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184
Notes
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Submitted: 10 August 1995
Accepted: 8 April 1996
Amended: 20 July 1996
1997, 184-192
Society
of Limnology
and
Oceanography,
Inc
Some aspects of the analysis of size spectra in aquatic ecology
Abstract-The
established approach to model seston size
distributions involves the grouping of particles within logarithmic size classes and the examination of the relationship
between density, or normalized biomass, and the characteristic
sizes of the classes. Here we examine the distributional basis
of the established approach and draw a connection between
the biomass size spectrum and the Pareto distribution, a model
widely used in other disciplines dealing with size-structured
systems. We provide efficient estimators of the parameters and
also suggest that datasets exhibiting significant departures
from a smooth power function decline can be adequately modeled using a Pareto type II distribution.
Current instrumental developments in the analysis of individual particles have fostered research approaches based
on individual particles (rather than on volume-averaged
compound samples) as the units of analysis in biological
oceanography (Legendre and Le Fevre 1991; Falkowski et
al. 1991). This approach originated with the advent of au-
tomatic particle-sizers and the discovery of fundamental regularities in the size distribution of oceanic seston (Sheldon
et al. 1972). These findings were followed by research, both
experimental and theoretical, on the implications of the observed regularities in the size distribution of marine (e.g.
Borgmann 1982, 1987; Rodriguez and Mullin 1986a,b) and
freshwater seston (Sprules et al. 1983; Peters 1983, 1985)
and benthos (Schwinghamer 1981; Hanson et al. 1989). The
established approach to model seston size distribution involves grouping particles within logarithmic size classes and
examining the relationships between their density, or biomass normalized to the width of each size class, and a characteristic value of the size classes (Platt and Denman 1978;
Sprules and Munawar 1986). The distributional basis and
implications of this procedure, however, have not been fully
addressed (Ahrens and Peters 1991; Blanc0 et al. 1994).
Here we examine some mathematical properties of the
so-called normalized biomass-size
spectra (hereafter
NB-SS) and discuss their effect on the inferences drawn
from this model. We suggest that the description of plank-
185
Notes
tonic-or
organismal in general-size distributions should
be viewed in terms of distributional statistics and then show
the relationship between the NB-SS approach and the Pareto
distribution, a model widely used in other disciplines dealing
with size-structured systems. Although the two approaches
are not incompatible, we point out the weaknesses and disadvantages of the NB-SS procedure and identify some new
implications of the Pareto model. We then argue for the
adoption of a more flexible model-the Pareto distribution
of the second type. By using data from diverse aquatic ecosystems, we show that the Pareto model provides a better fit
to the data and also yields a direct estimate of the allometric
relationship between the size and abundance of system components.
Modeling biomass-size spectra in aquatic systems essentially amounts to describing accurately the size-frequency
distribution of the particles. Once this distribution is defined,
it can be integrated to calculate the probability that a particle
taken at random (or fraction of all particles) will fall within
a given size interval such that
proWs,ower< s < Supper)=
Fig. 1. Size data for east Atlantic Ocean fishes (MacPherson
and Duarte 1994) showing long right-tail distribution.
N&ucr-S”ppcr)
N
T
where s is size and pdf(s) is the probability density function
of the underlying distribution. The number or abundance of
particles (N) falling within this size range is simply the calculated probability multiplied by the total abundance (NT) of
all particles [N = N,prob(s,,,,, < s < supper)].If the chosen
measure of size is weight, then the biomass of particles within any size range can be easily calculated because the biomass and size of a single particle are then the same such
that
supper
biomass (‘l,uur~~~~“pper)
Size classes (cm)
= N,
s pdf(s)ds.
(2)
J hwrr
If size is expressed differently, say as a linear dimension of
the particles, then s in Eq. 2 can be replaced by the function
[f(s)] relating weight to size. For simplicity, we assume that
size is expressed as weight.
