Electronic Supplementary Materials
Nutrient Excretion
The two most commonly applied methods to estimate fish excretion are
experimentation (Schaus 1997; Whiles et al. 2009) and bioenergetics models (Schreck
and Moyle 1990). We used both methodologies in a Bayesian framework, whereby our
empirical data were informed with data generated from a bioenergetic approach. This
approach allowed us to underpin extensive empirical data to produce extremely robust
models with realistic error. Specifically, we ran Bayesian simple linear regression models
on all output data generated by the bioenergetics models (see detailed methods for
bioenergetics models below) using uninformative priors. The model output from these
regressions generated the prior distributions used to inform the empirical data (McCarthy
2007). In this way, we took advantage of all available data and multiple approaches to
generate robust estimates of nutrients supplied by aggregating grouper.
Empirical Estimates
Excretion rates for grouper, captured using hook and line or traps, were
determined following the methodologies of Schaus et al. (1997) as modified by Whiles et
al. (2009). Grouper were incubated in bags containing a known volume of prefiltered (0.7
µm pore size Gelman GFF) seawater for ~30 min. The time interval was chosen based on
the recommendations of Whiles et al. (2009) and our own experimental time trials
assessing excretion rates every 5-15 min for up to 2 h. Incubation bags were placed in a
holding tank of water at similar ambient temperature (20-23oC). Excretion rates (g·h-1)
were calculated as the difference between dissolved nutrient concentrations (soluble
reactive phosphorus (SRP-P) and ammonium (NH4-N)) before and after the incubation.
Excretion rates were control corrected with values obtained through multiple (typically
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n=6) identical control incubation bags without grouper. Water samples were immediately
filtered (0.45 m Whatman nylon membrane filters) and placed on ice. Samples were
analyzed for NH4 within 10 h using the methodologies of Taylor et al. (2007). Samples
collected for SRP analysis were frozen for transport to the Odum School of Ecology
(UGA) where SRP was determined using the persulfate digestion method (Murphy and
Riley 1962).
Each grouper used for excretion experiments was weighed for wet mass (mean =
324.3 ± 67g), measured to standard length (mean = 212 ± 378 mm), dissected to remove
stomach contents, and then frozen for transport to the Odum School of Ecology. Samples
were lyophilized to a consistent dry weight, blended to homogeneity, and then ground to
a powder with a ball mill grinder. Ground samples were analyzed for %C and N content
with a CHN Carlo-Erba elemental analyzer (NA1500), and for %P using dry oxidationacid hydrolysis extraction followed by a colorometric analysis (Aplkem RF300;
Solorzano and Sharp 1980). Elemental content was calculated on a dry weight basis.
Grouper were captured under permits provided by The Bahamas Department of Marine
Resources. The University of Georgia’s Institutional Animal Care and Use Committee
approved protocols for the capture and handling of fish (AUP # A2009-10003-0).
Bioenergetics Models
Bioenergetics modeling estimates nutrient excretion rates of an organism using a
mass balance approach given a priori knowledge of the natural history (e.g., diet, growth
rate), physiology (e.g., stoichiometry of predator and their prey, assimilation efficiency of
nutrients, consumption rates, energy density of prey), and environmental conditions
(temperature; Schreck and Moyle 1990; Hanson et al. 1997).
Stoichiometry of grouper was determined by averaging the percent nutrient
content of all grouper samples. Energy densities of prey items, as determined by analysis
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of stomach contents, were obtained from Cummins and Wuycheck (1971). Assimilation
efficiencies, which marginally influence model estimates (Hood et al. 2005), were
assumed to be 80% for N and 70% for P based on literature recommendations (Schreck
and Moyle 1990; Hanson et al. 1997). The growth rate of an animal is an influential
parameter in bioenergetics (Hood et al. 2005). As such, published growth rate values
were obtained from Fishbase (Froese and Pauly 2000). Models were parameterized using
diet data collected from hundreds of grouper by the authors (Layman and Silliman 2002;
Layman et al. 2007; Hammerschlag-Peyer and Layman 2010; Layman and Allgeier 2012;
J.E. Allgeier unpublished data).
We determined consumption rates for grouper using Fish Bioenergetics 3.0
software (Hanson et al. 1997). Bioenergetics models were run using R software. To
account for inherent error associated with parameterizing such models, we propagated
uncertainty associated with diet content and consumption rates, two of the most
influential parameters (Schreck and Moyle 1990; Hanson et al. 1997; Schindler and Eby
1997), through the models using Monte Carlo simulations. Specifically, a normal
distribution of values was created for each parameter with a standard deviation of 5% of
the maximum potential value of that parameter. In both cases the parameters represent a
proportion, thus: maximum value = 1, and standard deviation = 0.05. For each model run,
random draws were taken from within these distributions 5,000 times.
