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\begin{document}

\title{Population density effects on gamete traits and fertilisation dynamics
under varying sperm environments in mussels}



\author[1]{Craig Sherman}%
\author[2]{Vincent Careau}%
\author[3]{Clelia Gasparini}%
\author[1]{Kim Weston}%
\author[4]{Jonathan Evans}%
\affil[1]{Deakin University Faculty of Science Engineering and Built Environment}%
\affil[2]{University of Ottawa}%
\affil[3]{University of Padova}%
\affil[4]{The University of Western Australia}%


\vspace{-1em}



  
  \date{May 28, 2024}


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\selectlanguage{english}
\begin{abstract}
Gamete traits can vary widely among species, populations and
individuals, influencing fertilisation dynamics and overall reproductive
fitness. Sexual selection can play an important role in determining the
evolution of gamete traits with local environmental conditions
determining the strength and direction of sexual selection. Here we test
for signatures of post-mating selection on gamete traits in relation to
population density, and possible interactive effects of population
density and sperm concentration on sperm motility and fertilisation
rates among natural populations of mussels. Our study shows that males
from high density populations produce smaller sperm compared with males
from low density populations, but we detected no effect of population
origin on egg size. Our results also reveal that females from low
density populations tended to exhibit lower fertilisation rates across a
range of sperm concentrations, although this became less important as
sperm concentration increased. Variances in fertilisation success were
higher for females than males and the effect of gamete compatibility
between males and females increases as sperm concentrations increase.
These results suggest that local population density can influence gamete
traits and fertilisation dynamics but also highlight the importance of
phenotypic plasticity in governing sperm-egg interactions in a highly
dynamic selective environment.%
\end{abstract}%



\sloppy


\textbf{Population density effects on gamete traits and fertilisation
dynamics under varying sperm environments in mussels}

Craig D.H Sherman\textsuperscript{1*}, Vincent
Careau\textsuperscript{2}, Clelia Gasparini\textsuperscript{3}, Kim J.
Weston\textsuperscript{1}, Jonathan P. Evans\textsuperscript{4}

\textsuperscript{1}School of Life and Environmental Sciences, Deakin
University, Victoria 3216, Australia.

\textsuperscript{2}Department of Biology, University of Ottawa, Ottawa,
ON, Canada.

\textsuperscript{3}Department of Biology, University of Padova, Padova,
Italy

\textsuperscript{4}Centre for Evolutionary Biology, School of Biological
Sciences, University of Western Australia, Crawley 6009, WA, Australia

*Corresponding author

E-mail address: craig.sherman@deakin.edu.au

Running title: Gamete traits and fertilisation dynamics

Gamete traits can vary widely among species, populations and
individuals, influencing fertilisation dynamics and overall reproductive
fitness. Sexual selection can play an important role in determining the
evolution of gamete traits with local environmental conditions
determining the strength and direction of sexual selection. Here we test
for signatures of post-mating selection on gamete traits in relation to
population density, and possible interactive effects of population
density and sperm concentration on sperm motility and fertilisation
rates among natural populations of mussels. Our study shows that males
from high density populations produce smaller sperm compared with males
from low density populations, but we detected no effect of population
origin on egg size. Our results also reveal that females from low
density populations tended to exhibit lower fertilisation rates across a
range of sperm concentrations, although this became less important as
sperm concentration increased. Variances in fertilisation success were
higher for females than males and the effect of gamete compatibility
between males and females increases as sperm concentrations increase.
These results suggest that local population density can influence gamete
traits and fertilisation dynamics but also highlight the importance of
phenotypic plasticity in governing sperm-egg interactions in a highly
dynamic selective environment.

\textbf{KEY WORDS} : sexual selection, sperm competition, polyspermy,
maternal effect, genotype by environment, cryptic female choice.

It is now widely recognised that in most sexually reproducing taxa
sexual selection can continue after mating in the form of sperm
competition, where ejaculates from rival males compete for fertilisation
(Parker 1970), and cryptic female choice, where females influence the
outcome of these contests (Eberhard 1996; Birkhead and Moller 1998;
Parker 2020). This has resulted in a myriad of adaptations in both
sexes; for example, selection can favour specific gamete traits that
make ejaculates more competitive in the race to fertilise eggs (Pizzari
and Parker 2009; Simmons and Fitzpatrick 2012; L\selectlanguage{ngerman}üpold et al. 2020),
gamete plasticity in response to local environmental conditions (Crean
and Marshall 2008), sperm chemoattractants that function to attract
sperm from specific (e.g. compatible) males (Evans et al. 2012; Oliver
and Evans 2014; Kekäläinen and Evans 2017; Lymbery et al. 2017), or
gamete recognition proteins that ultimately determine whether sperm can
fuse with an egg (Palumbi 1999; Swanson and Vacquier 2002; Levitan and
Ferrell 2006; Evans and Sherman 2013).

Post-mating sexual selection has been argued to be particularly
important in broadcast spawning organisms that release their gametes
into the water for external fertilisation (reviewed in Evans and Sherman
2013; Kekäläinen and Evans 2018; Evans and Lymbery 2020). Indeed, one of
the only opportunities for mate choice and mating competition in
broadcast spawning organisms occurs through gamete-level interactions.
However, broadcast spawning marine invertebrates face unique challenges
that are linked to the spawning environment. In particular, variation in
adult population density, and therefore the density of gametes in the
water, is predicted to influence the intensity and direction of
post-mating sexual selection (Parker et al. 1997; Franke et al. 2002;
Levitan 2004; Levitan and Ferrell 2006; Marshall and Bolton 2007;
Sherman et al. 2015; Hadlow et al. 2022). In low density populations,
the rapid dilution of gametes can result in low fertilisation rates
(Vogel et al. 1982; Levitan and Petersen 1995; Styan and Butler 2000;
Levitan 2004), thereby generating selection on gamete traits in both
sexes to increase the probablity of egg-sperm encounters and fusion. For
example, in females this may include the production of fewer, larger
eggs to increase egg-sperm collision rates, greater investment in
sperm-attracting chemoattractants, greater egg longevity, and less
selective membrane blocks to sperm penetration (Yund 2000; Riffell et
al. 2004; Marshall and Evans 2005; Levitan 2006; Levitan and Ferrell
2006; Kosman and Levitan 2014; Evans and Lymbery 2020). Under these
sperm-limiting conditions males will maximixe their fitness by
increasing gamete encounter rates, for example by producing a smaller
number of larger and/or longer lived sperm or altering swimming patterns
(Parker 1993; Benzie and Dixon 1994; Parker 1998; Yund 2000; Snook 2005)
(but see Crean and Marshall 2008).

