Present address and correspondence: Department of Biological Sciences, Stanford University, Stanford, CA 94305–5020, USA (e-mail firstname.lastname@example.org).
1Knowledge of the impact of oil spills on coastal communities, in California and elsewhere, is currently limited by a lack of long-term data, the inability to infer causality from monitoring studies, and the necessarily limited spatial and temporal scales of experimental studies.
2This study therefore used a modelling approach to investigate the combined effects of different intensities of an oil spill and recruitment variation on a barnacle Chthamalus fissus population. The methodology and results are likely to apply to any similarly open marine populations with dispersive larval forms.
3The model consisted of a source population comprising individuals that reproduced based on size and probability of mortality. Larvae from the source population entered a larval pool. A proportion of the larvae from the larval pool recruited to a focal population within the region.
4The model was used to assess the effects on recruitment to the focal population of (i) the size structure of the source population, (ii) the intensity of oil spills in the source population, and (iii) recruitment intensity to the focal population.
5Differences in the size structure of the source population had little effect on the reproductive output of the population relative to the intensity of the oil spill. Similarly, the intensity of the oil spill had a stronger influence on recruitment to the focal population than the size structure of the source population. Size structure of the source population was important, however, when evaluating the seasonal trajectory of the focal population.
6Modelling provides a format in which questions about the effects of human impacts can be addressed that would be intractable using experiments. The results of this model suggest that recruitment variation, along with the processes underlying recruitment variation, are critical to predicting the effects of disturbance on open marine populations.
As with most anthropogenic impacts, there is a need for well-designed research on the effects of oil spills on coastal marine habitats. The central and southern California coastline (USA) is susceptible to oil spills due to high amounts of tanker traffic and offshore oil drilling. Past experiments and monitoring programmes in this region have provided information and predictions regarding the effects of oil spills on nearshore habitats in the region, particularly following the Santa Barbara oil spill in 1969 (Foster et al. 1970). Further research assessing the consequences of oil spills for coastal marine habitats along the California coast, and world-wide, is needed because many of the conclusions that can be drawn from the results of work to date are somewhat limited. This is due to a lack of long-term data, the inability to infer causality in monitoring studies, and the limited spatial and temporal scales of experimental studies as mentioned above.
If a nearshore community has not been monitored prior to a spill, recovery from the impact must be assessed by comparing an approximation of the abundance and distribution of resident species prior to the spill with similar data collected after the spill. It is often difficult to determine if species distributions and abundances were estimated accurately prior to the spill (Nelson 1982; Foster et al. 1988; Jackson et al. 1989; KLI 1992). As a result, studies conducted after an oil spill are often unable to provide accurate predictions of recovery from the disturbance caused by oil spills or conclusively demonstrate that the oil spill was responsible for any presumed change.
An alternative approach to monitoring programmes is to estimate the effects of an oil spill through extrapolation from controlled experimental field studies where oil is applied to small replicate plots (McGuinness 1990; Bokn, Moy & Murray 1993). Although such experimental studies of oil and gas impacts have been done, it is difficult to generalize from these results to any particular situation due to the spatial and temporal differences among oil spills (Foster et al. 1988; KLI 1992). Further, realistic results from experimental studies are often unattainable due to the constraints of designing an experiment that would encompass the spatial scale over which an oil spill occurs (Foster et al. 1988; Gilfillan et al. 1999).
Incorporating data from post-spill monitoring programmes and experiments into models strengthens the conclusions of impact assessments. Models can be parameterized to include ‘pre-spill’ data (e.g. measures of natural growth rates, reproductive output, size structure and population size). Data from actual oil spills can be used to parameterize variability in the amount of oil cover, the probability of mortality due to cover, etc. Further, the results of experiments done over small spatial or temporal scales can be incorporated into a model to address the effects of the disturbance over larger and more appropriate scales.
The acorn barnacle Chthamalus fissus (Darwin) was used as a model organism for this study. Chthamalus fissus is common in the high intertidal zone along the California coast and much is known about its life-history traits and population dynamics. Therefore, realistic biological parameters could be incorporated into the model. In general, C. fissus suffers high mortality following oil spills. However, oiling may also have sublethal effects, e.g. reduced growth and/or reproduction (Foster et al. 1970; Nelson 1982; Southward 1982; Crothers 1983; Bokn, Moy & Murray 1993). The recovery rate of acorn barnacle populations following oil spills depends on recruitment rates (Bokn, Moy & Murray 1993). Chthamalus fissus has life-history characteristics similar to many other intertidal invertebrates, so the predictions of the model can be applied to other open marine populations that are at risk of disturbance due to oil spills.
