Based upon a global comparison of over 400 fisheries, the Principal Components Analysis (PCA) methodology was used to identify factors affecting the choice of growth estimation methods. Of the six factors examined, the growth rate (K) and asymptotic length (L8) explained most of the variations. Financial resources, i.e., Gross National Product (GNP), and latitude were also important factors

Halls, A.S.

Pilling, G.M.

Aquatic Commons

NAGA, WorldFish Center Quarterly  Vol. 26 No. 2 Apr-Jun 20034
articles
Fig. 1. Distribution of the 441 fisheries for which data were collected for the PCA
Age- or length-based methods of growth 
estimation. What drives the choice?
G.M. Pilling and A.S. Halls
Abstract
Based upon a global comparison of over 400 fi sheries, the Principal Components Analysis (PCA) methodology 
was used to identify factors affecting the choice of growth estimation methods. Of the six factors examined, 
the growth rate (K) and asymptotic length (L∞ ) explained most of the variations. Financial resources, i.e., Gross 
National product (GNP), and latitude were also important factors.
Introduction
Growth and mortality model parameter 
estimates required for analytical fi sheries 
management models are commonly made 
from either age-at-length data (“age-
based” methods) or the analysis of length 
frequency data (“length-based” methods).  
Mark and recapture methods may also be 
used.  However, this approach tends to be 
less common in tropical fi sheries, possibly 
due to a lower probability of returns in 
artisanal reef fi sheries when compared to 
industrial fi sheries.
The utility of length- compared to age-
based methods is a contentious issue 
(Hilborn and Walters 1992; Pauly 1994). 
Whilst age-based methods are generally 
regarded as being less prone to bias, 
particularly when applied to long-lived, 
slow-growing species (Langi 1990; Mees 
and Rousseau 1997), length-based 
methods require less expertise, fewer 
resources and may be more successful 
when applied to faster growing species 
which show distinguishable modes in their 
length-frequency distributions.
 
