ISSN 10630740, Russian Journal of Marine Biology, 2016, Vol. 42, No. 2, pp. 111–116. © Pleiades Publishing, Ltd., 2016.
Original Russian Text © V.V. Sukhanov, 2016, published in Biologiya Morya.
A catch curve describes the distribution of the
number of fish in a catch depending on their age and
body size. Mathematical processing and interpretation
of parameters of the catch curve are the most impor
tant stages of studies in commercial ichthyology. These
stages allow an assessment of the intensity of fish mor
tality, which is a key parameter of population dynam
ics. Moreover, by analyzing the catch curve, we can
obtain information on another parameter, viz., the
intensity of recruitment as a function of the fish age.
The present study is dedicated to a discussion of the
problems that are related to the phenomenology,
building, and identification of catch curves. It should
be noted here that this work does not consider the dis
tribution of the number of fish by body size, because
only curves for catches according to fish age can be
really helpful in solving demographic issues. More
over, converting data from the size scale to the age one
is not difficult if one knows the relationship between
the body length and age of individual.
The mathematical models that describe a broad
spectrum of catch curves are presented in the work.
Along with typical and frequently occurring curves, we
consider the curves that were built for more compli
cated cases. All of the models are accompanied by
illustrations of certain examples of catch curves; the
data for this were taken from the literature.
How a Catch Curve is Formed
A typical catch curve is based on two key functions
(Fig. 1). The first curve characterizes the dependence
of the population size (density) on the age of individ
uals, while the second one describes the averaged
dependence, which determines the probability at
which an individual of some age cohort occurs in the
catch. The catch curve that is characteristic for a pop
ulation in the stationary state, i.e., in the state of stable
equilibrium, is formed by multiplication of the first
function by the second one. This is usually achieved
only on average, by combining all of the data arrays for
a sufficiently long period of observation. In other
words, the parameters of catch curves are believed to
vary insignificantly over time.
The classical domeshaped catch curve is a mani
festation of two oppositely directed tendencies: the
process of recruitment over a prolonged period of time
and the influence of mortality. For young fish, the
recruitment flow into the exploited part of population
increases with acceleration: the older the age of the
recruits is, the greater the acceleration is. This process
of prolonged recruitment results in the formation of
the left (rising) region on the catch curve. At a suffi
ciently mature age, the year class to which recruits
belong almost completely transits into the harvested
stock and the probability of this transition tends to
unity. The recruitment is over. Approximately at this
age, the catch curve goes past the maximum and starts
to decrease monotonously, merging with the popula
tion curve (Fig. 1, as exponential one).
The age dependence that determines the probabil
ity at which an individual of some age cohort occurs in
the catch is shown in Fig. 2. Curve
probability of an Atlantic cod,
1758, occurring in a trawl net depending on age .
Young (small) fish are rarely caught by trawl nets; as
AgeDistribution Models for Fish in Catches
V. V. Sukhanov
Zhirmunsky Institute of Marine Biology, Far Eastern Branch, Russian Academy of Sciences,
ul. Pal’chevskogo 17, Vladivostok, 690041 Russia
Far Eastern Federal University, ul. Sukhanova 8, Vladivostok, 690950 Russia
Received September 24, 2015
—Models that describe the age distributions of fish in catches are discussed. On the logarithmic scale
of the Yaxis, the right (descending) part of these curves can be straight or can have an upward or downward
concavity, as well as a sharp bend in the middle. These properties of the curves can be explained by variations
in the intensity of mortality between different age groups or by demographic variations in the superpopula
tion systems. Illustrations of a catch using age curves are provided.
: logistic ogive curve, gammadistribution, selective catch, unevenaged maturation, mortality coef