters in an observation
period; SAS Institute, 1989).
All four factors were considered fixed effects, with two levels per factor.
Because encounters could be as short as 3 s, whereas matings were at least 5
min long, matings were more likely to be observed than encounters. Thus, the
proportion of successful encounters was overestimated by the fraction of
encounters missed in the scan sampling. All assumptions of ANOVA (normality
and homogeneity of variances) were tested and met prior to analysis.
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RESULTS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONREFERENCES |
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In this study, male mating success was estimated as the number of mating events per male per hour (i.e., mating frequency), which is composed of the number of male—hermaphrodite encounters per hour times the proportion of these encounters that resulted in actual mating. We first discuss our direct measure of male mating success (number of matings per male per hour) and then consider how encounters and the proportion of encounters resulting in mating combined to form this estimate of male mating success.
Mating frequency
The number of mating events per male per hour was significantly influenced
by two main effects: shrimp age and frequency of males
(Table 1). Three interaction
effects were also noted: age by density, male frequency by density, and age by
density by male frequency (Table
1). In the first interaction, mating events per male per hour did
not differ between densities for young shrimp (high: 0.85 ± 0.07; low:
0.94 ± 0.07), but there were significantly more mating events per male
per hour under high relative to low density (0.30 ± 0.07 vs. 0.16
± 0.07, respectively) for older shrimp
(Figure 1A). In the second
interaction, matings did not differ between densities for high male frequency
(high: 0.43 ± 0.07; low: 0.51 ± 0.07), but there were more
matings at high male relative to low male density (0.73 ± 0.07 vs. 0.59
± 0.07, respectively) at low frequency
(Figure 1A). The third
interaction (three-way) was most informative: younger males had uniformly more
matings under low male frequencies (regardless of density), whereas older
males had the highest matings at low male frequencies and high density,
intermediate success at high male frequency (regardless of density), and
lowest success at low male frequency and low density
(Figure 1A).
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Clearly, mating frequencies were modified by environmental characteristics,
and thus estimates of the behavioral components of (encounter rates
between males and hermaphrodites and the proportion of these encounters that
resulted in sperm transfer) were also dependent on environment. Because
is a relative value, relating the number of offspring sired by a male
relative to those produced by a hermaphrodite (see above), we needed to
multiply the hourly mating frequency (measured here) by the average time
required for a hermaphrodite to brood and release a fertilized clutch of eggs.
The latter is the amount of time available for males to fertilize multiple
hermaphrodites and thus allows a calculation of relative fertility of males to
hermaphrodites, or . The time between successive clutches has been
estimated elsewhere to be approximately 20 h
(Weeks et al., 1997). Thus, we
estimated the behavioral components of to range from 1.3 (old JT4
males at low frequency and low density) to 22.5 (young WAL males at low
frequency and low density; Table
2).
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Behavioral components of male mating success
To understand the behavioral components of male mating success, we also
compared numbers of encounters per male per hour and the proportion of these
encounters resulting in mating among treatments. The overall average
encounters per male per hour was 5.6 ± 0.5, whereas the number of
mating events per male per hour was only 0.56 ± 0.05
(Table 2). Thus, approximately
one-tenth of the encounters resulted in mating. Some treatments affected
encounter rates and mating frequencies similarly (Tables
1 and
3); for example, younger males
had greater encounter rates (8.0 ± 0.4) and mating frequencies (0.90
± 0.05) than older males (3.1 ± 0.4 and 0.23 ± 0.05,
respectively). Additionally, both encounter rates and mating frequencies were
greater under low male frequency (8.0 ± 0.4 and 0.66 ± 0.05,
respectively) than under high male frequency (3.1 ± 0.4 and 0.47
± 0.05, respectively; Tables
2 and
3). Therefore, for these two
main effects, encounter rates explained much of the differences seen in mating
frequencies.
