The role of growth in maintaining spatial dominance by mussels – Mytilus edulis
Peter S. Petraitis
INTRODUCTION
Many marine invertebrates show a strong negative correlation between body size and density, much like the self-thinning relationship seen in plants (Yoda et al. 1963, White and Harper 1970, Harper 1977). This is true not only for sessile invertebrates such as barnacles and mussels (Paine 1976, Hughes and Griffiths 1988, Ardisson and Bourget 1991) but also for mobile invertebrates such as limpets (Branch 1975) and sea urchins (Levitan 1988). As in plants, the explanations for self-thinning in marine organisms emphasize intra-specific competition. Thus crowded conditions reduce the per-individual ration of food and space, which in turn reduces the average body size. The result is a negative correlation between body size and density.
This covariation of body size and density also has important and unappreciated ramifications for the maintenance of spatial dominance by sessile marine invertebrates. While the role of size and growth in maintaining spatial dominance is well known for clonal animals (e.g., Hughes 1984), it is probably equally important for many non-clonal sessile invertebrates in which body size varies. Juvenile mussels for example join adult assemblages at sizes that are typically 0.01-0.001 times the size (i.e., length) of adults. As in plants, growth rates of small animals can be suppressed by crowded conditions but recover rapidly if crowding is reduced. This means that as a bed of individuals is thinned by predators or physical disturbance, growth by the survivors may be able to maintain spatial dominance (i.e., amount of cover) at the status quo.
Thinning by predators or disturbances differs from self-thinning. Self-thinning is an intraspecific process, and understandably, research has focussed on the consequences to individuals or populations (Harper 1977, Weller 1987). However, when predators attack individuals that are capable of indeterminate growth, then the ensuing trade-off between mortality and growth becomes a question at the community level. Quite simply, can growth prolong persistence of cover in the face of chronic mortality?
In marine benthic communities, the role of growth in prolonging spatial dominance has not been carefully considered. Currently, most researchers view the maintenance of spatial dominance as a balance between the acquisition of substrate (i.e., rates of recruitment) and the duration of occupancy (i.e., rates of mortality). When individuals of a single species occupy large contiguous areas on the shore as a monoculture (e.g., mussel or barnacle beds), it is assumed high rates of recruitment or low rates of mortality are the primary causes (e.g., Connell 1961, Dayton 1971, Menge 1976, Paine 1976). Yet sessile animals can blanket and preempt rocky surfaces as either many small juveniles or a few large adults. The covariation of body size and density suggests that growth plays an important role in determining the persistence of spatial dominance by a single species.
How important is growth in prolonging persistence of mussel beds on rocky shores? To address this question, I first develop a general graphical approach that displays the dependence of percent cover on rates of growth, mortality, and recruitment. The model is used to evaluate the relative importance of growth in maintaining cover by beds of the blue mussel Mytilus edulis. There is a vast literature on mussels, and I will restrict my review to M. edulis. I will use the term “mussel” to mean M. edulis unless I indicate otherwise. The model requires knowing the relationship between density and body size, and so data for M. edulis are used to establish a “self-thinning” line for mussels. Data on growth and mortality of M. edulis are briefly reviewed and then used to determine if growth can, in fact, offset the thinning effects of predation and disturbance. The interaction between growth and predation, which is often size specific, is shown to give unexpected results and may help explain the patterns of local and regional variation in body size of mussels.
LINKING PERCENT COVER TO GROWTH, RECRUITMENT, AND MORTALITY
The amount of surface occupied by sessile organisms, and thus percent cover, depends on both density and individual body size. The proportion of cover can be expressed in terms of average area per individual and density. If the average area per individual at time t equals a(t) and if number of individuals at time t in an area of size A equals N(t), then the proportion of cover at time t is p(t) and equals a(t)N(t)/A. This assumes individuals cover the surface as a single layer.