At the other end of the population density spectrum, males from
high-density populations face increased sperm competition, while females
face an increased risk of polyspermy - where eggs are fertilized by two
or more sperm (usually resulting in cell or zygote death). As a
consequence, selection may favour female reproductive strategies that
minimise the risk of polyspermy. Specifically, when sperm are abundant
and the risks of polyspermy are high, females are predicted to produce
smaller eggs, invest less in sperm-attracting chemoattractants, or
increase the selectivity of membrane gamete recognition systems to
reduce the risk of lethal polyspermy (Levitan and Ferrell 2006; Levitan
et al. 2007; Kamel et al. 2010; Kosman and Levitan 2014). Males, on the
other hand should produce higher numbers of smaller sperm (Parker 1998;
Snook 2005; Parker 2006) or release smaller quantities of sperm over a
longer period of time (Bode and Marshall 2007; Marshall and Bolton
2007). Consequently, as population density (and sperm abundance)
increases, selection should favour reproductive strategies in males that
further exacerbate the reproductive costs incurred by females
(polyspermy) (Evans and Lymbery 2020).This complex interplay between
population density and the differential selection pressures faced by
males and females can lead to sexual conflict, where the optimal mating
strategy of one sex reduces the reproductive fitness of the other
(Parker 2006; Kamel et al. 2010). Despite this prediction, however,
there are only a limited number of studies that have explored selection
on gamete traits and fertilization dynamics from natural populations
with varying adult densities (however, see Levitan 2002, 2004; Levitan
and Ferrell 2006; Levitan 2012).

Blue mussels of the genus \emph{Mytilus} are external spawners and
provide an ideal experimental system for understanding the combined
effects of population density, gamete traits and sperm abundance on
fertilisation dynamics (Evans et al. 2012; Sherman et al. 2015; Evans
and Lymbery 2020). Blue mussels are found on hard substrates of
nearshore and intertidal habitats in temperate and subarctic regions of
the northern and sourthern hemispheres (Hilbish et al. 2000) and are
predominant species found in temperate Australian waters (Westfall and
Gardner 2013; Ab Rahim et al. 2016; Popovic et al. 2020; Zbawicka et al.
2021). Populations vary naturally in population abundance (Cockrell et
al. 2015) with likely concomitant variation in sperm concentrations
among natural spawning events. Moreover, recent work on
Australian\emph{Mytilus} has revealed that ecologically relevant
variation in sperm concentrations can have dramatic effects on
fertilisation kinetics (Sherman et al. 2015). Furthermore, there is
evidence from\emph{Mytilus} for strong patterns of gamete selectivitiy,
such that specific combinations of gametes from both sexes generate
predictable differences in fertilisation rates and offspring viability
(Evans et al. 2012; Oliver and Evans 2014; Sherman et al. 2015; Lymbery
et al. 2017). However, the extent to which such patterns depend on the
fertilisation environment has yet to be determined.

In this study we explore the effect of adult population density on
variation in gamete traits and fertilisation dynamics across a range of
sperm concentration environments in mussels from natural populations. We
expected that selection will have acted on gamete traits in both sexes
to optimise fertilization success under different egg-sperm ratios.
Specifically, we explore whether population origin influences gamete
traits in both sexes, and whether experimental adjustments to sperm-egg
ratios during \emph{in vitro} fertilisation trials influence
fertilisation kinetics and pairwise patterns of fertilisation rates
(i.e. gamete compatibility). One expectation from the latter trials is
that eggs will become more selective as the risk of polyspermy (high
sperm concentrations) increase, resulting stronger gametic
(male-by-female) interactions under high sperm densities.

\emph{Materials and Methods}

\textbf{COLLECTIONS AND SPAWNING OF ANIMALS}

We collected mussel broodstock from high and low density sites within
each of three locations in Port Phillip Bay, Victoria, Australia during
the May winter spawning season. These included Williamstown
(-37.861695°, 144.912751°), Geelong (-38.148770°, 144.390864°) and
Portarlington (-38.111790°, 144.659556°). Mussels were transported to
the Victorian Marine Science Consortium research laboratories at
Queenscliff and held in flow-through tanks at ambient temperature (16
°C). All animals were cleaned of epiphytes and other debris and used for
spawning on the day of collection using the approach of Pettersen et al.
(2010).

\textbf{COLLECTION OF GAMETES}

Gametes were harvested by inducing spawning using standard thermal
stress protocols (Pettersen et al. 2010). This involved cycling seawater
temperature between 16-24 °C to induce spawning. Males and females were
identified at the time of gamete release, rinsed with filtered seawater,
and isolated into individual spawning chambers (120 × 175 × 70 mm). Eggs
were rinsed through a 125\selectlanguage{greek}μ\selectlanguage{english}m mesh, and sperm through a 30\selectlanguage{greek}μ\selectlanguage{english}m mesh, to
remove any debris released from the adult mussel during spawning. The
concentration of sperm for each male was determined from three replicate
counts using an improved Neubauer haemocytometer and sperm
concentrations were initially standardized to 2 \selectlanguage{ngerman}×
10\textsuperscript{8}sperm ml\textsuperscript{-1}. A serial sperm
dilution was then carried out to obtain the desired experimental
concentrations of sperm for our experiments: 2 × 10\textsuperscript{2};
2 × 10\textsuperscript{3}; 2 × 10\textsuperscript{4}; 2 ×
10\textsuperscript{5}; 2 × 10\textsuperscript{6}; and 2 ×
10\textsuperscript{8} sperm ml\textsuperscript{-1}. Egg concentrations
were estimated from three replicate counts using a Beckman multisizer\selectlanguage{english} 3
Coulter counter and standardized to 2000 eggs ml\textsuperscript{-1}
(stock egg solution).

