At mid-ocean ridges following magmatic eruptions, biogenic floc emerges from the seafloor and blankets regions of the seafloor in what have been called “snowblower” events. The floc often consists of filaments of elemental sulfur, and similar byproducts have been produced by hydrogen sulfide oxidizing bacteria in the laboratory. In this paper we estimate the rate of sulfur floc production in two ways. First, we compare the flux of H2S from high temperature vents and adjacent diffuse flow near 9°50′N on the East Pacific Rise to estimate the rate at which subsurface microbes use H2S to produce elemental sulfur in the shallow crust since the 1991 eruption. Second, we use the data from laboratory experiments to provide an upper estimate of sulfur floc production during a volcanic eruption. The results suggest that that the floc observed during “snowblower” events is most likely a combination of a bloom event and floc that has been stored in the crust between eruption cycles. The calculations also suggest that a ∼1% reduction in crustal porosity would result from the microbial production and storage of sulfur floc during the 1991 to 2000 time interval.
One of the most striking phenomena associated with seafloor volcanic eruptions and hydrothermal processes is the emission of large quantities of biogenic material commonly referred to as floc. White, biogenic deposits on glassy basalts were discovered 2 years following the 1986 event plume on the Cleft Segment of the Juan de Fuca Ridge (JDF) [Embley and Chadwick, 1994]. The first “live” detection of biogenic emissions occurred in 1991 by a team aboard the Alvin submersible at the 9°N site on the East Pacific Rise (EPR) [Haymon et al., 1993]. The team was onsite shortly after the volcanic eruption and witnessed widespread outpouring of high-temperature hydrothermal fluids through a network of seafloor cracks and fissures. Hydrogen sulfide and iron concentrations in the vent fluids immediately following the eruption were shown to be very high, supplying vent ecosystems with a large supply of nutrients [Shank et al., 1998]. Filamentous bacterial mats up to several meters thick covered the fresh basalt flows, and fragments of mat material were carried upward by the hydrothermal flow, forming a biogenic “blizzard” reaching heights of 50 m above the seafloor and being transported at least 100 m from the west side of the axial summit caldera [Haymon et al., 1993]. They coined the term “snowblower” vent to describe the hydrothermal flushing of biogenic material from beneath the seafloor. Early observations of flocculent sulfur discharge following the 1991 eruption place the thickness of sulfur deposited on the seafloor around 5 cm over many areas along the EPR from 9°45′ to 9°52′N [Taylor and Wirsen, 1997].
The filamentous biogenic material, or floc, was later found to be composed primarily of inorganic elemental sulfur [Nelson et al., 1991], and later laboratory experiments suggested that such sulfur-rich filaments could be excretions produced by H2S-oxidizing bacteria living near the oxic-anoxic interface [Taylor and Wirsen, 1997]. Taylor et al.  report evidence of rapid in situ biogenic production of filamentous sulfur in a warm water hydrothermal vent at the 9°N vent field on the EPR. Sulfur oxidizers have been reported to rapidly colonize new flows [Moussard et al., 2006] and can grow in the presence of very high H2S and very low oxygen concentrations [Sievert et al., 2007]. Sievert et al.  suggest that filamentous sulfur formation could be a very important process in the global sulfur cycle by potentially making hydrothermal environments more habitable to other forms of life. Floc emission and microbial mats were also observed following the eruption in the same region after the 2005 eruption [Shank et al., 2006].
Observations similar to those on the EPR were made following the diking and eruptive event on the CoAxial Segment of the JDF in 1993 [Embley et al., 1995; Holden et al., 1998]. In a region referred to as Floc, fragments of bacterial mat material rose to heights of 200 m above the seafloor for hundreds of meters across the axial valley [Embley et al., 1995; Holden et al., 1998; Delaney et al., 1998]. Bacterial mats covered the seafloor near the Floc site. The floc from the CoAxial event plume covered between 7 and 14% of the seafloor around the hydrothermally active part of the new lava flow [Juniper et al., 1995]. The floc formed small drifts on the seafloor hundreds of meters west of the center of the axial valley at the Floc site [Embley et al., 1995]. Although the venting temperatures were <50°C, sulfur-reducing and methanogenic thermophilic and hyperthermophilic organisms were cultured from the fluids [Holden et al., 1998], indicating that these organisms grew in a higher temperature environment beneath the seafloor. Studies of the floc material from the CoAxial segment revealed that they were composed of filamentous, coccoid, and rod-shaped forms that were coated with Fe and Si [Juniper et al., 1995]. Within a year following the CoAxial event, most of the filamentous sulfur material had completely disappeared, most likely due to invertebrate grazing or some unknown mechanism [Juniper et al., 1995].