The relationship between a(t) and N(t) at 100% cover (i.e., p(t) = 1) is analogous to the “self-thinning line” (Harper 1977, Westoby 1981). If the relationship between area and density is allometric, then [Mathematical Expression Omitted]. The constant, [K.sub.a], is the packing density of individuals, which depends on the shape of the individuals, and the exponent, [Alpha], is a shape parameter, which reflects changes in shape during growth (Norberg 1988a). Note that here I have replaced the average biomass in the usual self-thinning relationship with the average area per individual. The self-thinning line for area vs. density is log [Mathematical Expression Omitted] and is the isocline for 100% cover. On the self-thinning line, any increase in the average area per individual must be offset by losses in number. Again, this assumes individuals maintain a monolayer.
Below the self-thinning isocline, there must exist other isoclines for which percent cover is [less than] 100% (i.e., p(t) [less than] 1). These other isoclines will be parallel to and below the 100% isocline if growth trajectories of mussels of all sizes follow the same allometric relationships (Norberg 1988a, b). Norberg (1988b) calls this type of growth “geometrically similar.” If these other isoclines are parallel to the 100% isocline, then their slopes will be a but their intercepts will be [less than] [K.sub.a]. Fig. 1A shows that if log [K.sub.a,q] equals the intercept of the 100q% isocline, where q is the proportion of cover, and if the slopes of the isoclines are parallel, then [K.sub.a,q] = [K.sub.a]/[q.sup.[Alpha]]. If [Mathematical Expression Omitted] is the average area per individual at time t on the 100q% isocline, then
log [Mathematical Expression Omitted] = log [K.sub.a] – [Alpha] log q + [Alpha] log N(t). (1)
If q = 1, then Eq. 1 reduces to the self-thinning line.
Parallel isoclines imply mussel growth is geometrically similar regardless of the amount of cover. The isoclines need not be parallel, but parallel isoclines allow me to estimate the entire surface from a single isocline, such as the 100% self-thinning line. There are few data to support or refute the assumption of parallel isoclines. On one hand, Seed’s (1968) data suggest mussel growth may be geometrically similar, but the data do not address differences in percent cover. On the other hand, Frechette and his co-workers (Frechette and Lefaivre 1990, Frechette et al. 1992) suggest the slope of the self-thinning line changes as the balance between food limitation and space competition shifts. I suspect that the slopes of the isoclines would not be parallel if the amount of cover changes the balance between food limitation and space competition.
Each isocline is a plot of log average area per individual vs. log density for a particular level of percent cover [ILLUSTRATION FOR FIGURE 1B OMITTED]. A point on the surface of isoclines defines not only the amount of cover but also the density and the average areal cover of an individual.
Changes in cover form a track across the isoclines. The track is the combined result of recruitment, individual growth, and mortality. Each can be represented as a vector [ILLUSTRATION FOR FIGURE 1B OMITTED]. The vectors for growth and mortality (if mortality is not size specific), lie parallel to the axes. Size-specific mortality changes density and average area per individual, and so the direction of the vector may vary in this case. Recruitment is the arrival of new individuals, and because recruiting individuals tend to be small and may be sparse to numerous, the direction and length of the vector for recruitment depends on the size and number of the new arrivals.
Can rapidly growing mussels offset losses due to predation or physical disturbance? The answer depends on the length and direction of the vectors for growth and mortality. Graphically, the growth vector must compensate for the mortality vector [ILLUSTRATION FOR FIGURE 1C OMITTED]. The crucial issue is how much growth is needed for a particular level of mortality. The answer requires defining the trade-off between rates of mortality and growth that maintains percent cover at the status quo.
The levels of growth and mortality are defined by the lengths of their vectors [ILLUSTRATION FOR FIGURE 1C OMITTED]. During a time interval from t to t + h, the change in individual area due to growth is log [Mathematical Expression Omitted], which is the length of the growth vector. Let g be the proportional increase in individual area, i.e., [Mathematical Expression Omitted], and thus the growth vector equals log g. The change in number (i.e., crude mortality rate) is log N(t + h) – log N(t), and this is the length of the mortality vector. The equation N(t + h) = (1 – m)N(t) defines the per capita rate of mortality, m, if mortality is not size specific. The mortality vector therefore equals log(1 – m).