\textbf{FERTILISATION ASSAYS}

Our block cross-classified design involved a series of 2x2 \emph{in
vitro} fertilisation trials (following the analogous block North
Carolina II quantitative genetic breeding design described by Lynch and
Walsh (1998)), each involving two males (one from a high density and one
from a low density site from the same location) crossed with two females
(one from a high and one from a low density site from the same location)
in every pairwise combination. For each male-female cross, two replicate
fertilisation assays were carried out across each of the six different
sperm concentrations, giving a total of 48 fertilisation assays per
block. A total of five blocks were carried out for each of the three
locations sampled, giving a total of 15 blocks and 720 fertilisation
assays across all three locations. We conducted fertilisation assays in
sterile 24-well cell culture plates with a total fertilisation volume of
2 ml. This consisted of 1 ml of the stock egg solution (2000 eggs
total), and 1 ml of sperm solution, resulting in a final egg
concentration of 1000 eggs ml\textsuperscript{-1} and sperm
concentrations of: 1 x 10\textsuperscript{2}; 1 x 10\textsuperscript{3};
1 x 10\textsuperscript{4}; 1 x 10\textsuperscript{5}; 1 x
10\textsuperscript{6}; and 1 x 10\textsuperscript{8} sperm
ml\textsuperscript{-1}. All fertilisation assays within a block were
conducted immediately after gamete standardisation and within 1 minute
of each other although we also ensured that the time from the start of
spawning to fertilisation was recorded and included in the analysis to
control for potential gamete aging effects (`gamete age' in the model).
Fertilisation assays were left at room temperature for 3 hours before
samples were fixed with 1\% formalin. For each fertilisation assay, a
random sub-sample of approximately 100 eggs were observed under an
inverted microscope at 400x magnification and the number of fertilised
eggs were distinguished from unfertilised eggs by counting the number of
cells that had undergone cell division, or had a clearly visible
fertilisation envelope. Unfertilised eggs were identified from the lack
of cell division or the absence of a fertilisation envelope (Sherman et
al 2015). Abnormal eggs were identified by signs of irregular cleavage,
incomplete blastula development and by dissolution of the egg membrane
resulting in deformed embryos and/or the breaking apart of the
developing cell cluster (Lewis and Galloway 2009).

\textbf{GAMETE TRAITS AND MEASURES OF ADULT BODY CONDITION}

Female egg size was assessed from three replicate counts using a Beckman
multisizer\selectlanguage{english} 3 Coulter counter (mean number of eggs per female = 8,371 +-
1140 SE). To estimate sperm size, digital photographs of sperm were
taken using a digital camera attached to a microscope (OLYMPUS IX53, 20X
objective). Sperm length was measured for each male using the software
ImageJ (http://rsb.info.nih.gov/ij). Sperm length was measured in \selectlanguage{greek}μ\selectlanguage{english}m as
the distance from the tip of the head (excluding the protruding
acrosomal cap or `beak') to the end of the tail. Ten sperm were measured
for each male, and the average of the 10 measures was used in the
analysis.

Sperm motility was assessed using computer-assisted sperm analysis
(CEROS sperm tracker, Hamilton-Thorne, Beverley USA). Sperm motility was
assessed at two sperm concentrations (10\textsuperscript{6} and
10\textsuperscript{8}). For each individual, two 4 \selectlanguage{greek}μ\selectlanguage{english}l aliquots of the
sperm solution were placed in two separate wells of a 12-well Multi-test
slide and then covered with a coverslip. Sperm motility was therefore
assessed in two subsamples for each male at both sperm concentrations.
Given the high reported repeatability of sperm motility measures in blue
mussels (Fitzpatrick et al. 2012), we recorded the average of the two
subsamples for the ensuing analysis, and caution was taken to analyse
sperm in a random order with respect to the sperm concentration used.
From the CASA analyses, we obtained the percentage of motile sperm and a
series of parameters describing velocity and trajectory of motile sperm.
These parameters include average path velocity (VAP), straight-line
velocity (VSL), curvilinear velocity (VCL), lateral head displacement
(ALH), beat cross frequency (BCF), straightness (STR) and linearity
(LIN). Cut offs for static cells were the same as those used in previous
experiments by Eads et al. (2016). An average of 276.8 \selectlanguage{ngerman}± 37.0 SE sperm
tracks were analysed for each male at each concentration.

As body condition may influence fertilisation success (i.e. mussels in
better condition may have higher quality gametes) we controlled for this
potential confounding effect in our analysis. We recorded shell length
(mm) and flesh mass (g) from each brood parent and used these to
calculate a condition index using the residuals of flesh weight against
shell length.

\textbf{STATISTICAL ANALYSIS}

Differences in egg size between high- and low-density sites were
assessed using a General Linear Mixed Model (GLMM). This included egg
size as the response variable, density as a predictor (fixed effect),
location (random effect) and female condition as a covariate. Similarly,
differences in sperm length between low- and high-density sites were
assessed using sperm length as the response variable, density as a
predictor (fixed effect), location (random effect) and male condition as
a covariate.

Principal component analysis (PCA) was used to reduce the motility
parameters to two PCs with eigenvalues more than 1, explaining
respectively 60.75\% and 23.35\% of the variance (total variance
explained: 84.10\%). PC1 was predominantly loaded by the three velocity
measures (VAP, VSL \& VCL) and is therefore interpreted as a measure of
sperm swimming speed; PC2 was loaded most strongly by STR and LIN and is
therefore interpreted as a measure of sperm swimming straightness. These
two PCs (PC1 and PC2) were used in all subsequent analyses, and their
relationship with the original motility parameters is detailed in Table
1. We analysed differences in sperm motility between low- and
high-density populations at the two sperm concentrations
(10\textsuperscript{6} and 10\textsuperscript{8}, see above) using a
General Linear Mixed Model (GLMM) within the lme4 package of R using PC
scores (PC1 and PC2) as dependent variables, population density and
sperm density as fixed factors with their interactions, location as a
random effect and male condition as a covariate. The same model was run
to analyse the percentage of motile sperm (arcsine-transformed before
use). Means are presented with their standard errors (SE).

We analysed fertilisation success using Markov-chain Monte-Carlo
generalized linear mixed models in R (package MCMCglmm, (Hadfield
2010)). With this Bayesian mixed model approach, we modelled the
proportion of normally and abnormally fertilised eggs following a
binomial distribution and obtained both an estimate of the components of
variance and an estimate of the interval of credibility. All models were
run for 1.3 × 10\textsuperscript{7} iterations, with a thinning interval
of 100 (i.e., only one iteration from every 100 in the Markov chain was
used to estimate the posterior distribution of the parameters to reduce
the occurrence of autocorrelation between successive iterations), and a
burn-in of 3 × 10\textsuperscript{5} (i.e., we discarded the first 3 ×
10\textsuperscript{5} models of the simulation to avoid issues with
autocorrelation).