Although there is no doubt that floc emission following these eruptive events is biogenic in origin, the timescale on which it is being created in the subseafloor is unclear. Whether the floc emitted in “snowblower” vents represents (1) a microbial “bloom” following a pulse of nutrients triggered by the magmatic event and enhanced hydrothermal flow or (2) a sudden release of floc that has formed and been stored within the shallow crust over a considerable time is also unclear. Moreover, if floc is being stored in the shallow crust, its effect on subsurface porosity and permeability, and hence on hydrothermal circulation, may be significant, but it is entirely unknown at present. Because we cannot directly measure subseafloor sulfide oxidation rates in situ, we attempt to address these issues through the development of mathematical models.
In this paper, we address these questions by two different methods. In one method we use H2S, Si, and Fe data from the high-temperature and diffuse-flow vents near 9°50′N on the EPR [Von Damm and Lilley, 2004] to estimate flux of H2S in diffuse flow and the fraction of H2S used by biota. We are then able to determine the rate of generation of sulfur floc in the shallow oceanic crust and hence whether a “snowblower” discharge can represent a flushing out of floc that has been stored over a considerable time. Moreover, by calculating the rate of growth of sulfur floc, its impact on the porosity and permeability of the shallow oceanic crust following the 1991 eruption at 9°N on the EPR can be ascertained. We call the first method the “Quasi-Steady State Model.”
In the second method, we calculate the maximum rate of sulfur floc production by using laboratory measurements on the growth of filamentous sulfur. This analysis will provide a lower limit on the timescale for the development of a “snowblower” event as a microbial bloom. We call this method the “Maximum Production Model.” Details of the methodology are presented below. We recognize that both of these methods are somewhat flawed, but we believe the results shed insight into the likely mechanisms for sulfur floc production and the effect of floc production on porosity of the shallow crust. Hopefully, the results will lead to better experiments and observations to address these issues.
2.1. Quasi-Steady State Model
In this model, we estimate the rate of sulfur floc production and the volume of sulfur floc produced in the shallow oceanic crust using H2S, Si, and Fe concentrations from high-temperature and diffuse-flow fluids obtained between 1991 and 2000 at a number of vent sites near 9°50′N on the EPR [Von Damm and Lilley, 2004] in conjunction with simple mixing and flow models for diffuse-flow fluid. The vent fluid data comes from Bio9 and Bio9Riftia vents and diffuse flow areas on what is termed the northern transect (NT) and tube worm pillar (TWP) on the southern transect (ST) [Von Damm and Lilley, 2004; Figure 1]. The data listed in Table 1 for the NT represent averages of data sampled at the vent sites collected in the years shown, whereas the data for the ST come only from TWP.
Table 1. Summary of Fluid Data Used for Creation of Quasi-Steady State Modela
To determine the rate at which H2S is oxidized by subsurface microbial activity in diffuse-flow fluid, we first recognize that diffuse flow is a mixture between seawater and high-temperature vent fluid [Von Damm and Lilley, 2004]. We calculate the mixing ratio using Si as a conservative tracer, assuming that the Si concentration in high-T vent fluid is one end-member and that the concentration of Si in seawater is zero. We then assume that the concentration of H2S of the high-T fluid entering the diffuse flow regime is the same as that observed in the high-T vents (Table 1). By knowing the H2S concentrations in the diffuse flow fluid, we can calculate the amount lost in the subsurface at each discrete time. For simplicity, we consider only two loss terms for H2S. First, we consider the amount lost to pyrite formation, again by considering the difference between Fe in the high-T and diffuse-flow vents. We assume that the remainder is consumed by microbial activity. To study the rate of floc production as a function of time, we compute the rate of production of floc for each of the dates in Table 1 and linearly interpolate between each of the discrete dates to obtain a continuous rate of floc production. We also need to determine the flux of fluid through the system.