Individual variation in reproductive output was incorporated into a population model using a dynamic state variable model (Mangel & Clark 1988; Mangel & Ludwig 1992; Clark & Mangel 2000) in order to address three questions. First, given that individuals within a population show considerable variation in reproductive output (Stearns 1992), what is the effect of this variation, conditional on size and the probability of mortality, on a population comprising different-sized individuals? Secondly, does the interaction between variation in reproductive output and subsequent recruitment affect population dynamics? Finally, how are these dynamics influenced by variation in recruitment, combined with different intensities of oil spills? The results of the model were also used to make general predictions regarding the effects of varying intensities of oil spills on intertidal and subtidal organisms with open population dynamics.
STUDY SYSTEM AND LIFE HISTORY OFchthamalus fissus
Chthamalus fissus occurs in the upper rocky intertidal zone along the coast of California. The life history of C. fissus consists of a sessile adult phase and a planktonic larval phase. Adult C. fissus live for about 2 years and are reproductive within the first year (Wethey 1984). Chthamalus fissus is internally fertilized and an internal brooder. Therefore, the number of nauplii (the initial larval stage of barnacles) is correlated with adult size, measured as rostrocranial aperture (Morris, Abbot & Haderlie 1980; Wethey 1984). Chthamalus fissus has up to 16 broods per individual per year, primarily from spring to autumn (Morris, Abbot & Haderlie 1980). Two-hundred to 3000 nauplii are released per brood (Morris, Abbot & Haderlie 1980). Barnacle larvae spend 4–6 weeks in the plankton before settling into the adult habitat, and settlement peaks in the spring.
AN OVERVIEW OF THE MODEL
The model progressed in two stages. First, it was necessary to identify the resource allocation strategy that would be predicted under natural disturbance and mortality schedules. This was done by calculating reproductive output and growth as a function of time and C. fissus size, given a baseline probability of mortality. Secondly, these results were incorporated into a population model by quantifying reproductive output of size-structured source populations to the larval pool, under different oil spill intensities (Fig. 1). A proportion of the larval pool recruited to a focal population elsewhere on the coast.
INDIVIDUAL REPRODUCTIVE OUTPUT
The state variables
Consider a sessile invertebrate characterized by a life-history trade-off between growth and reproduction. At a given point in time (t), an individual can either grow or reproduce under a certain probability of mortality due to natural causes, such as predation, competition and abiotic factors.
The state of the organism is defined by its size, here measured by the length of the rostrocranial aperture, L(t), measured in millimetres. Time is divided into 104 weeks to represent the life span of C. fissus (2 years): the first year is represented by t= 1–52, and the second year by t= 53–104. At the end of each year (late autumn through early winter), individuals grew and did not reproduce, thereby incorporating seasonality into reproduction (Hines 1978).
Changes in the state variables
The state variable, length (L(t)), changes over time as follows:
L(t + 1) = L(t) + (k)(L∞ − L(t))q(eqn 1)
where L∞ is the maximum length of C. fissus, and k and q are parameters in the equation used to fit an asymptotic curve that represents a realistic maximum growth function, assuming an individual grows rather than reproduces at each time step (Table 1 and Fig. 2).
Table 1. Parameters and values used in the model
The maximum time that includes two reproductive periods in the life span of a barnacle
The current time, where t < T, in weeks
The state variable (size in mm) at time t
The maximum size (rostrocranial aperture length) of an individual barnacle
Parameter in growth equation
Parameter in growth equation
Size at time t in mm
Reproduction at size l (number of larvae)
Mortality rate per week
The probability of mortality in 1 week, calculated as 1 − e−u
0·5 larvae mm−3
Reproduction coefficient converting size to number of larvae
The maximum number of individuals in the focal population
Proportion of the larval pool recruiting to the focal population
A positive correlation between length and fecundity was assumed (Wethey 1984; Stearns 1992), such that if an individual reproduces (i.e. no growth) at a given time step, reproductive output (R(L)) depends on length as defined by:
R(L(t)) = β(L(t)3 − 1)(eqn 2)
where β is a coefficient that converts rostrocranial aperture length into number of larvae as a function of test volume (Table 1).