The examination of size distributions is not restricted to
biological oceanography, and the modeling of the size distribution of objects is a major goal of many disciplines dealing with size-structured systems. The description of size distributions is an important aspect of research in many fields,
including geophysics (Carder et al. 1971), marine geology
(Bader 1970), biogeochemistry (Wells and Goldberg 1994),
geography (Korcak 1938; cf. Mandelbrot 1982), earth sciences (Richter 1958; cf. Winiwarter and Cempel 1992), astronomy (Winiwarter 1983), engineering (Cempel 199 1;
Gaston 1993), economy (Pareto 1897; Simon and Bonini
1958), sociology (Auerbach 19 13), scientiometrics (Price
1967), and even semiotics (Zipf 1949). Scientists working
in these disciplines have long struggled to find the best model to represent the size distributions of their study objects.
Surprisingly, the distributions appropriate for such widely
differing objects and systems are all characterized by very
long right tails, a feature also ubiquitous to aquatic populations (Fig. 1). An examination of the models used to describe
size distributions in these disciplines also shows a remarkable convergence toward the use of a common underlying
distributional model (Table 1) of the general (cumulative)
form
N r2.5 = cd-~,
(3)
where A& is the number of objects greater than a threshold
size (S), and (Y and p are the fitted parameters describing the
total number of objects in the dataset and the logarithmic
rate of decline in number of objects with size, respectively.
Although several distributions can display such a power
function decline under certain parameter specifications (e.g.
the exponential and power functions distributions), the above
model corresponds to the Pareto distribution, first introduced
a century ago for the analysis of income distribution in society (Pareto 1897). The Pareto distribution has a probability
density function defined as
pdf(s) = ckc~-(~+”
(c > 0, s 1 k > 0),
(4)
where s is size and c and k are the distribution’s shape and
scale parameters, respectively. The parameter k is a constant
that represents either the size of the smallest object (for the
standard range of the Pareto variate, i.e. k < s < ~0) or a
compounded measure of the observed range of size. The
latter is more relevant to our case since no organism is of
infinite size. The parameter c is an empirical constant that
describes the decline of probability as size increases. Figure
2 shows the shape of the Pareto distribution for various values of c.
If we assume for a moment that this distribution adequately represents the size distribution of particles, then the
number of particles and biomass within any size range can
be calculated by integration after substituting this probability
density function into Eq. 1 and 2 as
186
Notes
Table 1. Models used to describe size distributions in different disciplines, showing remarkable similarity among them.
Subject
Discipline
Model
Economy
Incomes
n = aSPy
Sociology
Cities within a country
S(j) =
Biology
Species within genera
SCj) = aj-S
Geography
Aegean Islands
N(a) = const. amB
Semiotics
Words within texts and babbling
of babies
p,, = AnPB
Earth sciences
Energy release of seisms and
gaps between them
p(S, 2 S) = (S/So)-~
Economy
Business firms
P(S, 2 S) = (s/sp
Marine geology
Cosmic and terrestrial dust, seston, and fine sediments
N = K(xlx,)-c
Ecology
Patches of vegetation
Ecology
Parasites on a host, individuals
within species, genera within
families
Astronomy
Chemical elements within stars
or in the entire cosmos
Astronomy
Masses in the solar system or in
the Saturn system
Engineering
Vibrational amplitudes in mechanical systems
Biogeochemistry
Colloids in seawater
aj--P
Definition
y1= number of people
having the income %S;
a, y = const.
j = rank number, S(j) =
size of the object
ranked j; a, p = const.
j = rank number, S(j) =
size of the object
ranked j; a, p = const.
N(a) = number of islands
of area la: B = const.
IZ = rank number, p,, =
size of the object
ranked n; A, B =
const.
S = size, S, = min size,
S, = measured values
of a symptom (size);
y = const.
S = size, S, = min size,
S, = measured values
of a symptom (size);
y = const.
N = number of particles
> a given size x; K, c
= const.
prob(A < a) = const. amB
a = area, A = measured
value of area; B =
const.
pn = A(n + m)-”
n = rank number, pII =
size of the object
ranked n, m = parameter influencing the distribution for small n
only; A, B = const.
pn = A(n + rnmB
n = rank number p, =
size of the object
ranked n, m = parameter influencing the distribution for small n
only; A, B = const.
pII = A(n + rneB
n = rank number, p, =
size of the object
ranked n; m = parameter influencing the distribution for small n
only; A, B = const.
p(S, 2 S) = (S/S,,)-~
S = any symptom (size)
p(S, 2 S) = exp-(S/S,)-?
of technical condition
p(S, 2 S) = l-exp-(S/S&Y
of a mechanical sysp(S, 2 S) = 1 + y - ~SLSJ
tern, S, = min size, S,
= measured values of
a symptom (size),
P(S, > S) = probability of operating in good
conditions; y = const.