To determine the flow rate of diffuse flow, we assume that this flow is a result of induced convection near a high temperature wall. The high-temperature wall forms as a result of deep-seated high-temperature flow that constitutes the discharge zone for black smoker vents. The diffuse flow may be generally segregated from the high-temperature flow as a result of anhydrite precipitation [Lowell et al., 2003, 2007]. This idealized diffuse flow regime is depicted schematically in Figure 2. Mathematically, it is modeled as a steady state thermal boundary layer [e.g., Bejan, 1995]. By using the boundary layer model, we can use permeability as a parameter to estimate the width of the diffuse flow zone. It may be that diffuse flow occurs as a result of vigorous mixing just below the seafloor, but such a model is difficult to quantify. The boundary layer model is based on reasonable physics and appears to be more consistent with the output of numerical models [Lowell et al., 2007] than shallow subsurface mixing. As we show below the mixing ratio tends to be small, so we ignore the effect of the high-temperature flow on the rate of diffuse flow.
There are several assumptions and simplifications in this model but, given the lack of subsurface data, these assumptions are not unreasonable. By simply constructing chemical balances, we do not need to know the details of reaction rates. Moreover, we are not concerned with what specific biota are consuming H2S in the system. By assuming that all the sulfide is either consumed biologically or converted to pyrite, we are ignoring other possible loss mechanisms for sulfide oxidation in the subseafloor (e.g., sulfide and oxygen can react abiotically), but we are also ignoring possible generation of H2S in the subsurface by sulfate reduction. For simplicity we are assuming the difference between these processes is sufficiently small to be neglected. We also recognize that the sulfur floc producing microbes cultured in the lab and observed in the seafloor environment require small amounts of oxygen and live at temperatures less than 30°C. There may be other sulfur producers that are anaerobic and themophilic that we simply do not know of yet, however. By ignoring details of microbial activity, which for the most part are unknown, and using the chemical data alone, we hope to obtain an estimate of the integrated effect of the microbes. Finally, we assume that the diffuse fluid is a well-mixed combination of high temperature fluid and seawater. Without this assumption, it would be impossible to use the chemical data to determine a rate of biogenic sulfur production. Despite these limitations, the results provide a useful first estimate of floc production and porosity evolution the upper crust. Additional data will lead to better models.
Assuming that the diffuse flow fluid is a mixture of the high-temperature fluid and seawater, as shown schematically in Figure 2, conservation of mass requires that the mass flow rate of seawater into the diffuse flow regime Qsw plus the mass flow rate of high-temperature fluid QhT is equal to the mass flow rate of fluid out of the system Qdiff. That is,
The key symbols used in this paper are listed in Table 2. Similarly, conservation of Si requires that
The mixing ratio is then used to find how much H2S is being utilized by the biota and how much is converted into pyrite (FeS2) through the reaction
First we construct a simple chemical balance for the total amount of H2S lost, which we call H2Ssink. Using the mixing ratio determined from equation (3), we write
Because some of the H2Ssink is a result of pyrite formation, we construct a simple chemical balance for the loss of Fe, assuming that the only loss of Fe from the diffuse flow fluid is from precipitation of pyrite. Thus
Because 2 moles of H2S are removed for each mole of Fe lost (equation (4)), this amount of H2Ssink is subtracted from the result of equation (5). The remainder, which we term H2Ssink(Bio), is number of moles assumed to be used by subsurface biota within in a given volume of the subsurface at a given instant in time. Then, to translate the moles of H2S utilized by biota into moles of sulfur floc produced, we note that 75% of the floc is elemental sulfur [Taylor et al., 1999] and that the molar mass ratio of elemental sulfur to H2S is 32/34. Since the molar ratio of H2S to S is 1 to 1, the ratio of the moles of floc produced to moles of H2S consumed is the molar mass ratio of elemental sulfur to H2S, 32/34, divided by the ratio of floc to elemental sulfur, 1/0.75, which is 64/51.
Table 2. Commonly Used Symbols
effective thermal diffusivity
bacterial count per unit volume of water
acceleration due to gravity
height of vertical boundary
molar mass of hydrogen sulfide
mass flow rate
radius of floc cylinders
mixing ratio of high temperature fluid and seawater
maximum growth rate of floc
coefficient of thermal expansion
boundary layer thickness
density of fluid
density of floc
Equations (1) and (2) do not constrain the flow rate through the system. Hence to obtain the rate at which sulfur floc is produced by the microbial consumption of H2S, we need to construct a flow model and calculate the mass flux rate of microbial H2S utilization within the shallow crust. That is,
where u is the Darcian velocity, ϕ is the porosity, ρf is the density of seawater, and m is the molecular weight of H2S.
