1. Fertilization Success in Altered Bivalve Populations: Implications for Restoration
Mark W. Luckenbach1, Elizabeth North2, M. Lisa Kellogg3, Roger Mann4, Steve M. Allen5 and Kennedy T. Paynter2,3
1Virginia Institute of Marine Science, College of William and Mary, Eastern Shore Laboratory
2University of Maryland Center for Environmental Studies,
3University of Maryland
4Virginia Institute of Marine Science, College of William and Mary
5Oyster Recovery Partnership

2. Problem Description
Fertilization success in free-spawning, sessile marine bivalves is dependent upon gametes making contact.
Many of the shellfish populations that we seek to protect or restore currently exist at low population density, e.g.,
Argopecten irradians Mercenaria mercenaria
Crassostrea virginica Arctica islandica
Restoration activities that add bivalves as broodstock do so with little basis for determining the density required to achieve high fertilization success.
Moreover, the addition of broodstock is often done without regard for the sex ratio, anticipated gamete production or potential fertilization success.

3. Problem Description
High fecundity in these species can lead to the expectation that a small population size is sufficient to effect a recovery.
For instance:
eggs per ♀ at a density of 100 – 102 ♀’s m-2 yields
1010 – 1013 eggs hectare-1
Assumptions about how many of these eggs are fertilized has the potential to propagate errors through demographics models that are several orders of magnitude.

4. Some Preliminary Findings with Crassostrea virginica
(Kellogg et al ICSR)
108
109
1010
1011
1012
High Sperm:Egg
Bolingbroke Sand
Low Sperm:Egg
Potentially Sperm Limited

5. Objectives
1) Better understand the factors that affect fertilization success, including…
gamete concentrations
fertilization efficiency (avg. # sperm to fertilize an egg)
turbulent mixing
2) Ultimately, we want to use this, coupled with density, size and fecundity estimates from the field, to estimate not only egg production, but also fertilization success in natural and restored bivalve populations.

6. Approach
Construct and parameterize a computational model which predicts fertilization success based upon contact between gametes in a turbulent medium.
2) Conduct laboratory experiments with Crassostrea gametes using field-relevant turbulent mixing conditions to test initial model predictions.
Refine the model predictions using experimental results.
4) Repeat 2 – 3 as necessary.

7. Fertilization Success Model
Predicts concentration of fertilized eggs over time when mixed with sperm of a given concentration:
where U = concentration of unfertilized eggs (number cm-3)
and
F = concentration of fertilized eggs (number cm-3)
f = fertilization constant (=1 if every contact results in fertilization)
dt = time interval (s)
ε = contact rate of sperm with each egg (number s-1).

8. Fertilization Success Model
The contract rate of egg and sperm (E) [After Rothschild & Osborn (1988), Evans (1989), Visser & MacKenzie (1998)]:
where c = concentration of ‘prey’ particles (e.g., sperm concentration, number cm-3)
and
R = reactive distance of ‘predator’ particles (e.g., effective egg radius, cm)
u = swimming velocity of ‘prey’ particles (e.g., sperm swimming speed, cm s-1)
v = randomly directed motion of ‘predator’ particles (e.g., v = 0 for eggs)
w = root-mean-square turbulent velocity, (cm s-1):
where a = constant [1.37 or 1.9 according to references in Visser and MacKenzie (1989)]
d = turbulence length scale [d = R according to Visser and MacKenzie (1989)]
ε = turbulent dissipation rate (cm2 s-3).

9. Preliminary model run examples
Turbulent energy dissipation rates
ε = cm2 s-3
ε = cm2 s-3
ε = cm2 s-3
Preliminary model run examples
Unfertilized egg conc. = cm-3
Sperm concentration = 1000 cm-3
Fertilization efficiency = 0.01
Fertilization efficiency = 0.03
Fertilization efficiency = 0.1
Fertilization efficiency = 0.2
Fertilization efficiency = 0.5
Fertilization efficiency = 1.0

10. Solutions for contact rates when the following parameters were varied: A) sperm concentration (note the log scale), B) sperm swimming speed and contact (egg) radius, and C) turbulent dissipation rate (e) and the constant a. Open symbols indicate ‘base-case’ solutions.

11. Turbulent mixing Grid-stirred chambers
Turbulent energy dissipation rates 1) measured in Chesapeake Bay and 2) occurring in the grid-stirred chambers with different motor speeds (colored lines).
Field data courtesy of Larry Sanford, UMCES Horn Point Laboratory
Turbulent mixing
Grid-stirred chambers
Mixing controlled by motor speed
Examples of initial release of dye (left) and final distribution of dye (right) in grid chambers.
Average turbulent energy dissipation rates (e, cm2 s-3), average turbulent shear (g, s-1), and Reynolds number at different motor speeds (RPM) predicted for the grid- stirred chambers.