Characterizing the trade-off between growth and reproduction
At each time step, there is a trade-off between present and future reproduction. On the one hand, the organism can continue to grow without reproducing but risks dying prior to reproduction, although, if it continues to grow, its future reproductive output should be greater. On the other hand, the organism can reproduce in the current time step, in which case it does not grow, possibly resulting in lower lifetime reproductive output but avoiding the potential loss of reproductive output in the future due to mortality.
Let F(L, t) = the individual's maximum expected reproductive success (= value), at length L, from period t to T, where T is the maximum lifetime of an individual (2 years)(eqn 3)
At the last time step (t = 104), maximum expected reproductive success (F(L, T)) is equivalent to reproductive output dictated by the individual's size R(L(t)).
The maximum fecundity, at a given length (L), and time (t), is defined as the maximum ‘value’ given either growth or reproduction:
F(L, t) = max(Fgrow, Freproduce)(eqn 6)
A backward iteration of the model predicted the optimal behaviour for an individual of a given length at each time step under probability of mortality due to natural causes such as predation, competition and abiotic factors. F(L, t) was calculated by working backwards in time from t=T · F(L, T) is equal to the reproductive output dictated by the individual's size at the last time step. F(L, T − 1) was calculated for each value of L, using F(L, T). This also gave the maximum value of growth or reproduction for each L. The procedure was repeated for F(L, T − 2) using the values of F(L, T − 1) calculated in the previous step. The same method was used for each time step (T − 1, T − 2, T − 3, etc.). For a given time step, an individual can either grow or reproduce.
The threshold length for reproduction indicated the optimal behaviour for a C. fissus at each length/time combination. The boundary on which the value of growing equals the value of reproducing dictated the threshold length for reproduction (Fig. 3). If the state of the individual at a given time was below the boundary, the optimal behaviour was to continue to grow, whereas if the state was above the boundary, lifetime reproductive output was greater if the individual reproduced. Again, this shows the optimal behaviour (i.e. to grow until a certain size and then reproduce), but an individual could reproduce in one time step and continue to grow in future time steps.
As time increased, the optimal size at reproduction decreased. In other words, maximum lifetime reproductive output for an 8-mm individual at 20 weeks would be achieved by continuing to grow and then reproducing at a larger size, whereas at about 80 weeks it would be achieved by reproducing at the current time step. These results were incorporated into the population model using a forward iteration of individual C. fissus behaviour based on different sizes at t= 1, which allowed for variation in reproductive output from the source population.
THE POPULATION MODEL
Individual differences in reproductive output were incorporated into an individual-based population model to investigate if these differences influenced the total reproductive output of the source population. The source population was defined as 3000 individuals. The reproductive output of the ith individual was determined by its size at time t, Li(t), and whether it reproduces or not. Size structures of natural C. fissus populations often vary spatially and/or temporally, depending on a variety of factors such as food availability, disturbance and recruitment rates (Roughgarden, Iwasa & Baxter 1985). Therefore, the size structure of the source population was varied to investigate if there were differences in the total reproductive output of populations characterized by different size structures. Thus, in each iteration of the model, the population consisted of different proportions of individuals in each size class, and each of these individuals either grew or reproduced at each time step, based on the maximum fecundity at a given length and time, as calculated by equation 6.
At t= 1 the source population was dominated by small, intermediate or large individuals (Fig. 4). The size frequency distribution of the 3000 individuals consisted of a recruit class plus a normal distribution of adults, which was calculated using the Box–Muller algorithm (with a mean of 5 mm for the small size structure, 6 mm for the intermediate size structure and 7 mm for a large size structure, and a variance of 1 mm; Press et al. 1986). As mentioned above, because the size structure of C. fissus populations can depend on recruitment rates (Roughgarden, Iwasa & Baxter 1985), the number of recruits in each population structure was also varied. The small size structure consisted of 1000 recruits, the intermediate size structure consisted of 750 recruits, and the large size structure consisted of 100 recruits. Thus, for each iteration of the model, the size structure of the source population was dominated by C. fissus of different sizes. This cohort of individuals was followed over the 2-year iteration of the model. The size structure of the source cohort changed over time due to growth and mortality, and therefore reproductive output changed over time. This model construction allowed the investigation of whether differences in size-based reproductive output at the individual level resulted in differences in the total reproductive output of the source population.