N = kd-0
N = number of particles
> diameter d; k, p =
const.
Reference
Pareto 1897 (cf. Winiwarter and Cempel
1992)
Auerbach 1913 (cf. Winiwarter and Cempel
1992)
Willis and Yule 1922 (cf.
Winiwarter and Cempel 1992)
Korcak 1938 (cf. Hastings and Sugihara
1993)
Zipf 1949 (cf. Winiwarter 1983)
Richter 1958 (cf. Winiwarter and Cempel
1992)
Simon and Bonini 1958;
Roehner and Winiwarter 1985 (cf. Winiwarter and Cempel
1992)
Bader 1970
Hastings et al. 1982
Winiwarter 1983
Winiwarter 1983
Winiwarter 1983
Cempel 1991, 1992,
1993
Wells and Goldberg 1994
187
Notes
1.6
l--m--
k=l
.*
if 1
43
SO.8
-si
n 0.6
2
a
1
2
3
4
5
6
Size (S)
Fig. 2. The probability density function of a Pareto variate for
different values of shape parameter c for k = 1.
Fig. 3. Expected normalized biomass-size distribution for a theoretical Pareto size distribution with c = 1.5 (Eq. 5).
normalized) would we observe were the particle sizes truly
distributed according to a Pareto law? This can be examined
by using the Pareto distribution (Eq. 6) integrated over equal
logarithmic (any base) size classes (i.e. by assuming Suppe/
Slower= J, a constant) and taking logarithms yielding
and
ckcs-Cds
+ ln[N,ck”(J-C+l - l)]
- ln(-c + 1).
(6)
respectively. Note that the only difference between Eq. 5 and
6 is the exponent associated with the size variable s, which
is more negative in Eq. 5 by exactly one unit.
The description of seston size distribution was prompted
by the advent of the electronic particle counter and sizer.
This instrument
S lower
gave the number
and volume
of particles
within logarithmic (base 2) size classes. Scientists adopted
the grouping of particles in log, size classes in their analyses
even when the sizes of individual particles were measured
directly under the microscope (e.g. Sprules et al. 1983; Gasol
et al. 199 1; Gaedke 1992). The size (S) dependence of particle abundance (N) and biomass (B) within each of the log,
size classes was then examined using regression analysis of
the form N (or B) = UV. However, this model was found
to be flawed by the differential width imposed by the logarithmic nature of the size classes, with small size classes
containing organisms of roughly similar sizes (e.g. l-2 pm)
and larger classes comprising organisms ranging meters in
size (cf. Blanc0 et al. 1994). The normalized spectrum,
where the biomass in different size classes is scaled to the
width of the size class, was proposed to solve this problem
(Platt and Denman 1978; Sprules and Munawar 1986). The
NB-SS has been adopted since as the model of choice to
examine plankton size spectra (Ahrens and Peters 1991;
Rojo and Rodriguez 1994).
What kind of biomass-size spectrum (normalized or un-
(7)
The slope of this Pareto-based biomass-size spectrum can
then be calculated by differentiating Eq. 7 with respect to
ln(S,,,,,), which is equal to the constant -c + 1. In other
words, if we plot the resulting biomass against X,,,,, (or Xupper)
on a double logarithmic scale, the resulting plot will be a
straight line with slope equal to -c + 1 (Fig. 3 shows a
hypothetical Pareto distribution with c = 1.5). Therefore, the
slope of the unnormalized biomass-size spectrum is an estimator of -c + 1, from which we can simply calculate the
parameter c of the underlying Pareto distribution. Normalizing (sensu Platt and Denman 1978)-the division of the
biomass within a size class by the width of the size classis done to estimate the average probability density within
each size range so as to obtain, in simple terms, a picture of
what the true histogram looks like. In the present context,
normalizing has the net result of subtracting one from the
slope of the unnormalized spectrum, thereby providing directly an estimator of the exponent -c of the biomass-size
distribution (see Es. 6). Thus, fitting straight lines to NB-SS
has corresponded, apparently unwittingly, to assuming that
the particle sizes are distributed according to a Pareto distribution. More remarkably, the slope of the normalized
spectra is an unbiased (although inefficient; see below) estimator of the exponent of the “biomass distribution” (Eq.