Field and Laboratory Methods for Bioenergetics Models
We used empirical data to parameterize diet nutrient content data for bioenergetics
models. Prey items, identified through analysis of stomach contents of grouper, were
caught using hook and line, traps, or netting. Gut passages were cleared, either through
live captivity without feeding or via dissection. Samples were frozen and transported to
the University of Georgia for nutrient analysis. Samples were dried to a constant weight
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in a lyophilizer and ground to a fine powder, using a ball mill grinder. When necessary,
large samples were first ground in a blender. Crustacean samples were acidified to
remove inorganic carbon. Nutrient content (%C, N, and P) were determined from ground
samples as described above. Elemental content was calculated on a dry weight basis. See
Allgeier et al. (2013) and Burkepile et al. (2013) for further details on bioenergetics
models.
Bayesian Models for Nutrient Supply
Bioenergetics models were used to inform empirical estimates of fish excretion
through Bayesian linear regression models. For example, the final model to estimate
excretion rates for grouper was generated using the slope and intercept posterior
distributions from the bioenergetics model to set the bounds on the Bayesian priors that
informed the empirical excretion data. Models were run using a Markov Chain Monte
Carlo with three chains for 50,000 iterations with a burn-in period of 1,000. Data for
excretion models were not transformed, as assumptions of normality were met. Bayesian
analysis was run using the “rjags” package in R (Plummer 2013).
Aggregation Loading Models
Current Aggregation
Estimates of Nassau grouper abundance, length frequency distributions, and the yearly
durations for current fish spawning aggregation (FSA) were collected from the Little
Cayman FSA (2004 through 2009) as described in Heppell et al. (2012). The Little
Cayman FSA, located off of Little Cayman Island, British West Indies, has been
monitored since 2003 (Fig. 1; Whaylen et al. 2004; Whaylen et al. 2006; Heppell et al.
2012). N and P loading rates were estimated separately for each year. Because it was not
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logistically possible to measure the length of each fish on the aggregation each day, a
random subset of fish on the FSA that year were measured using the methods presented
in Heppell et al. (2012) which was used to create a discrete empirical length frequency
distribution. A length (mm) was assigned to each fish on the aggregation (based on daily
abundance estimates) by sampling with replacement from the empirical length frequency
distribution. Lengths were converted to mass following Sadovy and Eklund (1999). Mass
was used to estimate N and P excretions using the excretion models described above.
Individual N and P estimates were summed to get a daily estimate of excretion. An
estimate of N and P was generated for each day the grouper remained on the FSA. This
process was repeated 10,000 times, allowing for variation in fish lengths and the
coefficients of the excretion model. For each iteration, the coefficients of the excretion
model were randomly drawn from the posterior distributions of the Bayesian models
described above. While the aggregation occurs at depths of 24-33 m, when not spawning,
aggregating fish typically stay within 6 m of the bottom over an area of approximately
5,000 m2 (Whaylen et al. 2004). Therefore, in order to facilitate comparisons with other
published estimates of consumer-derived nutrient loading, we present N and P nutrient
load estimates in g m-2 day-1 (Allgeier et al. 2013). It is important to note that grouper do
appear to feed, at least opportunistically, while on the aggregation (personal observation)
and spawning anorexia has not been reported for this species. As a result some of the
nutrients excreted may simply represent recycling of nutrients within the aggregation site
with some exportation of nutrients away from the aggregation site, pathways with
potentially important ecological implications as well. Additionally, while feeding does
influence excretion rates the impact is seen immediately after feeding and dissipates
within hours. While some of the groupers used to determine the empirical estimates of
excretion rates had undoubtedly fed recently it is unrealistic to assume all had done so.
This, along with the combined approach of empirical estimates and bioenergetic models
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reduces the likelihood of drastic overestimation of excretion rates due to any differences
in feeding rates.
Historic Aggregation
Anecdotal reports of fishermen, recorded by Smith (1972), assert that the
Bahamas supported many similarly sized aggregations at the time that Smith made his
observations. By the time Smith (1972) observed and described the aggregation had
already been heavily fished. Therefore, our estimate of historic nutrient supply is likely
an underestimate.
To obtain an estimate of the standard deviation in daily fish abundance at the
historic aggregation we used a linear equation generated from regressing the standard
deviation of the daily abundance of fish on the log10 of the peak grouper abundance for
each year of the Little Cayman FSA. The equation:
standard deviation = 2541.1*log10(peak number of grouper)-7878.6
was used to approximate the standard deviation of the number of fish on the aggregation
for both the conservative (30,000) and upper end (100,000) abundance estimates for the
historic aggregation. The daily fish abundance on the aggregation was selected by
generating a vector with six (the duration of the aggregation in days) numbers pulled
from a normal distribution with a mean of 30,000 (conservative) or 100,000 (upper end)
and the calculated standard deviation.
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