Theory and empirical work suggest that populations with obligate dispersive stages are defined as open on a small scale (i.e. metres to kilometres); larval supply is independent of local population and community dynamics (Gaines & Lafferty 1995; Connolly & Roughgarden 1999). In contrast, at a regional scale (tens to hundreds of kilometres), production of larvae is a major determinant of recruitment levels (Hughes et al. 2000). Thus, at larger scales, population sizes are determined in part by adult stock sizes, which are affected by benthic interactions such as competition, predation and disturbance (Connolly & Roughgarden 1999). In this model, the focal population is open; recruitment is not a direct function of local larval production. At a regional scale, benthic and pelagic processes are coupled. Reproductive output from the source population is linked to the dynamics of the focal population through a regional ‘larval pool’.
Constructing the larval pool
Total reproductive output (Lp(t)) that enters the larval pool in the water column, is the sum of the reproductive output of the 3000 individuals in the source population:
Lp(t) = Σδ(i, t)(eqn 7)
where δ(i, t) is the reproductive output of the ith individual at time t. Reproduction for each individual was calculated based on equation 5. Total reproductive output of the source population was then calculated for each size structure.
Recruitment and population dynamics
Recruitment at time t is equal to a proportion of the larval pool:
R(t) = φ(Lp(t))(eqn 8)
By varying φ, the proportion of larval recruitment from the water column into the focal population was varied; thus φ accounts for various pre-recruitment factors that influence the proportion of larvae recruiting to the focal population (e.g. larval mortality in the plankton, the influence of current patterns, etc.).
The population size at time t+ 1 depends on the population size at time t, and recruitment at time t:
The number of individuals killed by a disturbance, such as an oil spill, can be variable. For the purposes of this model, it was assumed that the focal population consisted of 10 individuals at t= 1. Thus, the population model predicts the growth trajectory of the focal population over 2 years (the same time span used when modelling individual variation in reproductive output), starting with only a few individuals. Oil spills of varying intensities (10% and 70% of the source population killed) were then incorporated into the model. Thus, the overall structure of the model consisted of three different size structures of the source population (small, intermediate and large), three different oil spill intensities in the source population (no spill, 10% killed and 70% killed) and three different recruitment intensities (low, intermediate and high). All possible combinations of these factors were iterated to assess (i) how differences in size structure affect the reproductive output of the source population; (ii) how different intensities of an oil spill interact with variation in size structure to affect reproductive output from the source population; and (iii) how the interaction between different oil spill intensities and recruitment variation influenced the dynamics of the focal population.
REPRODUCTIVE OUTPUT OF THE SOURCE POPULATION
Differences in the size structure of the source population resulted in small differences in the cumulative reproductive output of the source population (Fig. 5), which was due to individual variation in the timing and magnitude of reproductive output (Fig. 3). For no spill and 10% killed, the cumulative reproductive output of the source population was about 10% greater when the source population was dominated by large individuals than when it was dominated by small individuals. When small individuals dominated the source population, fewer individuals reached the threshold length for reproduction than when large individuals dominated the population, resulting in slightly lower cumulative reproductive output.
Increased oil spill intensity resulted in a considerable decrease in total larval production (Fig. 5). The magnitude of the effect of oil spills far exceeded the effect of different size structures in the source population (note y-axis). Thus, cumulative reproductive output to the larval pool depended more on the intensity of the oil spill than on the size structure of the source population.
RECRUITMENT AND DYNAMICS OF THE FOCAL POPULATION
Increased oil spill intensity in the source population resulted in a sizeable decrease in recruitment to the focal population (Fig. 6). The magnitude of recruitment was a direct product of recruitment intensity. Recruitment was slightly higher when the source population was dominated by large individuals than when it was dominated by small individuals for all oil spill and recruitment intensities. Therefore, as with reproductive output of the source population, recruitment to the focal population depended more on the intensity of the oil spill than on the size structure of the source population.
The size structure of the source population was important, however, when looking at the seasonal trajectory of the focal population. The simple mathematical relationship between the intensity of the oil spill, the proportion of larvae recruiting and recruitment to the focal population disappeared when the focal population size was plotted over time. The seasonal dynamics of the focal population depended on the intensity of the oil spill, recruitment intensity and the size structure of the source population. The population size over time was plotted under no oil spill and when 70% of the source population was killed (Fig. 7). Under both oil spill intensities, seasonal declines in the focal population were greater under small and intermediate size structures than under a large size structure. In fact, there was no seasonal decline in the focal population when the size structure of the source population was large and recruitment intensity was intermediate or high. Differences in recruitment intensities resulted in time lags in increases in the focal population size (i.e. the rate of population increase was slower when recruitment was low than when it was high), particularly under small and intermediate size structures. Although the focal population reached similar maximum sizes under intermediate and high amounts of recruitment in all cases, it took 5–10 weeks longer for the population to reach the maximum size when recruitment intensity was intermediate than when recruitment intensity was high. The focal population did not reach the maximum size when recruitment intensity was low.