For the Bayesian models we included the fixed effects of population (3
levels, Geelong, Portarlington, and Williamstown), gamete age (time
elapsed between spawning and fertilisation), body condition (see above),
sperm concentration (fitted both as a linear and quadratic term),
density of the male (high vs low), density of the female (high vs low),
their interaction with each other and with sperm concentration. The
random effects used in the model included block (\emph{V}
\textsubscript{block}), identity of male (\emph{V}
\textsubscript{male}), identity of female (\emph{V}
\textsubscript{female}), and an interaction between male and female IDs
(\emph{V} \textsubscript{male × female}). The residual variance
(\emph{V\textsubscript{e}} ) of the model represents the variance
between replicates within a given male and female pair.

A necessary step in Bayesian statistical analyses is to set priors
before running the models. The term prior refers to the prior
distribution of a parameter before the data are analysed. The level of
information of the prior can vary from noninformative to highly
informative. When knowledge about the relationship between the variables
in the model is low, it is best to run the model with different priors
and to check whether these different priors provide different posterior
distributions (Hadfield 2010). We therefore ran the models using inverse
Wishart priors (equivalent to an inverse gamma distribution with
shape=scale=0.001; V=1, nu=0.002), parameter expanded priors (V=1, nu=1,
alpha.mu=0, alpha.V=1000), and non-informative improper priors (V=1e-16,
nu=-2). Although we present results from the model using parameter
expanded priors, the conclusions did not qualitatively change according
to prior specifications. We inspected the 95\% highest posterior density
(HPD) intervals associated with each fixed effect to check whether they
overlapped with zero. A 95\% HPD interval contains most of the posterior
distribution and is analogous to a confidence interval in the
frequentist approach; we considered estimates with 95\% HPD intervals
overlapping with zero as non-significant.

We ran an initial model for the proportion of normally fertilised eggs
while excluding data from the highest sperm concentration to facilitate
the interaction between sperm concentration and population density
(i.e., including the highest sperm concentration made the fertilisation
curve very complex). To model the proportion of abnormally fertilised
eggs, we ran a second model while keeping data in the highest sperm
concentration. The proportion of abnormally fertilised eggs was very low
at other sperm concentrations.

We ran a third model, this time including data from all sperm
concentrations and allowed variance components to vary with sperm
concentration. We used the ``idh()'' function to model heterogeneous
variance components for \emph{V} \textsubscript{male},\emph{V}
\textsubscript{female}, and \emph{V} \textsubscript{male × female}
according to each concentration. Hence, there were 20 variance
components estimated in this model (i.e., \emph{V}
\textsubscript{male},\emph{V} \textsubscript{female}, and \emph{V}
\textsubscript{male × female} estimated separately for sperm
concentrations and a single\emph{V} \textsubscript{block} and
\emph{V\textsubscript{e}} ). By contrast to Gaussian data, with binomial
data it is not recommended to compare different models using the
deviance information criteria (an index produced by MCMCglmm models that
balances the fit of the model based on the number of parameters used in
the model). Thus, we cannot formally test whether model fit was improved
by allowing heterogeneous variance components across sperm
concentrations. Instead, we inspected the 95\% HPD intervals associated
with each random effect to check whether they overlapped. We considered
estimates with non-overlapping 95\% HPD intervals as significantly
different (Hadfield 2010). Note that, as the lower limit of a variance
component is bound to zero, its lower 95\% HPD can be extremely close
to, but cannot overlap zero. Thus, inspection of the HPDs cannot be
formally used to test whether a variance component is significantly
greater than zero (Hadfield 2010). Nevertheless, the 95\% credible
intervals around the variance estimates provide a measure of the
precision of the estimate and allowed us to test whether \emph{V}
\textsubscript{male × female} differed across sperm concentrations.

Data Availability statement

Data and associated r-code for the fertilisation analysis can be found
here:
https://datadryad.org/stash/share/Yx-wxEJsD-SjrHkHG9lVShv1Qw-KFTAT55vBMvUBVQ4

\emph{RESULTS}

\textbf{GAMETE TRAITS}

Egg size did not differ significantly between females from high and low
density sites (mean egg size: Female\textsubscript{(high)} = 64.36 \selectlanguage{greek}μ\selectlanguage{english}m \selectlanguage{ngerman}±
0.359 versus Female\textsubscript{(low)} = 64.35 \selectlanguage{greek}μ\selectlanguage{english}m \selectlanguage{ngerman}± 0.244 , GLMM:
F\textsubscript{1, 29} = 0.01, P = 0.939). However, we did detect a
significant difference in egg size among locations (mean egg size:
Williamstown = 64.27 \selectlanguage{greek}μ\selectlanguage{english}m; \selectlanguage{ngerman}± 0.233 Geelong = 65.65 \selectlanguage{greek}μ\selectlanguage{english}m \selectlanguage{ngerman}± 0.179;
Portarlington = 63.43 \selectlanguage{greek}μ\selectlanguage{english}m \selectlanguage{ngerman}± 0.308, GLMM: F\textsubscript{2, 29} = 18.39,
P \textless{} 0.0001). Our analysis of sperm length revealed a
significant difference between high- and low-density sites (GLMM:
F\textsubscript{1, 29} = 5.01, P = 0.035), with sperm from low density
sites being longer compared with sperm from high density sites (mean
sperm length: low density = 51.13 \selectlanguage{greek}μ\selectlanguage{english}m \selectlanguage{ngerman}± 0.547 cf. high density = 49.86 \selectlanguage{greek}μ\selectlanguage{english}m
\selectlanguage{ngerman}± 0.387). There was no significant difference in sperm length among
locations (GLMM: F\textsubscript{2, 29} = 0.11, P = 0.893).

There was no effect of population density (F\textsubscript{1,24.159} =
0.4036, P = 0.531) or sperm density (F\textsubscript{1,25.2} = 0.520, P
= 0.478) on sperm motility PC1 scores, or their interaction
(F\textsubscript{1,25.1} = 0.04, P = 0.845). Similarly, PC2 scores were
not affected by population density (F\textsubscript{1,28.5} = 0.25, P =
0.620), sperm density (F\textsubscript{1,29.8} = 0.24, P = 0.627) or
their interactions (F\textsubscript{1,29.6} = 0.07, P = 0.797). Male
condition also did not affect sperm motility PC1
(F\textsubscript{1,37.6} = 0.13, P = 0.909) or PC2
(F\textsubscript{1,43.9} = 0.63, P = 0.431) scores. The percentage of
motile sperm was not affected by population density
(F\textsubscript{1,27.6} = 0.04, P = 0.841), but it was affected by
sperm density (F\textsubscript{1,27.1} = 0.45, P \textless{} 0.001). We
also detected no significant effects of the interaction between
population and sperm density (F\textsubscript{1,26.9} = 0.014, P =
0.907) or the effect or male condition (F\textsubscript{1,37.1} = 1.80,
P = 0.882) on the percentage of motile sperm. Sperm were on average more
motile at the 1 × 10\textsuperscript{8} concentration (31.82\% ± 2.22)
compared to the 1 × 10\textsuperscript{6} concentration (14.42\% ±
2.85).