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However, in general, mating frequencies were not a simple proportion of encounter rates (e.g., 10% of encounters), but rather, the relationship between these two measures was much more complex. The two populations significantly differed in encounter rates (JT4: 4.6 ± 0.4; WAL: 6.5 ± 0.4), but this difference was not significant for mating frequencies (JT4: 0.52 ± 0.05; WAL: 0.61 ± 0.05). The encounter rate difference between populations was driven by very low encounter rates for older JT4 shrimp (old: 1.5 ± 0.6; young: 7.7 ± 0.6). The magnitude of difference between young and old was not reflected in WAL (old: 4.7 ± 0.6; young: 8.4 ± 0.6). This difference caused the significant population-by-age interaction (Table 3). Again, this interaction did not translate into an interaction for mating frequencies (Table 1). Overall, the pattern for encounter rates was more encounters for younger shrimp, especially at low male frequency (Figure 1B).
Because mating frequencies were not simple proportions of encounter rates, we needed to analyze the second behavioral component of male mating success: the proportion of encounters resulting in matings. Higher density led to a significantly greater proportion of encounters resulting in mating (high: 0.15 ± 0.01; low: 0.09 ± 0.02; Table 4), but this effect was countered by a nonsignificant, lower number of encounters per male at high density (high: 5.1 ± 0.4; low: 6.0 ± 0.4; Table 3), resulting in no significant difference in mating frequency at higher density (high: 0.58 ± 0.05; low: 0.55 ± 0.05; Table 1). Although higher male frequency led to a significantly greater proportion of encounters resulting in mating (high: 0.15 ± 0.01; low: 0.09 ± 0.02; Table 4), this was countered by many more encounters per male at lower male frequency (high: 3.2 ± 0.4; low: 8.0 ± 0.4; Table 3), yielding a significantly higher mating frequency for males at low male frequency (high: 0.47 ± 0.05; low: 0.66 ± 0.05; Table 1). Younger males had a marginally greater proportion of encounters resulting in mating than older males (young: 0.14 ± 0.01; old: 0.10 ± 0.02; Table 4), which when added to the higher numbers of encounters (young: 8.0 ± 0.04; old: 3.1 ± 0.04; Table 3) explained the overall greater mating frequencies observed for younger males (young: 0.90 ± 0.05; old: 0.23 ± 0.05; Table 1). The greater numbers of encounters in WAL (WAL: 6.5 ± 0.4; JT4: 4.6 ± 0.4; Table 3) was countered by the fact that JT4 males had a marginally greater proportion of encounters that resulted in mating than did WAL males (WAL: 0.10 ± 0.01; JT4: 0.14 ± 0.02; Table 4), resulting in a nonsignificant difference between the two populations in mating frequencies (WAL: 0.61 ± 0.05; JT4: 0.52 ± 0.5; Table 1).
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Two-way and three-way interactive effects were also observed for the proportion of encounters that resulted in matings (Table 4). Again, the three-way interaction was most informative: for younger males, the proportion of successful mating events increased dramatically when going from low to high male frequency, more dramatically so at high density (Figure 1C). This was not reflected for older males: the proportion of successful mating events increased from low to high male frequency at low density, but this pattern was reversed at high density, with the greatest proportion of successful mating events occurring at low male frequency (Figure 1C). The combination of encounter rate with proportion of encounters that were successful resulted in the observed patterns of mating frequencies. Younger males had greater encounter rates at low male frequencies (Figure 1B) and also a greater proportion of mating events at high male frequencies (Figure 1C), which resulted in overall greater rates of mating for younger relative to older shrimp under both conditions, with low male frequencies slightly edging out high male frequencies for younger shrimp (Figure 1A). For older shrimp, the simple pattern of increased encounter rates at low male frequency (Figure 1B) was modified by a complex pattern of proportion of encounters resulting in successful mating (Figure 1C), resulting in the observed pattern of highest mating frequencies at high density and low male frequency, followed by intermediate rates of mating at high male frequency (regardless of density), with the lowest mating frequencies at low density and low male frequency (Figure 1A).
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONREFERENCES |
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The current study was motivated by two goals: to understand how environmental factors may affect the likelihood of mating in E. texana and to understand the maintenance of androdioecy in this species by noting the relative effectiveness of males to fertilize the eggs of one or more hermaphrodites (
; Otto et al.,
1993). Below, we explore both of these issues.