No change in cover means that log p(t) and log p(t + h) will lie on the same isocline. Recall that the slope of the isocline is [Alpha], and so,
[Mathematical Expression Omitted].
Substituting in log g and log(1 – m) gives
[Alpha] = log g/log(1 – m). (3)
Eq. 3 defines the required relationship between mortality and growth for no net change in cover over a given time period. Knowing the proportional increase in individual area and the slope [Alpha], the maximal per capita rate of mortality at which p(t) = p(t + h) can be estimated.
Using area as a measure of size presents a practical problem since length, not area, is the standard measure of size in mussels. Therefore the slope for the 100% isocline must be re-cast in terms of length. Assuming the relationship between length and area is allometric, then [Mathematical Expression Omitted] where [Mathematical Expression Omitted] is average length at time t, s is a constant, and b is a shape parameter.
The relationship between average length and density is also allometric and can be written as: [Mathematical Expression Omitted] or log [Mathematical Expression Omitted]. Log [K.sub.L] and [Beta] are the intercept and slope respectively of the self-thinning line in terms of length rather than areal extent. Note that the slope [Beta] equals [Alpha]/b, and [Beta] can be determined empirically from data on average length and density.
Finally, re-writing Eq. 3 in terms of length rather than area gives,
[Beta] = log [g.sub.L]/log(1 – m) (4)
where log [g.sub.L] = log [Mathematical Expression Omitted].
Whether growth can offset mortality depends on the slope [Beta] and the realized rates of growth and mortality. [Beta] can be estimated from data on density and length, but the relationship between growth, mortality, and [Beta] depends on several crucial assumptions. Estimations of growth and mortality rates are also difficult because these rates depend on initial body size (Seed 1968, 1969b, 1976, Mallet and Carver 1993). The next section provides an estimate of the slope and a discussion of three assumptions, and presents a short review of the published data for Mytilus edulis on the rates of growth and mortality.
DETERMINATION OF PARAMETERS
The slope [Beta]. – I used data from two sources to estimate [Beta]. First, I used data from Reynolds (1969: Tables 1, 2, and 3), which provided 38 data points. These data were from mussel beds with 100% cover in the Conway Estuary, Wales. This was the only set of published data [TABULAR DATA FOR TABLE 1 OMITTED] from which I could extract mean lengths and corresponding densities unambiguously. Second, I collected data on average length and density from areas in which mussels formed monospecific beds with 100% cover on Swan’s Island, Maine. Sixty-six 10 x 10 cm samples were collected from low intertidal mussel beds. Samples were collected during the summers of 1987, 1989, 1991, and 1992 from seven locations on Swan’s Island, Maine. Six locations have been used in previous studies (Petraitis 1987a, b, 1989, 1990, 1991), and are Long Cove, Mackerel Cove, Mill Pond South, Hockamock Head, Inside Hockamock Head, and Outside Hockamock Head. The seventh location was Hockamock Ledges, which is 700 m northwest of the Outside Hockamock Head study site. Data from 1987 and 1989 are reported in part in Petraitis (1991). Lengths of mussels were measured with dial calipers, and numbers per quadrat were counted. In nine samples, mussels were so numerous that not every mussel was measured. In seven of the nine samples, mussels that passed through a 2-mm sieve were assumed to be 2 mm in length. In the two other samples, subsamples of 30 mussels chosen at random were measured.
Reduced major axis regression (RMA regression) was used to estimate slope and intercept because both average length and density are subject to error (McArdle 1988, LaBarbera 1989). The data, which were mean length in millimetres and total number of mussels per 10 x 10 cm sample, were [log.sub.10] transformed.
The slope from the combined data equals -0.741 (95% confidence limits are -0.692 and -0.793, using Jolicoeur and Mosimann’s formula in McArdle 1988). Although the slopes from the two data sets separately differ (Table 1), I combined the two data sets to obtain a single estimate of the slope rather than arbitrarily choosing one over the other [ILLUSTRATION FOR FIGURE 2 OMITTED]. The slopes probably differ because my data included much larger, sparser mussels (Table 1, [ILLUSTRATION FOR FIGURE 2 OMITTED]).