\textbf{FERTILISATION}

The percentage of successfully fertilised eggs steeply increased with
sperm concentration but dropped significantly beyond 1 ×
10\textsuperscript{6} (Fig. 1a). Beyond this concentration,
\textasciitilde{}60 to 80\% of eggs were abnormally fertilised (Fig.
1b). Therefore, had we simply counted fertilised vs unfertilised eggs,
without making a distinction between normally vs abnormally fertilised
eggs, we would have seen a continuous increase in proportion of
fertilised eggs (Fig. 1c) while in fact many of the fertilised eggs at
the highest sperm concentration (1 × 10\textsuperscript{8}) were
non-viable.

In the first Bayesian model, we analysed the proportion of normally
fertilised eggs after excluding the highest sperm concentration (1 ×
10\textsuperscript{8}). There was a significant effect of population of
origin, sperm concentration (both linear and quadratic terms), female
density, and a significant interaction between female density and sperm
concentration (Table 2). Females from low density areas had lower
fertilisation success across all sperm concentrations (Fig. 1a), but the
significant interaction indicated that this effect becomes less
important as sperm concentration increases (Table 2). We detected no
effect of male density on fertilisation success (Table 2). In the second
model, in which we analysed the proportion of abnormally fertilised eggs
at the highest sperm concentration (1 × 10\textsuperscript{8}), we found
no significant effect of population, body condition, gamete age, female
density, male density (or their interaction) on the proportion of
abnormally fertilised eggs (Table 3).

Finally, our third Bayesian model revealed some differences in the
variance estimates across sperm concentrations. The variance estimates
associated with intrinsic male effects (\emph{V} \textsubscript{male})
were low across all sperm concentrations (range: \textless{}0.01 to
0.01; Table 4). By contrast, effects attributable to females (\emph{V}
\textsubscript{female}) were relatively high (range: 0.62 to 4.96; Table
4). The ``male × female'' interaction effects (\emph{V}
\textsubscript{male × female}) were relatively low at low sperm
concentration (Fig. 2), but increased at higher sperm concentration
(Table 4, Fig. 2).

\emph{Discussion}

In this study we tested for signatures of post-mating selection on
gamete traits in relation to population density, and possible
interactive effects of population density and sperm concentration on
sperm motility and fertilisation rates. Our study yielded four key
results: 1) males from high density populations produce smaller sperm
compared with males from low density populations, although we found no
difference in egg size between females from different population
densities; 2) females from low density populations have lower
fertilisation success, although this becomes less important as sperm
concentration increases; 3) variances in fertilisation success were
higher for females than males; and 4) gamete compatibility between males
and females increases as sperm concentrations increase.

We found that males from high density populations, where sperm
competition would be expected to be more prevalent (Evans and Lymbery
2020), produced smaller sperm compared to males from low density
populations. To the extent that sperm production trades-off against
sperm size (Parker 1982; Gomendio et al. 1991; Tourmente et al. 2011),
this result supports the prediction that an increase in the overall
magnitude of sperm competition should select for a greater number of
smaller sperm, while lower sperm competition risk should result in the
production of fewer longer sperm (Parker 1982; Stockley et al. 1997;
Gage and Morrow 2003; García-González and Simmons 2007; Lüpold et al.
2020). These results support comparative studies of fish that show sperm
length decreased with sperm competition risk (Stockley et al. 1997),
although some studies have found the opposite, with among species
comparisons showing a positive relationship between sperm competition
risk and sperm size (Gage 1994; Byrne et al. 2003; Lifjeld et al. 2010;
Johnson et al. 2013). The reason for such varying and contrasting
results likely arises from the complex relationship between sperm
morphology and sperm performance (e.g. swimming speed and/or
fertilisation potential). In some species (especially internally
fertilisation taxa) longer sperm may be associated with improved
swimming performance and provide a competitive advantage under sperm
competition (Gomendio et al. 1991; Parker et al. 2010; Johnson et al.
2013). However, sperm length may also be associated with sperm
longevity, with longer, larger sperm living longer than smaller sperm.
If so, producing longer-lived sperm may confer an important advantage in
broadcast spawners in low density populations, allowing more time for
sperm-egg encounters and increased fertilisation success (however see,
Levitan 2000). A study of the broadcast spawning
tubeworm\emph{Galeolaria gemineoa} showed that sperm with small heads
but long tails were favoured in high-concentration environments, whereas
sperm with long heads were favoured at low concentrations and old ages
(Johnson et al. 2013). The longer sperm produced by males from low
density populations detected in this study may provide an advantage if
they have greater longevity, although longevity was not directly
assessed in this study. Our analysis also showed that longer sperm from
low density populations did not show greater motility or swimming
speeds, suggesting that the larger size did not confer a swimming
advantage. The relation between sperm size and fertilisation success
under sperm competition is complex and appears to be highly context
dependent and likely to covary with sperm swimming traits and longevity.

Theoretical and empirical studies predict that egg size should reflect
adult density, with females from low-density populations producing
larger eggs than their high-density counterparts, because larger eggs
present larger targets for searching sperm (Levitan 2006; Crean and
Marshall 2008; Evans and Lymbery 2020). In the present study we found no
difference in mean egg size between females from high- and low-density
populations. However, egg size is not the only mechanisms available to
females for increasing the effective target size of their eggs. For
example, it is well established that the eggs of many broadcast spawners
release sperm chemoattractants, which are thought to increase the
effective target size of eggs, thus making them more `visible' to
searching sperm (e.g. for theory see Jantzen 2001). While we currently
lack explicit evidence that females can facultatively adjust the
production of sperm chemoattractants to match the fertilisation
environment, or that selection may favour increased production of such
attractants in populations with persistently low adult densities (and
therefore sperm limited), the idea of testing for differences either in
the composition or volume of sperm chemoattractants across populations
has merit. Such an adaptation may represent a more cost-effective
mechanism for increasing the target size of eggs compared to increasing
the structural size of eggs in sperm-limited environments and offers an
exciting area for future research.