Mating propensity
Successful outcrossing in E. texana should be a product of three
components: (1) encounter rates of males with hermaphrodites, (2) proportion
of encounters that result in sperm transfer from males to hermaphrodites
(i.e., matings), and (3) proportion of eggs fertilized by male sperm once
transfer occurs. The current study examined the first two of these three
components; the third component has been estimated elsewhere
(Weeks et al., 2000b).
The most straightforward combination of the above components would be if
some invariant proportion of encounters resulted in successful sperm transfer
and some invariant proportion of eggs were then sired by a male. These
proportions might then be best explained by simple biological processes, such
as differences in swimming speeds affecting encounter rates
(Medland et al., 2000) or
increased sperm production favoring one genotype over another
(Parker, 1998;
Rakitin et al., 1999). Some of
the differences in mating frequencies measured herein did appear to be best
explained by these types of straightforward processes. For example, the
greater mating frequencies of younger males appeared to be largely driven by
the higher encounter rates of young relative to older shrimp. This difference
makes sense if we assume younger males are more vigorous swimmers and thus
encounter hermaphrodites at a higher rate. Another straightforward example was
found in the greater matings per male when males were in lower frequency,
which again is easily interpreted when noting that lower male frequency led to
greater numbers of encounters per male.
However, it is clear from the several other comparisons that differences in
mating frequencies in E. texana were not only driven by underlying
simple biological processes, but rather that most of the observed differences
were due to apparent switches in male or hermaphroditic behaviors in the
differing environments. The three-way interaction in mating frequencies of
male frequency, shrimp age, and density was not explained by differences in
encounter rates, but rather appeared to be a behavioral change by one or both
sexes. In matings with younger shrimp, the proportion of encounters that
resulted in successful mating was lowest when encounters were highest (at
lower male frequency). This pattern could be explained if either sex were more
selective when encounters were more common
(Crowley et al., 1991;
Hubbell and Johnson, 1987).
For example, it is conceivable that males switch from a mate-guarding tactic
(where males hold on to any hermaphrodite they encounter waiting until the
hermaphrodite is receptive) when hermaphrodites are not much more plentiful
than males, to a sampling tactic (where males encounter but immediately
release hermaphrodites that are not receptive) when hermaphrodites are far
more plentiful than males. Thus, the combination of higher encounter rates but
an apparently more selective mating strategy led to more nearly equivalent
mating frequencies at high and low male frequency than would be predicted on
the basis of encounter rates alone.
In older shrimp, a different pattern was observed. Older males also had
higher encounter rates at low male frequency, but the difference was not as
dramatic as in younger males. However, in older shrimp, the proportion of
encounters resulting in successful mating events was dramatically lower at low
male frequency and low density, highest at low male frequency and high
density, and intermediate at high male frequency. This pattern was
significantly different from the younger shrimp, suggesting a different
behavioral strategy for the older shrimp. A number of studies have shown
independent effects of age, density, and male frequency on mating behavior.
For example, different patterns of receptivity and mating attempts were
documented in female and male (respectively) biting midges (Culicoides
nubeculosus; Mair and Blackwell,
1998), and courtship behavior was age dependent in the cockroach
Diploptera punctata (Woodhead,
1986). Relative male frequency has also been documented to affect
female water striders, Gerris odontogaster: females were more
receptive to mating when male frequency was high
(Arnqvist, 1992). Population
densities have been shown to affect mating behavior in male guppies
(Jirotkul, 1999).
Additionally, studies of water striders have shown that interacting
environmental variables lead to complex mating dynamics. Sih and Krupa
(1995) reported that complex
interactions among male density, female density, and predation risk resulted
in variations in male mating success, which may be explained by shifting
mating behavior in both males and females due to intersexual conflicts
(Krupa and Sih, 1993). Future
studies in E. texana designed to study changes in specific mating
tactics under differing conditions would help us understand these complex
patterns of male mating success in these shrimp.