Eq. 3, which links growth and mortality to the slope of a self-thinning line, incorporates three crucial assumptions about the slope, [Beta], that may not hold. While these assumptions may be far too simplistic, refining the model to include more realistic assumptions requires data that are not available for mussels.
First, I have assumed mussels form a single layer. Under very crowded conditions this is clearly not the case. Multi-layering of mussels, in effect, means that the self-thinning line will underestimate the number of individuals at any given size. However, as long as the underestimate is constant across all sizes and densities, the slope should remain the same. For example, if a bed with two layers of mussels simply has twice the density at any given size, then the slope will still be [Beta]. Including multi-layering in the model would require defining an isocline plane for constant cover in three dimensions: average area, density, and average number of layers.
Second, I have assumed that average size and density alone can be used to estimate the proportion of cover. If individuals vary in size, then percent cover equals the sum of the number of individuals in each size class times the area of an individual in each size class per unit area (e.g., Roughgarden et al. 1985). Addition of variation in size to the model is possible, but published data of this sort are rare.
Third, I assume the relationship between average area and average length is allometric. However average area is not a simple function of average length. Assume an individual of size i covers an area of [a.sub.i] and has a length of [L.sub.i]. Also assume the relationship between area and length can be expressed as [a.sub.i] = s[[L.sub.i].sup.b]. Now let [n.sub.i](t) = the number of mussels of size i at time t in a total area of A. Thus [Mathematical Expression Omitted] equals [Sigma] [a.sub.i][n.sub.i](t)/[Sigma] [n.sub.i](t) and density, N(t), equals [Sigma] [n.sub.i](t), The proportion of cover equals the area covered by mussels divided by the total area, or [Sigma] [a.sub.i][n.sub.i](t)/A. This is identical to Roughgarden et al.’s (1985) definition of cover by barnacles except they define i as age rather than size. For mussels, classification by age is difficult because mussels of the same age vary tremendously in size (e.g., Baird 1966, Seed 1976). Substituting s[[L.sub.i].sup.b] for [a.sub.i] in the equation [Mathematical Expression Omitted] = [Mathematical Expression Omitted]. Thus average area depends on individual lengths rather than the average length. If mussels don’t vary much in size, then [Mathematical Expression Omitted]. Mussels, however, do vary greatly in size, and the allometric relationship between average area and average length may be quite different.
Growth rates. – Initial body size is one of the most important determinants of growth in mussels, and many studies of mussel growth have used the yon Bertalanffy equation to summarize the dependence of growth rate on body size. The von Bertalanffy equation assumes that [Mathematical Expression Omitted], the average size at time t + 1, is a linear function of the average size at time t, i.e., [Mathematical Expression Omitted]. For mussels, the equation is usually written as
[Mathematical Expression Omitted]
where k is the growth parameter and [e.sup.-k] = w. [L.sub.[infinity]] equals the asymptotic body length, and b is the correction factor for length at time zero, i.e., [Mathematical Expression Omitted]. Most analyses of mussel growth assume b = 1, and so [Mathematical Expression Omitted].
I defined growth as log [Mathematical Expression Omitted] (see Eq. 4). Using the von Bertalanffy equation and assuming h = 1 and b = 1,
[Mathematical Expression Omitted].
The proportional increase in average length, [g.sub.L], can be founded by knowing the growth parameter, k, and relative length, [Mathematical Expression Omitted].
Published values for k and [L.sub.[infinity]] vary wildly, and values for k range from 0.022 to 1.138 (Theisen 1968, 1973, Seed 1976). Based on Eq. 6, growth of a mussel (i.e., [g.sub.L]) with a relative length of 0.25[L.sub.[infinity]] ranges from 6.5%/yr (k = 0.022) to 303.8%/yr (k = 1.138). Fig. 3A shows that [g.sub.L] declines with relative body length. Smaller mussels grow more quickly than larger mussels. Mussels grow more slowly (i.e., smaller values of k) in locations with less submersion, colder water, and shorter growing seasons (e.g., Theisen’s (1973) estimates for mussels in Greenland, which range from k = 0.022 to k = 0.162). The largest values are from estuaries in which mussels are grown commercially, and the overlying water is extremely productive (e.g., range 0.393-1.138; Theisen 1968, Seed 1976).