12. Summary of sperm dilution experiments with species, gamete concentrations, gamete ratios and mean % of eggs fertilized. Values for % fertilized are means of three treatment replicates.
Species
Sperm Dilution
Gamete Concentration
Sperm ml-1
Eggs ml-1
Sperm:Egg
Mean % Fertilized
101
9.63 x 106
104
9.63 x102
66.67
102
9.63 x 105
9.63 x101
8.94
C. virginica
103
9.63 x 104
9.63 x100
2.06
9.63 x 103
9.63 x10-1
2.22
105
9.63 x 102
9.63 x10-2
1.89
106
9.63 x 101
9.63 x10-3
2.28
107
9.63 x 100
9.63 x10-4
1.94
1.71 x 107
1.71 x 103
93.67
1.71 x 106
1.71 x 102
69.83
C. ariakensis
1.71 x 105
1.71 x 101
9.00
1.71 x 104
1.71 x 100
0.33
1.71 x 10-1
0.00
1.71 x 10-2
1.71 x 10-3
100
1.46 x 106
1.46 x 103 92
1.46 x 104
1.46 x 101
12.5
1.46 x 102
1.46 x 10-1
9.19 x 105
9.19 x 103
99.25
9.19 x 101
81.63
9.19 x 10-1
1.25
9.16 x 105
9.16 x 103
97.5
9.16 x 101
53.5
9.16 x 10-1
3.43 x 105
3.43 x 102
55.67
3.43 x 103
3.43 x 100
13.50
3.43 x 101
3.43 x 10-2
0.50
1.42 x 106
1.42 x105 90
1.42 x 104
1.42 x103 94
1.42 x 102
1.42 x101
66.17

13. Summary of sperm dilution experiments with species, gamete concentrations, gamete ratios and mean % of eggs fertilized. Values for % fertilized are means of three treatment replicate.
Species
Egg
Dilution
Gamete Concentration
Sperm:Egg
% Fertilized
Sperm ml-1
Eggs ml-1
C. virginica
103
5.54 x 104
101
5.54 x 103
98.50
102
5.54 x 102
88.17
5.54 x 101
35.67
6.98 x 104
6.98 x 103
97.17
6.98 x 102
6.98 x 101
67.67
94.17
65.83
33.67

14. Examples of mean % eggs fertilized at varying sperm density
C. virginica
100 eggs / ml
C. ariakensis
10,000 eggs / ml

15. = Fertilization Efficiency
Percent fertilization as a function of sperm : egg ratios
where x was the ratio of initial sperm and unfertilized egg conc.
Fertilization
Efficiency =

16. Model predictions of fertilization success after 30 min at different initial egg concentrations: A) 10 eggs cm3, B) 100 eggs cm3, and C) 1000 eggs cm3. (1 RPM, ε = cm2 s-3; 3 RPM, ε = cm2 s-3; 6 RPM, ε = cm2 s-3; 12 RPM, ε = 0.18 cm2 s-3).

17. Conclusions
Observed fertilization success is very low at sperm:egg ratios ≤ 102 and generally only high above
. . . even at high gamete concentrations.
Model predictions suggest that at high mixing rates fertilization success below this sperm:egg threshold should increase. . .
. . . however, this neglects the high dilution rate at high turbulence.

18. Implications
Under conditions of low population density, such as exists for many overexploited bivalve species,
or when a single age class dominates the population, as often exists in areas of sporadic recruitment
or at restoration sites where single cohorts are planted,
population growth may be seriously constrained by low fertilization success.

19. Future Directions
Investigate fertilization success in the laboratory at higher mixing rates.
Make the model open, i.e. allow for dilution of gametes.
Extend the experiments to other bivalve species.
Conduct fine scale spatial surveys of “restored” bivalve populations to more accurately map densities and distributions of the sexes.

20. Acknowledgments
Funding was provided by the NOAA Chesapeake Bay Office and the Keith Campbell Foundation for the Environment.
We thank Larry Sanford and Steve Suttles for field data and construction of the turbulence mixing chamber, respectively.

21. Sperm swimming speed
Sperm and egg suspensions were added to opposite ends of a flat capillary tube.
Observed under an inverted light microscope with attached low light video camera.
With a frame grab frequency of 0.01 s-1 we measured the movement of individual sperm for 0.6 – 1.0 s.
8 cm
3.5 mm
Egg suspension
Sperm suspension
Number
Swimming speed (mm/sec)
Measured distribution of swimming speeds for C. virginica sperm. Each bar is from a single video record and observations are ranked in increasing order.
Mean υ = cm s-1

23. Size-specific Fecundity in Males
Species, sample size and range of shell heights used in determination of male size-specific fecundity.
Species n
Range in Shell Height
(mm)
Crassostrea virginica 55
17.4 – 135.7
C. ariakensis (West Coast strain) 18
65.3 – 140.1
C. ariakensis (South China strain) 23
62.1 – 88.0
Estimated sperm (in billions) vs. shell height for Crassostrea virginica ( ), west coast strain of C. ariakensis ( ) and south China strain of C. ariakensis ( ).
100
200
300
400 50
150
Shell Height (mm )