We calculate u from scale analysis for thermal boundary layer flow along a vertical wall of constant temperature [Bejan, 1995]. This analysis gives
where a* is the effective thermal diffusivity, y is the height above the base of the wall, and Ray is the Rayleigh number. The Rayleigh number is expressed by
where β is the coefficient of thermal expansion, g is the acceleration due to gravity, k is the permeability, ΔT is the temperature difference between the wall and the far-field background temperature, and ν is the kinematic viscosity of the fluid. The boundary layer width δ is related to the Rayleigh number and the height of the layer y through
Figure 3 shows how the temperature and velocity profiles vary across the boundary layer.
The rate of floc production in the shallow crust given by equation (7) thus depends upon the permeability of the shallow crust, through equations (8) and (9) and the width of the boundary layer δ, through equation (10). We consider crustal permeabilities in the range 10−10–10−14 m2 that are thought to be characteristic of layer 2A extrusives [e.g., Fisher, 1998; Lowell et al., 2007] in a layer 100 m high and a wall temperature of 100°C. The wall height represents a reasonable thickness over which mixing is occurring [e.g., Ramondenc et al., 2008] and the temperature is a rough bound for the existence of life. Using a somewhat higher wall temperature (e.g., 120°C) [Holden and Daniel, 2004] would not change the results appreciably. The values of permeability used reflect the fact that permeability is controlled by fractures. Using a porous medium model with such high permeabilities merely says that the scale of fracturing in the upper crust occurs on a fine scale (∼0.1 m). These parameter values, coupled with the parameter values of Table 2, yield boundary layer thicknesses between ≈0.3 and 10 m.
The volume Vfloc of floc produced beneath the seafloor along a length l of ridge in a time interval Δt is
In equation (11), the factor of two arises from symmetry; floc may be produced from both sides of the discharge zone. To find Vfloc during a time interval between the dates of sampling in Table 1, we use the average value of H2Ssink(Bio) to find qfloc in equation (11), and Δt is the time interval between two dates. The results are given in Figure 4.
2.2. Maximum Production Model
In the second model, we use laboratory data from Taylor and Wirsen  and Taylor et al.  to estimate the composition and growth rate of the sulfur floc. Because this growth occurs under idealized laboratory conditions in which hydrogen sulfide, oxygen, and carbon dioxide are abundant, an upper limit for the production rate of filamentous sulfur is obtained. When coupled with an estimate of the concentration of sulfide oxidizers in the subseafloor, the laboratory-based growth rate can be used to estimate the total volume of floc created in a given volume. We use this maximum floc production rate to put a lower limit on the timescale for floc to be produced in a “bacterial bloom” event.
We once again recognize that our approach involves many assumptions, some of which may not be easily justified. For example, the microbial phylotypes cultured by Taylor and Wirsen  may not represent those actually present in hydrothermal systems. If they are present, these microbes tend to live at temperatures less than 30°C and require low levels of oxygen. The sulfide oxidization rates determined in the laboratory are likely to be much higher than in situ because competition for limited amounts of nutrients among different microbes reduces the efficiency of production from the sulfur producing microbes. Sulfur production rates of anaerobic sulfur producing microbes that may be living at higher temperatures are unknown but are likely to be much less smaller than assumed here. Despite these limitations, utilizing the laboratory rates for floc production provide the best initial estimate for the rate of floc production during an enhanced period of growth resulting from an enhanced carbon supply (i.e., a “bloom” related to volcanic input of CO2). As such they represent and end-member calculation.
Taylor and Wirsen  find that cylindrical filamentous sulfur with a radius of ∼1.0 μm is produced at a rate Xfloc = 0.05 μm/s. The volume of floc Vfloc being produced along a length l of ridge axis in a time interval Δt is then
where uδ(y) represents the volume flux of fluid across the seafloor per length of ridge axis. As in equation (11), the factor of 2 in equation (12) comes from the symmetry of the system. The population of microbes B(t) can be expressed by the Pearl-Verhulst equation for population growth [Adomian et al., 1984]
where K is the carrying capacity and R is the growth rate. For the ridge-crest hydrothermal environment, these are both unknown, so we assume B(t) is a constant in a range between 104 to 1010 bacteria/m3 H2O. These values essentially cover the range of 1010–1011 bacteria/m3 H2O counted for the total microbial population via epifluorescent microscopy following the 1996 CoAxial event plume on the Juan de Fuca Ridge [Holden et al., 1998]. The values found by Holden et al.  represent the total bacterial population cultured, and the number of sulfide oxidizers would be expected to be much less than this, perhaps many orders of magnitude lower.