Tests of the Otto et al. model
The Otto et al. (1993)
model attempts to predict the equilibrium frequencies of the three mating
types in this system [males (u), monogenic (w), and
amphigenic (v) hermaphrodites] based on four relevant parameters:
, the relative male mating success; ß, the proportion of eggs that
are not fertilized by a male that are then self-fertilized by the
hermaphrodite; (1 — ), relative viability of males to
hermaphrodites; and , inbreeding depression experienced by selfed
offspring. The model assumes that outcrossing rate is related to male
frequency, u. Relative male mating success () can vary from 0
to 
, but is constrained such that 0 
u 1
(Otto et al., 1993). Thus,
can be viewed as the average number of hermaphrodites that can be
fertilized by a single male. For example, if an average hermaphrodite's total
egg production is 1000, and a male sires an average of 2000 eggs in its
lifetime, then a male fertilizes an average of two hermaphrodites, and
= 2 (Otto et al., 1993).
Clearly, larger values of can only occur when males are rare, because
an average male cannot fertilize many hermaphrodites when males are common
(e.g., u = 0.5; Otto et al.,
1993).
The combination of male frequency in the population and relative male
mating success dictates the expected proportion of hermaphroditic eggs that
will be outcrossed (i.e., u). The remaining proportion of eggs
[i.e., (1 — u)] is then available for selfing. The model
allows for some proportion, (1 — ß), of these non-outcrossed eggs
to remain unfertilized. This would occur if some eggs were
"earmarked" for outcrossing or if the hermaphrodites were unable
to produce enough sperm to fertilize all of their eggs in the absence of males
(as in C. elegans; Hodgkin and
Barnes, 1991; Van Voorhies,
1992; Ward and Carrel,
1979). The model also incorporates the commonly observed
difference in viability between the sexes in conchostracan shrimp, defined as
(1 — ). Finally, the model provides for the commonly documented
decrease in viability observed in self-fertilized offspring
(Husband and Schemske, 1996;
Jarne and Charlesworth,
1993).
Estimates of relative male mating success () are divided into mating
frequencies (measured here as a product of hourly encounter rates and
proportion of encounters resulting in sperm transfer, extrapolated to a 20-h
period) and the proportion of eggs actually fertilized by male sperm once
sperm transfer has occurred (allowing for some proportion of eggs to be
fertilized by hermaphroditic sperm). The current data reveal that male mating
success is environmentally sensitive (Table
2), and thus we have chosen to use the highest and lowest
estimates of from both populations to represent the range of
that we expect in these two populations. We have combined these estimates with
estimates of the other three parameters for both populations in
Table 5. The
"worst" column is the worst case scenario for the maintenance of
males in the Otto et al.
(1993) model, whereas the
"best" column is the best case scenario (choosing the worst and
best combinations of the four parameters for the maintenance of males,
respectively). These values do not represent confidence limits per se, but
rather represent the range of estimates that we have gathered while studying
this species. The range of relative male mating success () for JT4 was
1.3-20.0 and 2.8-22.5 for WAL (Tables
2 and
5). In a previous study, Weeks
et al. (2000b) found that only
a proportion of the eggs from a mating event are actually fertilized by male
sperm (% fertilized in Table
5), and thus the current estimates of need to be reduced
by the previous estimates of percentage of a clutch sired by a male.
Therefore, ranges from 0.7-10.4 in JT4 and from 1.0-7.7 in WAL
(Table 5).
|
We should note that our higher measurements of are probably
overestimates for two reasons. First, our extrapolation of the mating
frequency in a 1-h observation period to a 20-h period will be clearly
incorrect if it predicts that males successfully fertilize >100% of the
available hermaphrodites. When sex ratios are more nearly equal, many
encounters are likely to be between two males, and males may attempt to
fertilize the same hermaphrodites more than once. Second, extrapolating the
1-h observations to 20 h also assumes that males are producing copious
quantities of sperm. For the lower estimates of mating frequencies, sperm
limitation is probably not an issue. However, it is unclear whether males can
produce enough sperm to fertilize 20 hermaphrodites in 20 h. Without further
information (e.g., sperm replenishment rates in males), we cannot correct the
larger estimates of . We therefore present the current values as our
best estimates of male mating success to date.