Seed (1968: [ILLUSTRATION FOR FIGURE 2 OMITTED]) provides the best data for mussel growth on rocky shores in more temperate regions but does not provide estimates of k and [L.sub.[infinity]]. I estimated k and [L.sub.[infinity]] for Seed’s (1968) data by measuring the position of the data points in his Fig. 2 with calipers and fitting von Bertalanffy curves. My growth analysis, including estimates of [L.sub.[infinity]] and b, are unpublished. Values for k ranged from 0.092 (low shore at Filey Bay) to 0.175 (M.L.W.S. [mean low water springs] at Whitby Harbor).
Mortality rates. – Predators of mussels are well known and well studied (e.g., Seed 1976, Menge 1978, 1983, Hughes and Dunkin 1984), but data on rates of mussel mortality are meager at best. Predation studies focus on the predator and thus are not specifically designed to estimate per capita rates of mussel mortality. For example, some studies document the effects of predators on mussels and express the intensity of predation in terms of changes in prey biomass or percent cover (e.g., Menge 1978). Other studies provide estimates of feeding rates of particular predators (e.g., Walne and Dean 1972, Menge 1983, Burrows and Hughes 1991). Unfortunately these studies lack information about per capita rates of mussel mortality.
Survivorship data provide the best estimates of mortality rates under natural conditions, yet I have found only four studies with adequate data for estimating per capita rates of mortality for Mytilus edulis in the field.
Gardner and Thomas (1987) estimated mortality from collections taken at intertidal sites in the Bay of Fundy. They collected mussels from quadrats in July and December of one year and assumed the change in the number of mussels per quadrat from July to December was due to mortality alone. They estimated the mortality rate to be 42% during that period. The initial length of mussels averaged 9.6 mm.
Theisen (1968) estimated the annual rate of mortality in the commercial beds of the Conway Estuary, Wales in a similar fashion. His mortality estimates were based on natural losses of mussels that were seeded into the beds, and ranged from 65% to 34% for mussels that were 26 and 49 mm in length, respectively. Theisen cautioned against extrapolating beyond this size range.
Seed (1969b) gives the best estimates of mortality under natural conditions. Seed marked samples of 500 mussels and counted the remaining mussels on a monthly basis at two intertidal levels at one location and at three intertidal levels at another on the exposed shores of Yorkshire. Seed (1968, 1969a) described both locations, Ness Point and Filey Brigg, as wave-swept and extremely exposed. Annual mortality ranged from 9% to 78%. Rates varied between locations, but rates at both locations declined with intertidal height.
A fourth study by Mallet et al. (1990) also provides good survivorship data, but the mussels (initial size range 30-60 mm in length) were kept in cages and also were protected from predators. Mortality during the summer (June to September) ranged from 9% to 41%. Winter mortality (October to May) was [less than]3%.
THE SIZE-SPECIFIC INTERACTION OF GROWTH AND MORTALITY
Even though rates of growth and mortality vary widely, mussels may grow rapidly enough so that cover remains unchanged even in the face of high rates of mortality. Based on Eq. 4, the amount of mortality that a mussel bed could sustain depends on [Beta], which defines the relationship between length and density, and on [g.sub.L], which is the measure of growth. Table 1 gives [Beta] = -0.74 and Eqs. 4 and 6 suggest that the [g.sub.L] of a mussel with a relative length of 0.25 [L.sub.[infinity]] ranges from a low of 0.065/yr (k = 0.022, from Theisen 1973) to a high of 3.038/yr (k = 1.138, from Seed 1976). This translates into the ability to offset between 8.2% and 77.7% mortality per year, respectively (based on Eq. 4). At 0.25 relative length, the mussel beds studied by Seed (1968) at Filey Bay (k = 0.092) and Whitby Harbor (k = 0.175) have the potential to withstand 27.1% and 41.2% annual mortality, respectively.