The recovery of open populations from oil spills depends on the interactive effects of the size structure of the source population, the intensity of the oil spill (and the resulting adult mortality) and recruitment intensity. Although the size structure of the source population had little effect on reproductive output and recruitment to the focal population, there was a considerable influence of size structure on the seasonal dynamics of the focal population. Source populations consisting of larger individuals were less likely to result in recruitment limitation on a regional scale in the face of disturbance and reduced survivorship of propagules than those consisting of small individuals.
The results of the model are consistent with past research on the relationship between recruitment and the dynamics of the adult population (reviewed by Caley et al. 1996). Under low amounts of recruitment and if resources are available, a population is defined as recruitment-limited. In the low-recruitment run of the model, the recovery rate of the focal population was slowest, the population size never reached the maximum (i.e. resources, specifically free space for recruitment, were still available) and seasonality in recruitment was apparent in the population dynamics.
At high amounts of recruitment, populations are defined as recruitment-unlimited. In recruitment-unlimited populations, recruitment is sufficiently high such that any further increase in the number of individuals entering a population does not result in a further increase in adult abundance (Raimondi 1990; Menge 1991; Caley et al. 1996; Connolly & Roughgarden 1998, 1999). Under intermediate and high levels of recruitment, whether the focal population was recruitment-limited or unlimited depended on the size structure of the source population and on oil spill intensity. More importantly, conclusions regarding recruitment limitation depended on seasonality in recruitment. When the source population consisted of large individuals, there was no oil spill and recruitment was intermediate or high, the population remained at a maximum size over time. In contrast, in all other runs of the model, conclusions regarding recruitment limitation depended on time.
The results of the model have implications for managing open populations because decisions are often based on whether or not a population is recruitment-limited. If a population was sampled at the maximum population size, managers might conclude that an anthropogenic impact resulted in little to no change in the population and recruitment was sufficiently high to allow for full recovery (Fig. 7; intermediate size structure, 70% spill at week 40). In contrast, if the same population was sampled at a different time of year, managers might conclude that the impact resulted in a change in the population size and further monitoring of the population was required to assess recovery (Fig. 7; intermediate size structure, 70% spill at week 60). Thus, the results highlight the importance of long-term monitoring of open populations in order to accurately assess both pre- and post-impact population dynamics.
Although this is a somewhat simplified model of an open marine population, it illustrates that recruitment variation is a critical factor in predicting the effects of disturbance on populations with dispersive larval phases. The model illustrates that size structure of a population is a key element in determining the degree to which recruitment variation will exert an effect at a regional scale. Past research has shown that recruitment (Caley et al. 1996) and disturbance, particularly due to oil spills (Foster et al. 1988; Jackson et al. 1989; KLI 1992; Gilfillan et al. 1999), can vary considerably in space and time. Further, empirical work has shown that colonization of free space depends on when a patch is created relative to seasonality in larval abundance (Kay & Keough 1981). Therefore, recovery from an oil spill will depend on the timing and intensity of the spill relative to the timing and intensity of reproduction in the region and subsequent recruitment to the population in question. The results of the model suggest we need to understand stock–recruitment relationships and what processes underlie recruitment variability in populations with obligate dispersive phases. Without this knowledge, we cannot evaluate accurately the consequences of anthropogenic impacts on populations with dispersive phases.
I thank Marc Mangel for his enthusiasm, guidance and untiring assistance through all of the stages of the model and the paper. In addition, I thank Pete Raimondi and Craig Syms for their feedback on the model and for reading multiple drafts of the paper. I appreciate the comments of N. Barlow, L. Botsford, A. Boxshall, E. Danner, S. Henson-Alonzo, T. Minchinton, Y. Springer and four anonymous referees on previous versions of the paper. This research was supported in part by the Partnership for Studies of Coastal Oceans, a grant from the David and Lucille Packard Foundation, an NSF Graduate Research Training grant (GER-9553614), and the Minerals Management Service, US Department of the Interior, under MMS Agreement no. 14-35-0001-30761. The views and conclusions contained in this document are those of the author and should not be interpreted as necessarily representing the official policies, either express or implied, of the US Government.