6). The underlying Pareto size distribution has an exponent
one unit more negative at -c - 1 (Eq. 4, Table 2).
The foregoing discussion illustrates how the normalized
biomass-spectrum approximately correctly depicts how the
biomass is distributed as a function of size. Given that for a
Notes
188
Table 2. Summary of exponents from the different representation of the size spectra in relationship to the parameter c of the
underlying Pareto size distribution.
Size spectrum representation
Total biomass over log classes
Biomass distribution
Abundance distribution
Exponent
-(c - 1)
-C
-(c + 1)
broad range of organisms the exponent of the NB-SS of
seston is often in the neighborhood of - 1, particle biomass
declines as the reciprocal of particle size (i.e. the biomass
of small particles is much larger than that of big particles).
This allometric decline does not in any way invalidate the
claim that the biomass over logarithmically widening size
classes will be independent of size (although not necessarily
equal or constant; Harris 1994), i.e. a flat Sheldon-type spectrum. There is no contradiction between the two last statements. However, we think that some confusion has arisen in
the interpretation of how biomass is related to size because
of the use of logarithmic size classes.
A more statistically sound way would have been to group
the individual weights into arbitrary but equal arithmetic size
classes, construct frequency or biomass histograms from
those, and then express them on a double-logarithmic scale.
It can be shown that, at the limit (AS 3 0), the resulting
plot of log biomass vs. log size would converge toward the
usual logarithmic normalized biomass-size spectrum, thereby demonstrating that biomass distribution is negatively related to size as a power function with an exponent close to
- 1. As an analogy, the difference in interpretation is equivalent to claiming that data truly originating from a log-normal distribution are in fact distributed symmetrically simply
because when we plot the frequencies with logarithmic size
classes, the resulting histogram seems symmetrical. If the
question is about the distribution of X, and X comes from a
log-normal distribution, then it is asymmetrically distributed
irrespective of the way we choose to visualize the histogram.
Incidentally, any distribution can be made to seem approximately flat upon appropriate nonlinear scale transformation
(of which the logarithmic progression is one), so the flatness
of the Sheldon-type spectrum should not be over-interpreted.
Misconceptions about the interpretation of the NB-SS,
however, extend beyond a misleading inference about the
allometric scaling of biomass distribution. Normalized biomass spectra are often interpreted as a plot of numerical
abundance vs. size (Platt and Denman 1978). Although they
do represent the abundance (because biomass divided by individual average weight equals numerical abundance) within
discrete log size classes as a function of a representative
value of the size classes (usually the minimum size, but cf.
Blanc0 et al. 1994), it is inappropriate to interpret these spectra as correctly representing the continuous size distributions
of particles. To obtain such a distribution, one would have
to further “normalize” the abundance-size spectrum, similar
to Blanco’s superspectrum (Blanc0 et al. 1994). More simply, one can use the above equations to infer how particle
abundance and size are related. We emphasize that the slope
of the NB-SS does not describe the allometric scaling of
abundance but rather corresponds to the allometric scaling
of biomass to size (Table 2).
Modern sizing instruments (e.g. flow cytometers, advanced electronic and laser particle counters) and microscopic techniques are now able to produce estimates of the
size of each individual particle examined. Grouping these
individual values into logarithmic size classes therefore represents a substantial loss of information by reducing the degrees of freedom available for statistical analyses. With the
computers now available, this thwarting of statistical power
cannot be justified on the basis of data reduction needs.
Moreover, estimates of the number of particles in classes of
larger particles are generally based on fewer data points than
are those in size classes of small particles, resulting in an
uneven weight of the individual observations when constructing normalized size spectra; that is, individual observations of large particles have a disproportionate weight on
the analysis compared to those of small particles. Even the
choice of the logarithmic base will influence the ensuing
results on at least two counts. First, it will create more or
fewer empty classes. Although empty classes are a common
observation in planktonic and benthic ecosystems (e.g.