We assessed fertilisation rates of females from low- and high-density
populations across a range of sperm concentrations. As population
densities decrease and the risk of sperm limitation increases, we
expected that females would produce eggs that are more readily
fertilised (i.e. greater fertilisation success at lower sperm
concentrations), while in high sperm density environments females should
increase ovum defences to reduce the risk of polyspermy (Frank 2000;
Firman and Simmons 2013; Kosman and Levitan 2014). Surprisingly, we
found no evidence to support these ideas. Indeed, we found that females
from high density sites produced eggs that were more readily fertilised
at lower sperm concentrations than eggs from females originating from
low density populations, although this difference became progressively
less apparent as sperm concentrations increased. Furthermore, our
finding that at the highest sperm concentration (2 ×
10\textsuperscript{8} sperm ml\textsuperscript{-1}), females from both
high- and low-density populations experienced similar magnitudes of
abnormally fertilised eggs fails to support the idea that females from
high density populations are better at blocking polyspermy compared to
females form low density populations (Kosman and Levitan 2014).

Interestingly, we found that the variance components for (normal)
fertilization rates across the range of sperm concentrations were
generally higher in females than in males, but also that variances for
females were initially high at lower sperm concentrations (2 ×
10\textsuperscript{2} \& 2 ×
10\textsuperscript{3}ml\textsuperscript{-1}), decreased when sperm
concentrations were at an intermediate level (2 × 10\textsuperscript{4}
\& 2 × 10\textsuperscript{5} ml\textsuperscript{-1}), before rising
sharply when sperm concentrations exceeded 2 ×
10\textsuperscript{6}ml\textsuperscript{-1}. Qualitatively similar
patterns have been reported in other broadcast spawning invertebrates
(Levitan 2004), suggesting that under sperm limitation, where average
fertilisation rates are low, there will be heightened opportunity for
selection on female traits that improve fertilisation rates. Under such
conditions, for example, we might expect stronger selection for
increased egg size and/or the heightened production of chemoattractants
that increase sperm-egg encounter rates (see Evans and Lymbery 2020).
Under intermediate sperm concentrations, fertilisation rates were
generally high (\textasciitilde{}80\%) and the variance in normal
fertilisation rates was consequently very low. By contrast, despite high
overall fertilisation rates in the highest sperm concentration groups
(\textgreater{}2 x 10\textsuperscript{6} ml\textsuperscript{-1}), the
proportion of normally fertilised eggs decreased dramatically at high
sperm concentrations with a concomitant increase in the variance in
normally fertilised eggs (see Fig. 1a). Together these findings suggest
that the opportunity for selection on egg traits will depend critically
on local spawning conditions, and that such patterns may be reflected on
a broader spatial scale in divergent populations with varying adult
densities.

Our fertilisation assays indicated that as sperm concentration
increased, gametic compatibility effects became increasingly important.
This suggests that under sperm limited conditions, where the risk of
fertilisation failure is higher, any benefits associated with selecting
genetically compatible sperm (Kosman and Levitan 2014; Oliver and Evans
2014) are offset by the direct costs of leaving many eggs unfertilised.
However, as sperm concentration increases, eggs can afford to become
`choosier' as this will ensure that fertilisations are biased toward
genetically compatible sperm (Sherman et al. 2015; Lymbery et al. 2017)
whilst avoiding the direct costs associated with polyspermy. Although we
have yet to understand the mechanistic basis that underlie these
dynamics patterns of sperm-egg interaction, we suspect that sperm
chemoattraction and gamete surface proteins play important roles in
differentially regulating sperm-egg encounter rates across the sperm
concentration continuum (Evans and Sherman 2013). Irrespective of the
underlying mechanisms, our results provide further support to an
increasing number of studies that have shown that local environmental
conditions can influence the magnitude of compatibility effects between
male-female combinations (Levitan and Ferrell 2006; Levitan et al. 2007;
Nystrand et al. 2011; Lymbery and Evans 2013; Sherman et al. 2015;
Rudin-Bitterli et al. 2018). Collectively, these studies highlight the
importance of testing for compatibility effects across a range of
ecologically relevant environmental conditions.

In conclusion, our study revealed significant effects of population
density and sperm concentration on gamete morphology and fertilisation
dynamics, respectively. While the extent of variation at the population
level may be determined by both environmental and/or genetic factors,
the critical importance of gamete-level natural and sexual selection in
broadcast spawners (Evans and Sherman 2013; Evans and Lymbery 2020)
leads us to predict that much of the variation we observe in these
populations is adaptive. However, we also report highly dynamic patterns
of fertilisation across experimentally altered sperm environments,
highlighting the importance of phenotypic plasticity in governing
sperm-egg interactions and the likely dynamic selective environment in
which fertilisation plays out. We eagerly anticipate future work that
seeks to understand the extent to which the mechanisms underlying these
dynamic patterns of sperm-egg interaction are themselves plastic in
their expression.

\emph{ACKNOWLEDGEMENTS}

The authors would like to thank the Victoria Shellfish Hatchery for
advice and support in the collection and spawning of mussels. Funding
was provided by grants from the Australian Research Council (ARC
Discovery) to JPE (DP150103266) and Deakin University to CDHS. We thank
the Deakin Queenscliff Marine Science Centre for use of the aquarium and
seawater systems.

\emph{Conflict of interest}

The authors declare no conflict of interest.

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Table 1. Principal component analysis of sperm motility parameters.
These parameters include average path velocity (VAP), straight-line
velocity (VSL), curvilinear velocity (VCL), lateral head displacement
(ALH), beat cross frequency (BCF), straightness (STR) and linearity
(LIN). Correlation coefficient (r) and the percentage contribution of
each parameter to the principal component score are provided.\selectlanguage{english}
\begin{longtable}[]{@{}lllll@{}}
\toprule
\textbf{Component} & \textbf{PC1} & \textbf{PC1} & \textbf{PC2} &
\textbf{PC2}\tabularnewline
\midrule
\endhead
& \textbf{r} & \textbf{\%} & \textbf{r} & \textbf{\%}\tabularnewline
VAP & 0.94 & 20.78 & -0.30 & 5.62\tabularnewline
VSL & 0.98 & 22.62 & 0.11 & 0.77\tabularnewline
VCL & 0.87 & 17.87 & -0.38 & 8.89\tabularnewline
ALH & 0.89 & 18.44 & -0.20 & 2.49\tabularnewline
BCF & -0.49 & 5.69 & 0.26 & 4.07\tabularnewline
STR & 0.38 & 3.40 & 0.90 & 49.86\tabularnewline
LIN & 0.69 & 11.21 & 0.68 & 28.30\tabularnewline
\bottomrule
\end{longtable}