Eq. 4 makes it clear that the trade-off between growth and mortality depends on [g.sub.L], which is the proportional change in body size (i.e., [Mathematical Expression Omitted]). Mussels, like many invertebrates, grow more slowly as they increase in size, and so the ability to offset the effects of mortality through growth declines with body size. Mortality rates may also be size dependent because a predator’s handling time and preference may vary with prey size. The interaction between size-specific growth and mortality has unexpected consequences.
Fig. 3B starts with the simplest case in which growth depends on body size but mortality does not. There is a single critical size at which growth can no longer compensate for mortality [ILLUSTRATION FOR FIGURE 3B OMITTED]. Below the critical point, smaller mussels with their rapid growth can easily maintain a constant level of percent cover. However, once the critical size is reached, the mussel bed will become sparser, and percent cover will decline. Several points are worth noting. First, as long as mussels are below the critical size, a mussel bed should appear unaffected by predation and other sources of mortality (i.e., percent cover will not decline). Second, once the critical size is reached, percent cover should decline rapidly unless recruitment occurs. Third, the critical size depends not only on the rate of mortality but also the rate of growth. Slower growing mussels will have a smaller critical size [ILLUSTRATION FOR FIGURE 3B OMITTED]. Fourth, observations suggest that per capita rates of mortality also decline with body size (e.g., Theisen 1968, Seed 1969b, Gardner and Thomas 1987, Mallet et al. 1990), and this will increase the critical size.
The outcome can be very different if predators are the major source of mortality because predators often prey on a narrow size range of prey. Predators of mussels often seem unable to attack large mussels (e.g., studies of Mytilus californianus by Paine 1976) or pass over small mussels for which the net energy yield is too low (e.g., studies of M. edulis by Hughes and Dunkin 1984). Per capita rates of mortality may also vary because of size-dependent handling time. Handling time, which includes capturing, subduing, ingesting, and digesting prey, often increases with prey size. Larger M. edulis take longer to open and to ingest (Walne and Dean 1972, Hughes and Dunkin 1984), and thus the realized rates of predation decline with prey body size even if predators do not favor a particular size class of prey.
Taken together, size-specific preference and handling time produce two critical points rather than one. Beds should be composed of patches of either small or large mussels [ILLUSTRATION FOR FIGURE 4 OMITTED]. Below the first point, small mussels, which are ignored by predators because of low net yield, are taken at such low rates that growth can offset the losses. At the second point, large mussels suffer low rates of predation because of very long handling times. If the predation rates are low enough, then the slow growth of these large mussels will be sufficient to offset predation. Large mussels will appear to have a size refuge at this upper point because no change in percent cover is observed and because rates of predation may be so low that successful attacks are very rare. This size refuge, however, is not absolute. Growth must still balance losses via predation. The absolute size refuge (sensu Paine 1976) occurs when predators do not take large mussels, which may be at a slightly larger size [ILLUSTRATION FOR FIGURE 4 OMITTED].
DISCUSSION
Field studies on rocky shores have shown how mortality can be regulated by biotic and abiotic processes, such as competition, herbivory, predation, and disturbance (e.g., Connell 1961, Paine 1966, Dayton 1971), and more recently, suggested how variation in settlement and recruitment can mold local interactions (e.g., Underwood et al. 1983, Keough 1984, Fairweather 1985, 1987, Sutherland and Ortega 1986).
Yet for mussels, as well as other organisms with indeterminate growth, persistent cover and thus dominance on rocky shores must be a balance between growth and recruitment on one hand and mortality and emigration on the other. Over the short term, mussel beds can suffer a large number of deaths and persist in dominating the substrate without any change in percent cover as long as the remaining mussels can grow fast enough to fill in the vacated space. Chronically sparse or episodic recruitment may be sufficient to replenish the bed as long as mussels can grow fast enough. My analysis of growth and mortality suggests that growth can more than compensate for the effects of predator-induced mortality because recruiting mussels are small (in the range of 0.5 to 1.0 mm) and grow to large size rapidly (2 to 10 cm). For example, mussels that are [less than]1 cm have the potential to double in length within a year (e.g., Theisen 1968, Seed 1976). If mussels follow the “self-thinning” relationship seen in Fig. 2 (i.e., [Beta] = -0.74), then a bed of small mussels in which all individuals doubled in length in 1 yr could suffer 60% mortality with no change in percent cover.