Echevam’a et al. 1990; Rodriguez et al. 1987; Sprules and
Munawar 1986; Schwinghamer et al. 198 l), they are usually
ignored as if they represented missing values and not the
absence of organisms. Second, such a choice will affect the
uncertainty on the slope estimates (Blanc0 et al. 1994). Figure 4 illustrates the substantial changes in the slope estimate
(and its associated uncertainty) of the normalized size spectrum for the size distributions of sestonic particles from
northwest Mediterranean surface waters (B. Vidondo unpubl.
data) with different logarithmic bases. Thus, estimating the
parameter of the underlying Pareto distribution by lumping
observations into equal logarithmic classes, normalizing, and
finding the slope of the resulting log biomass-log size relationship is, from a statistical point of view, a suboptimal
procedure indeed. It is analogous to estimating the mean of
a normal distribution by constructing a frequency histogram
and fitting it to the equation (1/2n+)05exp[(x - ~)*/20-3
with some nonlinear algorithm.
There are two well-studied methods to estimate the parameters k and c of a Pareto distribution (Eq. 4) that make
use of all the individual observations-the
least-squares and
the maximum likelihood estimators (Johnson and Kotz
1970). However, because much significance is given to the
exponent parameter c in ecological studies, simulation studies (not shown) suggest that the least-squares estimator is
less sensitive to sampling and sizing errors than is the maximum likelihood estimator. The least-squares estimator of c,
derived from the cumulative distribution function of Eq. 4,
can be obtained simply by plotting the probability that the
size (s) of a particle taken at random will be greater than
size S [prob(s 2 S)] as a function of S on a double-logarithmic scale. In practice, the term prob(s 1 S) is calculated for
each particle simply as the fraction of all particles larger than
or equal to itself (N&NT). If the particles are distributed
according to a Pareto model, this graph will display a
straight line. An ordinary least-squares regression line
passed through these points will produce all the necessary
statistics to evaluate the parameters of the underlying Pareto
Notes
189
-1.2
0.08 -
Fig. 5. The Pareto distribution plot for size distribution of sestonic particles in waters from the surface and 70-m depth of the
northwest Mediterranean (B. Vidondo unpubl. data).
0.06 0.04 0.02 -
0
2
4
6
8
10
Logarithmic base of size classes
Fig. 4. Variation of the slope and its standard error (SE) of the
normalized size spectrum with changes in the logarithmic base used
to build size classes for the size distribution of sestonic particles
from northwest Mediterranean surface waters (B. Vidondo unpubl.
data).
distribution. The slope is an efficient and unbiased estimator
of the parameter c (Eq. 4), and the parameter k can be estimated as the antilog of the ratio intercept/slope. In the process, each particle contributes one point on this plot and
therefore all of the information contained in the observations
is used.
By using this approach we were able to obtain very precise and robust estimates of the parameters of the underlying
Pareto distribution in several planktonic datasets (Fig. 5),
without having to group the data into different logarithmic
size classes or to deal with empty size classes. The nearly
perfect r2 (0.99) clearly indicates that the Pareto distribution
approximates these data extremely well, not unlike the excellent fit with which the Pareto describes the distributions
of income, cities, biological species within genera and within
families, words, business firms, earthquakes, chemical elements, vibration amplitudes in mechanical systems, etc. (cf.
Winiwarter and Cempel 1992). However, deviations from a
perfectly straight line are still apparent for very small particles.
Acknowledging that the underlying distribution of pelagic
particles is of the Pareto type may also pave the way for a
more general explanation for the observed size distribution
of aquatic organisms in nature. At the general level, this may
be done by carefully examining the inferences drawn from
similar Paretian models proposed in the other disciplines
dealing with size-structured systems (Table 1). More specifically, however, Pareto variables have several properties that
may be unusual or unfamiliar to many ecologists. For example, it is well known in statistical theory that the expected
value of a Pareto variate with exponent -2 or shallower (i.e.