3.1. Floc Production
The volume of floc produced at the northern and southern transects of the EPR per kilometer of ridge axis using the “Quasi-Steady State Model” is shown in Figure 4 for a range of permeabilities between 10−10 and 10−12 m2. For a crustal permeability of 10−10 m2, about 460 and 160 m3 of floc would be created per kilometer of ridge axis in the 9 year time frame for the northern and southern transects, respectively. Likewise, for a permeability of 10−11 m2, the amount of floc created will be 145 and 50 m3 per kilometer of ridge axis for northern and southern transects, respectively.
Observations from the “snowblower” event of 1991 on the EPR indicate that a highly porous floc was deposited on the seafloor with an average thickness of 5 cm up to a distance of 100 m from the ridge axis [Haymon et al., 1993; Taylor and Wirsen, 1997]. This would indicate a volume of 5000 m3 of floc per kilometer of ridge axis, but the actually volume of filamentous sulfur will be much less since the floc is highly porous. Porosities between 75 and 90 percent would yield between 1250 and 500 m3 of floc per kilometer of ridge axis, respectively. The calculated values of floc along the northern and southern transects fall below the range of observed floc during the 1991 EPR event. For a permeability of 10−10 m2 along the northern transect, the observed floc could be accounted for by floc stored in residence.
For the “Maximum Production Model,” the total volume of floc being created per km of ridge axis as a function of time is shown in Figure 5 for a range of constant population, B0, values. In Figure 5, we assumed a permeability of 10−10 m2. Because of the high flow rate that occurs with this value of k (equation (8)), the simulation represents a “bloom.” If the bacterial count is 1010/m3 H2O, then 500 m3 of floc will be created in 30 days and 1250 m3 will be created in 50 days. For a bacterial count of 108/m3 H2O, 500 m3 of floc will be created in 320 days and 1250 m3 in 505 days according to equation (12). By comparing the calculated production rate using optimum production conditions with the observed volume of floc produced during the 1991 “snowblower” event, it appears unlikely that the observed floc represents a simple bacterial bloom. This means that the volume of floc observed in the 1991 “snowblower” event at EPR was produced and stored in the crust over a significant period of time. According to the “Quasi-Steady State Model,” a sizable fraction of the observed floc could have been produced and stored during a time interval of 10–20 years, provided the permeability of layer 2A is ∼1010 m2 or greater and provided it is easily flushed out during an eruption. It is noteworthy that floc emission also accompanied the volcanic eruption from the same area of the EPR that occurred in late 2005 to early 2006 [Shank et al., 2006]. The volume of floc and microbial mat material emitted during this event appears to be smaller than that emitted in 1991 [Shank et al., 2006], but this is uncertain because observations following the more recent eruption were not made until several months after the event.
3.2. Theoretical Porosity Change due to Floc Production
A fundamental question that arises from the modeling of filamentous sulfur production is whether or not it will have an effect on the fluid flow by changing the porosity of the rock. For a length l of ridge axis, the total volume of the pore space will be
where ϕ is porosity of the system, which is set to 0.1. Using the “Quasi-Steady State Model,” a piecewise function of porosity change over the 10 year period after the 1991 eruption is developed by comparing the volume of floc produced in a given time interval (equation (11)) with the volume of pore space present given by equation (12). If a permeability of 10−10 m2 is assumed, one would expect 0.4% and 1% of the pore space to be filled with sulfur floc by April 2000 at the southern and northern transects, respectively (Figure 6). Because the ratio of the floc volume to pore space volume is a linear function of the flow rate u, the percent of pore space filled as a function of time is linearly dependent upon the permeability. Hence, as the permeability is decreased by an order of magnitude, the percent of pore space filled with floc is decreased by the same amount (Figure 6). If the relationship between porosity and permeability follows a Carmen-Kozeny type relationship such that k ∝ ϕ3, a porosity reduction of 1% would correspond to a permeability reduction of about 3%. This is not a significant factor. Consequently, floc production at EPR 9°50′ N between 1991 and 2000 would not be expected to affect the fluid dynamics of the diffuse flow.