Like self-thinning models, this analysis emphasizes the balance between growth and mortality, but unlike self-thinning, the cause is not intraspecific competition (Harper 1977, Westoby 1981). Although there is good evidence that intraspecific self-thinning occurs in mussels (e.g., Ardisson and Bourget 1991), my model addresses the balance between growth and mortality that determines spatial dominance. This is a community-level effect. Predator thinning and self-thinning are not mutually exclusive. Predators, in the process of thinning beds, may even relax intraspecific competition among the remaining mussels and thus slow the rate of intraspecific self-thinning.
Clearly a complete analysis of spatial dominance depends on knowing the rates of growth, mortality and recruitment, yet there are few studies that provide good estimates of these processes even though a vast literature on the biology of Mytilus edulis exists (e.g., see reviews by Seed 1976, Suchanek 1985). The lack of good estimates of per capita rates of mortality is especially distressing. Although many organisms eat mussels and do so in great numbers (see Hughes and Dunkin 1984: Table 1 and Seed 1976), per capita rates of mortality are rarely provided. The data for growth and recruitment are slightly better, but wildly variable. Recruitment may vary over several orders of magnitude (e.g., Bayne 1964, Petraitis 1991). Growth rates vary with body size, age, season, temperature, light, inter-tidal height, amount of food, and overcrowding (Coulthard 1929, Savage 1956, Boetius 1962, Baird 1966, Seed 1969b, 1976, Frechette and Bourget 1985b). Recruiting individuals, which may be [less than]0.5 mm in length, have reportedly grown to 60-70 mm within 12-18 mo (summary in Seed 1976). Small mussels (10-20 mm in length) usually show gains of [approximately equal to] 5-20 mm/yr but can grow as much as 9 mm/mo (Page and Ricard 1990, Mallet and Carver 1993).
How sparse or infrequent can recruitment be and still provide enough new individuals to offset losses due to mortality? This remains an open question since the answer depends on not only the rate of recruitment but also the rates of growth and mortality. Mussel recruitment in the Gulf of Maine can vary over four orders of magnitude (Petraitis 1991), and a strong pulse of recruitment will provide a complete cover by small mussels. Small mussels can grow rapidly – a 1 mm mussel can reach 5 mm in 35 days (based on Theisen’s [1968] estimate of parameters for the von Bertalanffy equation). Unfortunately, virtually nothing is known about mortality rates among very small mussels, and so it is not possible to predict if low but continuous levels of recruitment and rapid growth would be sufficient to offset ongoing mortality. A more precise determination of the relative importance of recruitment, growth, and mortality probably requires a detailed individual-based model that translates the effects of size-specific growth and mortality into changes in percent cover.
Even so, several general predictions about how growth rates may affect the longevity of mussel beds can be made. First, beds in highly productive areas should exhibit boom and bust cycles of mussel production. Crashes should occur when mussels, reach the size at which growth can no longer match the effects of mortality. Without massive recruitment, mussel beds should disappear quite rapidly. In resource-rich areas, mussels will grow rapidly, and beds will persist even in the face of high rates of mortality. Mussels in these beds, however, will reach their critical size quickly and thus will turn over quite rapidly. In fact, long-term records of mussel biomass in commercial beds show striking year-to-year variation (e.g., 40-yr record for the Wadden Sea in Danker and Koelemaij 1989).
Second, the size of a bed itself can affect the rates of growth and thus alter the rates of bed turnover. Average individual growth is slower in larger beds because of resource depletion and the width of the boundary layer (Frechette and Bourget 1985a, b, Wildish and Kristmanson 1985, Newell 1990, Frechette and Grant 1991). As mussels in large beds grow more slowly, the critical point will shift towards smaller mussels and thus change the rate of bed turnover.