c < 1) is undefined. In our context, this means that the
average size of organisms (and hence biomass) is unstable,
i.e. estimates of the mean will not converge as the number
of observations increases (Peters 1994). It is striking and
perhaps not aleatory that most size-frequency distribution of
aquatic organisms hover around this critical value (corresponding to a NB-SS slope of - 1). Similarly, power law
distributions such as the Pareto are intimately related to fractals (Schroeder 1991), a theory that is providing fertile
ground to several applications in ecology (Meltzer and Hastings 1992). The negative of the exponent of a Pareto distribution (c + 1) provides a direct estimate of the fractal
dimension of the process under study (Schroeder 1991; Hastings and Sugihara 1993). Systems with a fractal structure
lack an inherent characteristic scale, suggesting that a single
process operating on all scales may be underlying the observed size structure. Whether this view is compatible with
the prevailing notion of a directional biomass flow up the
size spectrum (Borgman 1982, 1987; Platt and Denman
1978) remains to be further explored.
190
Notes
Researchers examining biomass-size spectra have often
speculated about the existence of secondary ecological scalings whereby organisms within common functional groups
(phytoplankton, zooplankton, fish) display steeper biomasssize spectra than expected from the overall trend (Thiebaux
and Dickie 1992; Dickie et al. 1987; Boudreau et al. 1991;
Peters 1991). Apart from the possibility that such steeper
lines might be the artifactual result of using ordinary leastsquares regression on datasets covering different ranges in
the independent variable (Prairie et al. 1995), such secondary
scaling may also be a real feature of the size structure of
aquatic ecosystems (e.g. Gasol et al. 1991). We suggest that
this hypothesis could be tested by estimating and comparing
the parameters of the Pareto distribution estimated for each
group. Following Winiwarter and Cempel(1992), this should
be achieved by first standardizing the data to the minimum
size within each group, i.e. by dividing all the size observations by the size of the smallest organism (so) within that
group (s’ = s/s,). Significant differences between the within
and among functional groups c parameter of the Pareto distribution would provide strong evidence for such secondary
scaling.
The Pareto model, just like the NB-SS, may exhibit a lack
of fit in certain datasets in which the abundance or biomass
of small particles is lower than that predicted by a straight
line (e.g. Ahrens and Peters 1991; Wells and Goldberg
1994). Gasol et al. (1991) aptly handled such cases by nonlinear curve-fitting, although, as they pointed out, the ecological meaning of the polynomial coefficients is far from
obvious. Instead, we suggest that such lack-of-fit problems
may be overcome by using a Pareto distribution of the second type (see Johnson and Kotz 1970), whose probability
density function is given by
0
0
0
-3
-2
-1
0
2
1
y q 1.433xiog (-0.102 t l-232)-1.433 xLog(xt1.232)
3
R2q 0.99
pdf(s) = c(K + D)“(s + D)-(< +I).
(8)
Eq. 8 differs from the original Pareto model (Eq. 4) only by
the additive constant D. Estimators for the parameters K, c,
and D of this distribution can be derived again by using its
cumulative distribution function and are obtained by regressing log[prob(s 2 S)] on s by means of an iterative nonlinear
regression algorithm with the model
log[prob(s 2 S)] = c log(K + D) - c log(S + 0). (9)
Although somewhat more complicated to compute, application of this distribution provided excellent fits to a dataset
on macrophytes poorly modeled by the ordinary Pareto distribution (Fig. 6) and would undoubtedly provide an even
more perfect fit to the Mediterranean seston data (Fig. 5).
The Pareto II has the additional advantage that it is more
general and flexible because the ordinary Pareto can be considered a special case of the second type when D = 0. Although the parameters D and c may not have the same intuitive meaning as with the Pareto I, they can also be compared among systems.
Finally, we stress that there will always be datasets for
which neither the Pareto (I or II) nor the NB-SS will appropriately describe the size and biomass distribution of aquatic
organisms (e.g. multimodal distributions). For such cases,
attempting to force the data to these specific distributions is
ill-founded and can be highly misleading.
0
-3.5 .’
-3
”
” ”
-2
”
”
-1
”
”
”
0
”
”
1
”
”
’ “I
2
3
Log Weight (g FW)
Fig. 6. The size distribution of submersed macrophytes in Lake
Meiphremagog
(Canada; C. M. Duarte unpubl. d&j plotted as
cumulative probability plot (0). Dash line corresponds to best-fit
line assuming an underlying Pareto size distribution and solid line
corresponds to a Pareto II distribution.