\textbf{Table 2.} Parameters from a mixed model of proportion of eggs
normally fertilized across different sperm concentration in mussels,
fitted using a Bayesian approach. Shown are posterior means and the 95\%
highest posterior density (HPD) intervals for (\emph{a} ) random effects
of measurement block (\emph{V} \textsubscript{block}), male identity
(\emph{V} \textsubscript{male}), female identity (\emph{V}
\textsubscript{female}), specific combinations of males and females
(\emph{V} \selectlanguage{ngerman}\textsubscript{male × female}), and specific environment
(\emph{V\textsubscript{e}} ; residual variance) and (\emph{b} ) fixed
effects of population (3 levels; Geelong as the reference), body
condition, gamete age (minutes), sperm concentration (continuous
variable fitted both as a as linear and quadratic term), density of the
male, density of the female, and their interactions with each other and
with sperm concentration.\selectlanguage{english}
\begin{longtable}[]{@{}llllll@{}}
\toprule
& & & 95\% HPD interval & 95\% HPD interval &\tabularnewline
\midrule
\endhead
& & estimate & lower & upper & pMCMC\tabularnewline
(a) random effects: & (a) random effects: & & & &\tabularnewline
& \emph{V}\textsubscript{block} & 0.706 & 0.000 & 2.223 &\tabularnewline
& \emph{V}\textsubscript{male} & 0.058 & 0.000 & 0.184 &\tabularnewline
& \emph{V}\textsubscript{female} & 1.416 & 0.575 & 2.500
&\tabularnewline
& \emph{V}\selectlanguage{ngerman}\textsubscript{male × female} & 0.045 & 0.000 & 0.127
&\tabularnewline
& \emph{V\textsubscript{e}} & 1.430 & 1.224 & 1.630 &\tabularnewline
(b) fixed effects: & (b) fixed effects: & & & &\tabularnewline
& intercept & 0.443 & -2.076 & 3.276 & 0.770\tabularnewline
& population\textsubscript{{[}Portarlington{]}} & -0.702 & -2.262 &
1.056 & 0.398\tabularnewline
& population\textsubscript{{[}Williamstown{]}} & -1.411 & -3.393 & 0.345
& 0.132\tabularnewline
& \textbf{male body condition index} & \textbf{-0.255} & \textbf{-0.508}
& \textbf{-0.046} & \textbf{0.044}\tabularnewline
& female body condition index & -0.203 & -0.894 & 0.637 &
0.584\tabularnewline
& male gamete age & 0.001 & -0.008 & 0.010 & 0.904\tabularnewline
& female gamete age & 0.000 & -0.011 & 0.011 & 0.962\tabularnewline
& \textbf{sperm concentration} & \textbf{33.126} & \textbf{28.735} &
\textbf{37.249} & \textbf{\textless{}0.001}\tabularnewline
& \textbf{sperm concentration\textsuperscript{2}} & \textbf{13.124} &
\textbf{10.690} & \textbf{15.503} &
\textbf{\textless{}0.001}\tabularnewline
& male density\textsubscript{{[}low{]}} & 0.113 & -0.442 & 0.671 &
0.682\tabularnewline
& \textbf{female density\textsubscript{{[}low{]}}} & \textbf{-1.308} &
\textbf{-2.266} & \textbf{-0.225} & \textbf{0.014}\tabularnewline
& male\textsubscript{{[}low{]}} \selectlanguage{ngerman}× female\textsubscript{{[}low{]}}
density & -0.106 & -0.551 & 0.375 & 0.650\tabularnewline
& male density\textsubscript{{[}high{]}} \selectlanguage{ngerman}× sperm concentration & -0.027
& -0.178 & 0.113 & 0.696\tabularnewline
& \selectlanguage{ngerman}\textbf{female density\textsubscript{{[}low{]}} × sperm concentration}
& \textbf{0.195} & \textbf{0.062} & \textbf{0.341} &
\textbf{0.008}\tabularnewline
\bottomrule
\end{longtable}

\textbf{Table 3.} Parameters from a mixed model of proportion of eggs
abnormally fertilized at the highest sperm concentration in mussels,
fitted using a Bayesian approach. Shown are posterior means and the 95\%
highest posterior density (HPD) intervals for (\emph{a} ) random effects
of measurement block (\emph{V} \textsubscript{block}), male identity
(\emph{V} \textsubscript{male}), female identity (\emph{V}
\textsubscript{female}), specific combinations of males and females
(\emph{V} \selectlanguage{ngerman}\textsubscript{male × female}), and specific environment
(\emph{V\textsubscript{e}} ; residual variance) and (\emph{b} ) fixed
effects of population (3 levels; Geelong as the reference), body
condition, gamete age (minutes), density of the male, density of the
female, and their interaction.\selectlanguage{english}
\begin{longtable}[]{@{}llllll@{}}
\toprule
& & & 95\% HPD interval & 95\% HPD interval &\tabularnewline
\midrule
\endhead
& & Estimate & Lower & Upper & Probability (MCMC)\tabularnewline
(a) random effects: & (a) random effects: & & & &\tabularnewline
& \emph{V}\textsubscript{block} & 3.928 & 0.001 & 11.090
&\tabularnewline
& \emph{V}\textsubscript{male} & 0.834 & 0.000 & 3.418 &\tabularnewline
& \emph{V}\textsubscript{female} & 1.788 & 0.000 & 5.956
&\tabularnewline
& \emph{V}\selectlanguage{ngerman}\textsubscript{male × female} & 4.100 & 1.136 & 7.083
&\tabularnewline
& \emph{V\textsubscript{e}} & 0.113 & 0.031 & 0.203 &\tabularnewline
(b) fixed effects: & (b) fixed effects: & & & &\tabularnewline
& intercept & 2.762 & -3.245 & 7.958 & 0.282\tabularnewline
& population\textsubscript{{[}Portarlington{]}} & -1.504 & -4.822 &
2.203 & 0.356\tabularnewline
& population\textsubscript{{[}Williamstown{]}} & -3.039 & -6.818 & 1.163
& 0.130\tabularnewline
& male body condition index & 0.218 & -0.690 & 1.312 &
0.648\tabularnewline
& female body condition index & 0.460 & -0.827 & 1.963 &
0.528\tabularnewline
& male gamete age & 0.015 & -0.008 & 0.035 & 0.192\tabularnewline
& female gamete age & -0.010 & -0.029 & 0.011 & 0.324\tabularnewline
& male density\textsubscript{{[}low{]}} & -0.606 & -2.470 & 1.123 &
0.510\tabularnewline
& female density\textsubscript{{[}low{]}} & 0.725 & -1.007 & 2.613 &
0.416\tabularnewline
& male\textsubscript{{[}low{]}} \selectlanguage{ngerman}× female\textsubscript{{[}low{]}}
density & 0.618 & -1.378 & 2.896 & 0.548\tabularnewline
\bottomrule
\end{longtable}