Third, there is a cumulative effect of growth. Growing mussels can push adjacent mussels outward and expand the size of a patch. The distance that the outermost mussel must move is cumulative since each mussel is adding its individual growth increment to the expansion of the bed. For example, suppose all mussels in a circular patch grow, none die, and the patch expands outward to accommodate the growth. Let N(t) equal the number of individuals in an area of A(t) at time t. If no mussels die in the time interval from t to t + 1 and if the circular patch expands from A(t) to A(t + 1), then the ratio of the radii, r(t + 1)/r(t), equals [Mathematical Expression Omitted]. Assuming mussels double in size (i.e., [Mathematical Expression Omitted]) and [Beta] = -0.74 (Table 1), then r(t + 1)/r(t) = 1.60. To accommodate a doubling in individual body size, a patch of mussels that is 10 cm in diameter must expand to 16 cm in diameter, but a patch 100 cm in diameter must expand to 160 cm in diameter. Note that the expansion depends on the ratio of lengths, not the absolute size. For small mussels, which can double their size in a matter of weeks or months, it is improbable that the mussels on the outer edge of a 100-cm patch could move 60 cm in such a short time. Thus large patches of small mussels are likely to become multi-layered as individual mussels are pushed up and out of the patch.
A multi-layered bed carries its own set of risks. The attachment of the whole patch to the surface is much weaker, and the higher profile of the patch makes it much more susceptible to wave surge. As a result, large patches in which rapidly growing mussels become multi-layered may turn over more quickly than small patches of mussels growing at the same rate.
Finally, mussel beds that are a mosaic of large and small individuals may be the result of size-specific pre-dation [ILLUSTRATION FOR FIGURE 4 OMITTED]. Clusters of small mussels may be below the lower critical point and able to use growth to fill in gaps created by predation. Often interspersed with small mussels are groups of large mussels. The larger mussels may be above the upper critical point and thus have a refuge in size. This mosaic pattern may also reflect pulses of recruitment or predation events that are patchy on a very small scale. Resolving this issue, however, will require a detailed analysis of growth, recruitment, and mortality on a very local scale.
I believe growth plays an important role in structuring many marine communities because many of the plants and animals found in these communities have indeterminate growth patterns. Mussels are not the exception because many marine invertebrates exhibit large variation in adult body size. This suggests that Harper’s (1977) contention that the population dynamics of plants and colonial animals are fundamentally different from the dynamics of most animals is not a clear-cut distinction. For many marine invertebrates, as in plants and colonial animals, community-level effects such as changes in spatial dominance depend on “populational” changes in terms of biomass or cover. These may be far more important than changes in the number of genetically distinct individuals. I would also add that the effects of growth and the degree to which an animal can respond through growth (thus appear to be “plant-like”) will vary from place to place. In particular, animals with indeterminate growth that are capable of rapid growth in areas of high productivity may be able to use a plant-like response, that is rapid growth, to offset the effects of mortality. Animals in highly productive habitats may be more likely to withstand disturbances and predators and to maintain dominance through growth. This can only occur in areas where rapid growth is possible. Animals in low-food habitats have little potential for rapid growth, and here the maintenance of spatial dominance must rely on recruitment to offset mortality. Thus, site-specific growth rates may determine how individuals of the same species dominate a variety of different habitats. Our interpretation of the importance of recruitment vs. predator-induced mortality in specific marine communities may, in fact, depend on a species’s potential, both environmentally and evolutionarily, for growth. It raises the possibility that, at least for the question of spatial dominance, the distinction between plants or plant-like animals on one hand and non-colonial animals on the other is not as sharp as Harper (1977) suggested.
ACKNOWLEDGMENTS
Von Bertalanffy curves of Seed’s data were fitted by an iterative non-linear growth model written by Art Dunham. Peter Fairweather and Marcel Frechette made many helpful comments, which greatly improved the clarity of the manuscript.
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