58 
Abstract — A new description of 
growth in blacklip abalone ( Haliotis 
rubra) with the use of an inverse- 
logistic model is introduced. The 
inverse-logistic model avoids the dis- 
advantageous assumptions of either 
rapid or slow growth for small and 
juvenile individuals implied by the 
von Bertalanffy and Gompertz growth 
models, respectively, and allows for 
indeterminate growth where neces- 
sary. An inverse-logistic model was 
used to estimate the expected mean 
growth increment for different black- 
lip abalone populations around south- 
ern Tasmania, Australia. Estimates 
of the time needed for abalone to 
grow from settlement until recruit- 
ment (at 138 mm shell length) into 
the fishery varied from eight to nine 
years. The variability of the residu- 
als about the predicted mean growth 
increments was described with either 
a second inverse-logistic relationship 
(standard deviation vs. initial length) 
or by a power relationship (standard 
deviation vs. predicted growth incre- 
ment). The inverse-logistic model 
can describe linear growth of small 
and juvenile abalone (as observed in 
Tasmania), as well as a spectrum of 
growth possibilities, from determinate 
to indeterminate growth (a spectrum 
that would lead to a spread of maxi- 
mum lengths). 
Manuscript submitted 9 April 2007. 
Manuscript accepted 22 October 2007. 
Fish. Bull. 106:58-71 (2008). 
The views and opinions expressed or 
implied in this article are those of the 
author and do not necessarily reflect 
the position of the National Marine 
Fisheries Service, NOAA. 
Using an inverse-logistic model 
to describe growth increments of 
blacklip abalone ( Haliotis rubra) in Tasmania 
Malcolm Haddon (contact author) 
Craig Mundy 
David Tarbath 
Email address for M. Haddon: Malcolm.Haddon@utas.edu.au 
Marine Research Laboratory 
Tasmanian Aquaculture and Fisheries Institute 
University of Tasmania 
Nubeena Crescent 
Taroona TAS 7051, Tasmania, Australia 
Blacklip abalone (Haliotis rubra ) 
constitute the most valuable fishery 
in Tasmania, Australia, yielding 
approximately 30% (2500 tonnes) 
of the resource captured in the wild 
worldwide, worth more than AU$100 
million per year. There are signifi- 
cant difficulties in determining the 
age of blacklip abalone (McShane 
and Smith, 1992), making them good 
candidates for size-structured assess- 
ment modeling (Sullivan et al, 1990; 
Punt and Kennedy, 1997). Although 
used informally in the Tasmanian 
fishery, size-structured models are 
used formally to assess blacklip aba- 
lone stocks elsewhere in Australia 
(Worthington et al., 1998; Gorfine 
et al., 2005) and to assess Paua ( H . 
iris) in New Zealand (Breen et al., 
2003). With size-structured models 
it is important to generate a precise 
and unbiased mathematical descrip- 
tion of growth because the adoption of 
an inappropriate growth model could 
have significant effects on the outcome 
of an assessment. 
Day and Fleming (1992) reviewed 
a range of models previously used to 
describe abalone growth. In total, 59 
growth studies have been undertak- 
en on different abalone species. The 
von Bertalanffy growth curve (von 
Bertalanffy, 1938) has been used in 
42 (71%) of these studies and the 
Gompertz model (Gompertz, 1825). 
has been used in four studies (6.78%). 
The dominance of the von Bertalanffy 
growth model reflects its almost uni- 
versal adoption in abalone fisheries 
assessments and the relative ease 
with which it can be fitted to growth 
data taken from tagging experiments 
(Fabens, 1965; Francis, 1988; Had- 
don, 2001). In nine studies (15.25%), 
linear growth was proposed, but the 
focus of these nine studies was on 
juvenile and small abalone and that 
focus could imply that growth alters 
its character above a particular size, 
at least in some species. A flexible 
growth description has also been giv- 
en by Francis (1995) who generated a 
size-based analogue to the age-based 
growth description by Schnute (1981). 
Francis’s model has been used in New 
South Wales, Australia (Worthington 
et al., 1998), and New Zealand as- 
sessments of abalone (Breen et ah, 
2003). 
Sainsbury (1982a, 1982b) fitted 
von Bertalanffy growth curves to 
abalone tagging data from New Zea- 
land (H. iris). Instead of assuming 
that the familiar parameters (L x , 
the asymptotic maximum size, and 
K, the growth coefficient in the von 
Bertalanffy equation) were averages 
for the population, Sainsbury (1982a) 
inferred the growth dynamics implied 
when each individual had its own set 
of von Bertalanffy parameters. Es- 
sentially, the growth characteristics 
of individuals were assumed to be 
variable and were described by using 
probability density functions to repre- 
sent the model parameters. Similarly, 
a probability density function form of 
the Gompertz growth model was used 
in Victoria, Australia (Troynikov and 