To calculate the time to fill the pore space with the “Maximum Production Model,” we divided the volume of floc produced from equation (12) with the volume of pore space determined from equation (14). This shows that the time to fill the pore space Δt ∝ (B0k)−1/2. For example, with k = 10−10 m2 and a bacterial count of 108/m3 H2O, it would take approximately 8 years to fill the pore space. A decrease of two orders of magnitude in permeability or bacterial count would increase this time by a factor of 10. Conversely, an increase of either of these parameters by two orders of magnitude would reduce the time by a factor of 10. With the “Maximum Production Model,” biogenic sulfur floc could fill the pore space between the magmatic eruptions of 1991 and 2005; however, this model is probably not as realistic for long-term calculations as is the “Quasi-Steady State Model.”
4. Discussion and Conclusions
We have presented two models for the production of sulfur floc by microbial activity in the shallow oceanic crust in order to understand the nature of floc emission or “snowblower” events during volcanic eruptions at mid-ocean ridges and to determine whether floc stored in the crust affects the crustal porosity distribution. In both models we have assumed diffuse flow in the shallow crust can be adequately described in terms of vertical boundary layer flow in the upper 100 m of layer 2A that is induced by focused high-temperature discharge.
The “Quasi-Steady State Model,” which estimates the volume of floc stored in the crust by using geochemical data in conjunction with the boundary layer model, suggests that between 200 and 500 m3 of sulfur floc could be generated between 1991 and 2000. This volume is at the lower end of the estimated volume of floc emitted during the 1991 eruption [Haymon et al., 1993] but may be consistent with the volume emitted during the 2005/2006 eruption [Shank et al., 2006]. The results further suggest that the volume of floc stored during the 1991–2000 time interval would have a negligible impact on the porosity within the boundary layer. Note that we have used the entire boundary layer width to estimate the pore space; however, if the sulfur producing microbes are restricted to the region less than 30°C, the fraction of the pore space occupied would be smaller than assumed here, and the relative reduction in the pore space would be greater than calculated in this model. Since the boundary layer width depends linearly on the temperature difference ΔT, the reduction in pore space would increase by perhaps a factor of 3, but it is still small.
Although these results seem reasonable, given the current data and state of understanding of subseafloor microbial processes, the results must be viewed with some caution. By neglecting any details of processes within the subsurface biosphere, the model may not be taking into account all the sources and sinks of sulfur. For example, the metabolism of elemental sulfur by other microbes is not taken into account in the models, and this process could prevent sulfur from being stored in residence for long periods of time. The model also assumes that all the floc generated is simply stored in the crust until it is removed during the eruptive event. The model does not provide a mechanism for flushing the floc from the crust during an eruptive event. In effect we have assumed that during the eruptive process, fluid flow is greater than during the storage period and that this enhanced fluid flow is able to entrain the stored floc. Thus even if this model is essentially correct, further work is needed to address details of floc generation, storage, and removal.
The boundary layer flow model also needs additional work. It may be that diffuse flow, rather than being simply induced at the boundary of high-temperature discharge, is more complicated (e.g., see numerical models of Lowell et al.  and Ramondenc et al. ), and much of the mixing may occur in just the upper several meters of the crust. In this case, floc would be stored in a smaller volume, from which it might be more easily removed, and floc formation might have a greater affect on the porosity of the shallow crust.
The “Maximum Production Model,” by using laboratory data, likely provides an upper estimate for the volume of floc produced in a given time interval. Even so, this model predicts that to produce the volume of floc observed during the 1991 eruption would take at least 30 days and perhaps more than a year. This suggests that “snowblower” events do not simply represent a microbial “bloom” but rather represent the emission of floc stored over a considerable time, coupled with enhanced growth during the eruption when additional fluxes of volatiles and H2S are available. For this model the rate of reduction of porosity is significant over the time interval between 1991 and 2000; however, this model may not be very realistic on such a long timescale.
We thank the Editor Vincent Salters, Associate Editor William Seyfried Jr., and four anonymous reviewers for their helpful and encouraging comments on a previous draft of this paper and the current version. This research was supported through NSF grant OCE 0527208 to R.P.L.