The remaining three parameters ranged as follows. Hermaphrodites live
significantly longer than males in both populations
(Zucker et al., 2001), as has
been reported in other studies (Knoll,
1995; Strenth,
1977), resulting in estimates of relative male survival (1 —
) between 0.85 and 0.87 for JT4 and 0.67 and 0.94 for WAL
(Table 5). Estimates of the
ability of hermaphrodites to self-fertilize eggs that are not fertilized by
males (ß) indicate that a similar number of eggs are fertilized in the
presence or absence of males (i.e., ß = 1;
Table 5). Finally, inbreeding
depression () was noted at both early and late portions of the life
cycle, resulting in estimates of lifetime ranging between 0.47 and
0.53 for JT4 and 0.66 and 0.69 for WAL
(Table 5).
Using the current estimates of all four parameters, both best-case
scenarios suggest that mixed sex-types should be stable in these two
populations, whereas both worst case scenarios suggest that these populations
should go to 100% monogenics (Table
5). Using Otto et al.'s equations 2a—c, we can predict the
expected proportions of males, amphigenic, and monogenic hermaphrodites in
these two populations (Table
5). Clearly, the ranges of predicted proportions for the sex types
are quite wide, mainly due to the wide range in our current estimates of
(Table 2). At this
time, the predicted ranges for all three mating types are too broad to allow
any meaningful test comparing field-collected sex ratios to predicted sex
ratios.
Nevertheless, if we assume that the laboratory-collected estimates of these
four parameters are indicative of true conditions in the field, these data
suggest a number of interesting results. The model outlines three potential
benefits for males: sperm limitation in hermaphrodites, inbreeding depression
for selfed offspring, and potential for high outcrossing rates. The first of
these potential benefits, reduced ability of hermaphrodites to fertilize all
their own eggs if not mated by a male (ß), appears to be inconsequential
(i.e., ß = 1; Weeks et al., in press). The second, inbreeding depression
(), appears to be quite important in these populations. Lifetime
inbreeding depression was estimated at between 0.5 and 0.7 in these
populations (Weeks et al.,
1999,
2000a), which in most species
would be sufficient to maintain outcrossing
(Lande and Schemske, 1985).
However, in this system, these values alone are not great enough to select for
complete outcrossing (Weeks et al.,
2000a); the high levels of inbreeding depression are tempered, to
some degree, by lower male longevity (Table
5), requiring even greater levels of inbreeding depression for
males to be maintained (Otto et al.,
1993). Certainly, the levels of inbreeding depression detected in
these studies may underrepresent true values in the field
(Dudash, 1990;
Ramsey and Vaughton, 1998;
Schemske, 1983). If inbreeding
depression is significantly greater in the field, then this factor alone may
be sufficient to maintain males in both populations.
Yet, even with high levels of inbreeding depression, relative male mating
success, , may truly be the determining factor for the relative
abundance of males in this species (Otto
et al., 1993; Weeks and
Zucker, 1999) because the parameter is larger (perhaps by
an order of magnitude) than (1 - ), ß, or (1 - ), and thus
dominates Equation 1. Our estimates of suggest that relative male
mating success can range widely (Table
2), and the current data suggest that is negatively
related to male frequency, u (Tables
1 and
2), indicating that may
not be a fixed value but, rather, is frequency dependent. The original
formulation of assumed that it was a fixed quantity
(Otto et al., 1993). However,
Otto et al. suggested that if is high when males are rare, males can
be maintained in the population under most combinations of the other three
parameters.
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ACKNOWLEDGEMENTS |
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This article was taken in part from a master's thesis by V.G.H. We thank Drs. Milligan, Howard, and Huenneke for their input during the course of this study. This work was supported by the New Mexico State University Department of Biology, as well as by awards from the New Mexico Commission on Higher Education and Sigma Xi to V.G.H. and from the National Science Foundation (IBN-9631042 to N.Z. and IBN-9614226 to S.C.W.).
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