Pilling et al. (1999) concluded that more 
accurate and reliable management of the 
relatively long-lived, slow-growing tropical 
lethrinid Lethrinus mahsena can be achieved 
by using age-based rather than length-
based parameter estimation techniques.   
A UK Department for International 
Development (DFID)-funded study is 
currently underway to assess whether 
similar conclusions apply to species with a 
range of different life history strategies.
Based upon a global comparison of 
fi sheries, this paper seeks to identify 
potentially important factors, including the 
life history strategy of target fi sh, which 
infl uence the choice of growth parameter 
estimation methodology.  
Materials and methods
Biological, technical and country-specifi c 
variables postulated to affect the choice 
between age- and length-based growth 
estimation methods (Table 1) were 
assembled for 441 fi sheries located 
throughout the world (Figure 1).
Ordination of these data by the Principal 
Components Analysis (PCA) methodology 
was used to determine which factors 
infl uence the choice of age- or length-
Fig. 2. Two-dimensional PCA ordination of variables postulated to affect the choice between 
age- and length-based methods
5NAGA, WorldFish Center Quarterly  Vol. 26 No. 2 Apr-Jun 2003
articles
based growth assessment methods. 
Where necessary, data were log 
transformed (x+1) to ensure normality.  
To achieve reliable and easily interpretable 
PCA ordinations, 100 samples were 
randomly selected from the database (50 
corresponding to age-based assessments, 
and 50 to length-based assessments). The 
analysis was repeated using a second set 
of randomly sampled data to determine 
the effect of this sub-sampling procedure.  
Results
The process of random sampling from 
the 441 stocks identifi ed did not affect 
the results of the analysis. They are 
therefore presented for the fi rst random 
sample only. The fi rst two principal 
component axes explained 64 per cent of 
the variance in the set of factors 
examined. The majority of separation 
between stocks managed on the basis of 
age- and length-based growth parameter 
estimates was along the PC1 axis  
(Figure 2). Factor loadings on PC1 were 
highest for K and L∞ (Table 2), indicating 
that the choice of assessment method is 
based largely upon the growth 
characteristics of the stock. 
Length-based methods are generally used 
for species exhibiting faster growth rates 
(K) and lower L∞ values (Figure 3). 
Conversely, age-based methods appear to 
be employed for larger species with 
slower growth rates. 
These results may simply refl ect bias 
associated with length-based methods 
that tend to over-estimate K and 
underestimate L∞ particularly for long-
lived, slow growing species with relatively 
high levels of individual variability in 
growth (Pilling et al. 1999). 
The PCA was, therefore, repeated after 
omitting the growth variables (Figure 4).  
The fi rst two principal component axes 
explained 69 per cent of the variance in 
the remaining data. The majority of 
separation between fi sheries managed on 
the basis of length- or age-based growth 
parameter estimates was again along the 
PC1 axis (Figure 4). The factor loadings 
indicate that the Gross National Product 
(GNP) and Latitude are largely 
responsible for this separation (Table 3). 
Age-based methods tend to be employed 
in countries with high GNP or at high 
* - www.fishbase.org
Variable Details
Gross National Product (GNP) of country
in $ billions, from the World Bank Development 
Indicators, 2000.  Dependent territories were 
given the GNP of their “parent” country.
Latitude of stock assessed
absolute value used (i.e., distance from equator, 
rather than hemisphere in which the stock was 
located).
Most advanced stock assessment method 
used to inform management
exploitation rate (F/Z), yield-per-recruit, or 
VPA/cohort analysis (in order of increasing 
complexity).
Growth estimation method length- or age-based 
Von Bertalanffy growth parameter L∞ of 
target stock
from FishBase* for actual stock or nearby stock.
Von Bertalanffy growth parameter K of 
target stock
from FishBase for actual stock or nearby stock.
Trophic level of target species from FishBase for actual stock or nearby stock.
Table. 1. Biological, technical and country-specific variables assembled for each fishery
a.
b.
Fig. 3. Relationship between PC1 and log-transformed a) L∞ and b) K
NAGA, WorldFish Center Quarterly  Vol. 26 No. 2 Apr-Jun 20036
articles
Table. 3. Co-efficients in the linear 
combinations of variables in the 
Principal Components. The first two 
variables with the highest loading on 
each Principal Component are in bold
Variable PC1 PC2
GNP 0.570 0.075
Latitude 0.567 0.060
Assessment method 0.427 0.682
Trophic level 0.414 0.725
Table. 2. Co-efficients in the linear 
combinations of variables in the 
Principal Components. The first two 
variables with the highest loading on 
each Principal Component are in bold
Variable PC1 PC2
GNP 0.372 0.379
Latitude 0.413 0.359
Assessment method 0.383 0.407
L∞ 0.448 0.420
K 0.518 0.206
Trophic level 0.275 0.586
latitudes.  However, GNP and latitude are 
also positively correlated (R = 0.46).  
Discussion
Of the six factors examined, growth rates 
(K) and asymptotic length (L∞) explained 
most of the variation in the growth 
estimation method employed. The use of 
length-based methods is generally 
associated with small, fast growing species 
whilst age-based methods are more 
commonly used for larger species with 
slower growth rates.  Assuming that the 
growth parameter estimates used in this 
analysis are unbiased, these results suggest 
that, on the basis of current knowledge, 
methods are currently appropriately 
selected according to the life history 
characteristics of the stocks (Isaac 1990; 
Gulland & Rosenberg 1992) as well as 
largely infl uenced by the overall wealth of 
the nation. However, this also implies that 
where fi nancial resources might be 
limited, especially at low latitudes, the 
management of large, slow growing fi sh 
species important to the livelihoods of 
tropical artisanal fi shers may be sub-
optimal if length-based methods have 
been applied (Pilling et al. 1999; 2000).  
The results generated by the on-going 
DFID-funded study will determine 
whether the use of age-based assessment 
methods result in improved management 
for all species, or merely those with 
particular life history strategies.  
Acknowledgement
The authors would like to thank Chris 
Pearce at MRAG for help with preparing 
the fi gures. The study was funded by the 
DFID Fisheries Management Science 
Programme. The views expressed here are 
not necessarily those of DFID.  
References
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A review of length-based approaches 
to assessing fish stocks.  FAO Fish. 
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Hilborn, R. and C.J. Walters. 1992. 
Quantitative fisheries stock 
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uncertainty. Chapman and Hall, New 
York.
Isaac, V.J. 1990. The accuracy of some 
length-based methods for fish 
Fig. 4. Two-dimensional PCA ordination of stock characteristics where growth was 
assessed using length- or age-based methods
7NAGA, WorldFish Center Quarterly  Vol. 26 No. 2 Apr-Jun 2003
articles
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_______________________________
G.M. Pilling is from CEFAS, Fisheries 
Laboratory, Pakefield Road, Lowestoft, 
NR33 0HT, United Kingdom (email: 
g.m.pilling@cefas.co.uk) and A.S. Halls 
is from MRAG Ltd., 47 Prince's Gate, 
London, SW7 2QA, United Kingdom.


Age- or length-based methods of growth estimation. What drives the choice?

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Age- or length-based methods of growth estimation. What drives the choice?

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