\textbf{Table 4.} Variance estimates from a mixed model of proportion of
eggs normally fertilized across different sperm concentration in
mussels, fitted using a Bayesian approach. Shown are posterior modes and
the 95\% highest posterior density (HPD) intervals for random effects of
measurement block (\emph{V} \textsubscript{block}), male identity
(\emph{V} \textsubscript{male}), female identity (\emph{V}
\textsubscript{female}), specific combinations of males and females
(\emph{V} \selectlanguage{ngerman}\textsubscript{male × female}), and specific environment
(\emph{V\textsubscript{e}} ; residual variance).\emph{V}
\textsubscript{male}, \emph{V} \textsubscript{female}, and\emph{V}
\textsubscript{male × female} were fitted heterogeneously for each sperm
concentration.\selectlanguage{english}
\begin{longtable}[]{@{}llll@{}}
\toprule
variance component & posterior mode & 95\% HPD & 95\% HPD\tabularnewline
& & lower & upper\tabularnewline
\emph{V}\textsubscript{block} & 0.28 & \textless{}0.01 &
1.82\tabularnewline
\emph{V}\textsubscript{male} {[}2 \selectlanguage{ngerman}× 10\textsuperscript{2}{]} &
\textless{}0.01 & \textless{}0.01 & 0.05\tabularnewline
\emph{V}\textsubscript{male} {[}2 \selectlanguage{ngerman}× 10\textsuperscript{3}{]} &
\textless{}0.01 & \textless{}0.01 & 0.03\tabularnewline
\emph{V}\textsubscript{male} {[}2 \selectlanguage{ngerman}× 10\textsuperscript{4}{]} &
\textless{}0.01 & \textless{}0.01 & 0.08\tabularnewline
\emph{V}\textsubscript{male} {[}2 \selectlanguage{ngerman}× 10\textsuperscript{5}{]} & 0.01 &
\textless{}0.01 & 2.19\tabularnewline
\emph{V}\textsubscript{male} {[}2 \selectlanguage{ngerman}× 10\textsuperscript{6}{]} & 0.01 &
0.00 & 1.25\tabularnewline
\emph{V}\textsubscript{male} {[}2 \selectlanguage{ngerman}× 10\textsuperscript{8}{]} & 0.02 &
0.00 & 2.71\tabularnewline
\emph{V}\textsubscript{female} {[}2 \selectlanguage{ngerman}× 10\textsuperscript{2}{]} & 1.51 &
0.68 & 2.68\tabularnewline
\emph{V}\textsubscript{female} {[}2 \selectlanguage{ngerman}× 10\textsuperscript{3}{]} & 1.12 &
0.56 & 2.18\tabularnewline
\emph{V}\textsubscript{female} {[}2 \selectlanguage{ngerman}× 10\textsuperscript{4}{]} & 0.62 &
0.23 & 1.49\tabularnewline
\emph{V}\textsubscript{female} {[}2 \selectlanguage{ngerman}× 10\textsuperscript{5}{]} & 1.96 &
0.00 & 4.97\tabularnewline
\emph{V}\textsubscript{female} {[}2 \selectlanguage{ngerman}× 10\textsuperscript{6}{]} & 4.67 &
1.28 & 16.19\tabularnewline
\emph{V}\textsubscript{female} {[}2 \selectlanguage{ngerman}× 10\textsuperscript{8}{]} & 4.96 &
1.16 & 41.24\tabularnewline
\emph{V}\selectlanguage{ngerman}\textsubscript{male × female} {[}2 × 10\textsuperscript{2}{]} &
0.06 & \textless{}0.01 & 0.19\tabularnewline
\emph{V}\selectlanguage{ngerman}\textsubscript{male × female} {[}2 × 10\textsuperscript{3}{]} &
\textless{}0.01 & \textless{}0.01 & 0.12\tabularnewline
\emph{V}\selectlanguage{ngerman}\textsubscript{male × female} {[}2 × 10\textsuperscript{4}{]} &
0.18 & 0.09 & 0.42\tabularnewline
\emph{V}\selectlanguage{ngerman}\textsubscript{male × female} {[}2 × 10\textsuperscript{5}{]} &
0.75 & 0.27 & 1.65\tabularnewline
\emph{V}\selectlanguage{ngerman}\textsubscript{male × female} {[}2 × 10\textsuperscript{6}{]} &
0.56 & 0.11 & 1.17\tabularnewline
\emph{V}\selectlanguage{ngerman}\textsubscript{male × female} {[}2 × 10\textsuperscript{8}{]} &
2.33 & 0.99 & 4.47\tabularnewline
\emph{V\textsubscript{e}} & 0.05 & 0.03 & 0.07\tabularnewline
\bottomrule
\end{longtable}

\textbf{Figure 1.} Proportion of (a) normally, (b) abnormally, and (c)
total (=normally+abnormally) fertilized eggs as function of sperm
concentration in mussels collected from high (H) and low (L) population
density and mated in a fully factorial fertilisation design. For each
experimental block, four females were paired with four males
(and\emph{vice versa} ) at six different sperm concentrations. Each line
within a panel represent the mean of a specific male and female
population density. Hence, comparing the red vs blue lines shows the
difference between H and L females. Comparing squared vs circles shows
the differences between H and L males.

\textbf{Hosted file}

\verb`image1.emf`  available at \url{https://authorea.com/users/441240/articles/683471-population-density-effects-on-gamete-traits-and-fertilisation-dynamics-under-varying-sperm-environments-in-mussels}

\textbf{Figure 2.} Variance in fertilization success attributed to the
interaction between male and female identity (\emph{V}
\selectlanguage{ngerman}\textsubscript{male × female}) across sperm concentrations in mussels.
Black dots show posterior modes and the lines show 95\% confidence
intervals (CI; highest posterior density intervals) from the MCMCglmm
model.

\textbf{Hosted file}

\verb`image2.emf`  available at \url{https://authorea.com/users/441240/articles/683471-population-density-effects-on-gamete-traits-and-fertilisation-dynamics-under-varying-sperm-environments-in-mussels}

\selectlanguage{english}
\FloatBarrier
\end{document}