Our examination of the statistical basis of biomass-size
spectra has revealed peculiarities and caveats in the currently
accepted procedure. Although the slope of the NB-SS does
provide an estimate of the allometric exponent describing
the decline of biomass with increasing body size, the widespread conclusion, based on a slope of - 1, that biomass is
independent of size is misleading. Additionally, we showed
that the NB-SS approach is methodologically deficient. We
suggest that the distribution of particle sizes in aquatic systems should be considered as Paretian variates, either ordinary or modified (type II). This change in approach should
prove beneficial by rendering the results more general and
applicable to a wider range of datasets, as well as making
Notes
them more precise thus allowing more powerful tests of hypotheses. It may also prove a unifying approach to the study
of size-structured systems across other disciplines.
Beatriz Vidondo
Centro de Estudios Avanzados de Blanes-CSIC
Cami de Santa Barbara s/n
17300 Blanes, Girona, Spain.
Yves T. Prairie
Departement des sciences biologiques
Universite du Quebec a Montreal
Case postale 8888, succ. Centre-Ville
Montreal, Quebec H3C 3P8
Jose M. Blanc0
Station Zoologique, BP 28
06230 Villefranche-sur-Mer, France
Carlos M. Duarte
Centro de Estudios Avanzados de Blanes-CSIC
Cami de Santa Barbara s/n
17300 Blanes, Girona, Spain
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Submitted: 21 April 1995
Accepted: 1 April 1996
Amended: 25 November 1996
42( I ), 1997. 192-l 97
0 1997, by the American Society ofLlmnology and Oceanography,Inc
Charcoal analysis in marine sediments
Abstract-A
technique is described for measuring charcoal
in small samples (5 mg) of marine sediments to quantify the
contribution of charcoal to the total organic carbon loading of
marine sediments. Charcoal is measured as elemental carbon
by gas chromatography after acidification with hot concentrated nitric acid in situ within aluminum sample cups to remove calcium carbonate and refractory carbon such as coal,
pollen, and humic acids. The in situ acidification eliminates
sample loss during sequential decarboxylation and oxidation
and provides a precise (+2.2% of the measured value) and
rapid (-50 analyses per week per analyst) means to measure
charcoal in marine sediments. The absolute detection limit of
the charcoal determinations is 0.70 pg C (3 times mean blank
value) and the relative detection limit is 0.01%.
The records of total organic carbon (TOC) routinely reported from marine sediments include a mixture of carbon
from terrestrial (e.g. charcoal and noncharcoal) and marine
(e.g. primarily algae) sources. Studies that assess the relative
contributions of marine and terrestrial sources to the TOC
loading of marine sediments usually target bulk C : N ratios,
carbon isotopes, and biomarkers. An analytical technique is
described herein that uses elemental analysis to quantify one
component of terrestrial carbon-the
amount of charcoal
produced by terrestrial biomass burning and deposited in the
oceans. The burning of carbonaceous matter produces
charred particles that can be transported long distances via
winds and rivers to coastal, deltaic, and ocean environments
where they may become preserved in the sediments as a
means of long-term carbon storage. At present, charcoal’s
contribution to marine sediments is largely ignored, although
charcoal particles have been identified in Late Pleistocene
marine sequences of the tropical Atlantic Ocean (Verardo
and Ruddiman 1996) and in marine sediments from the Pacific Ocean at -65X lo6 yr (Herring 1985). The ocean acts
as a passive collector of charcoal, thereby making marine
sediments an excellent natural repository from which to
study the transfer of charcoal from terrestrial to marine environments.
As used here, charcoal refers to the pryolized remains of
terrestrial biomass (e.g. trees, grasses, plants) in the elemental state (Smith et al. 1975). Extracting this entirely terrestrial component from the TOC of ocean sediments leaves a
“residual” organic carbon signal (e.g. TOC minus charcoal)
that is a mixture of marine organic carbon and noncharcoal
terrestrial carbon. This distinction improves our understanding of true marine organic carbon burial from the marine
stratigraphic record and forces a reevaluation of marine pro-