302 
NOAA 
National Marine 
Fisheries Service 
Fishery Bulletin 
established 1881 
Spencer F. Baird 
First U S Commissioner 
of Fisheries and founder 
of Fishery Bulletin 
Sensifiwity of yield-per-recruit and spawning- 
biomass-per-recruif models to bias and 
imprecision in life bistory parameters: an 
example based on life history parameters of 
Japanese eel {Anguilla japonica) 
1 Institute of Oceanography 
National Taiwan University 
No.1, Sec. 4, Roosevelt Road 
Taipei 10617, Taiwan 
2 Department of Environmental Biology and Fisheries Science 
National Taiwan Ocean University 
No. 2, Beining Road 
Keelung 20224, Taiwan 
Abstract— Yield-per-recruit and 
spawning-biomass-per-recruit mod- 
els, are commonly used for evaluat- 
ing the status of a fishery. In prac- 
tice, model parameters are them- 
selves usually estimates that are 
subject to both bias (uncertainty in 
the mean) and imprecision (uncer- 
tainty in the standard deviation). 
Using Monte Carlo simulation with 
data for female Japanese eel ( An- 
guilla japonica) from the Kao-Ping 
River in Taiwan, we examined the 
sensitivity of such models to differ- 
ent degrees of bias and imprecision 
in the life history parameters. Posi- 
tive biases in natural mortality and 
the von Bertalanffy growth coeffi- 
cient led to larger relative changes 
in the mean and standard deviation 
of estimated fishing-mortality— based 
biological reference points (Egg p s ) 
than did changes under negative 
biases. Higher degrees of impreci- 
sion in parameters did not affect 
the means of FbrPs, but their stan- 
dard deviations increased. Compos- 
ite risks of overfishing depended 
mainly on the changes in the means 
of PjBRPs rather than on their stan- 
dard deviations. Therefore, reducing 
the biases in key life history para- 
meters, as well as the bias and im- 
precision in the current rate of fish- 
ing mortality, may be the most rel- 
evant approach for obtaining correct 
estimates of the risks of overfishing. 
Manuscript submitted 22 February 2014. 
Manuscript accepted 8 May 2015. 
Fish. Bull. 113:302-312 (2015). 
Online publication date: 2 June 2015. 
doi: 10.7755/FB.113.3.6 
The views and opinions expressed or 
implied in this article are those of the 
author (or authors) and do not necessarily 
reflect the position of the National 
Marine Fisheries Service, NOAA. 
Yu-Jia Lin 1 
Chi-Lu Sun (contact author ) 1 
Yi-Jay Chang 1 
Wann-Nian Tseng 2 
Email for contact author: chilu@ntu.edu. tw 
Yield-per-recruit (YPR) and spawn- 
ing-biomass-per-recruit (SPR) mod- 
els, in which the total yield or 
spawning biomass of a cohort is stan- 
dardized for the numbers of recruits, 
are commonly used in fisheries as- 
sessment (Beverton and Holt, 1957; 
Quinn and Deriso, 1999). They can 
be used to infer the total yield and 
spawning biomass of an entire popu- 
lation composed of different cohorts 
with an assumption of a steady state 
and with knowledge of equilibrium 
recruitment (King, 2007). Several 
fishing-mortality-based biological 
reference points (EbrPs) derived from 
YPR and SPR models can be used to 
evaluate whether the yield per re- 
cruit is optimal or the spawning bio- 
mass per recruit is sufficient for the 
population to persist under current 
fishing pressure. 
Uncertainties in the parameters of 
such models are inevitable and result 
from observation and process error 
(Charles, 1998). Ignoring uncertain- 
ties in parameters can lead to incor- 
rect estimation of Ebrp s , and conse- 
quently the examination of fishery 
status could be misleading, given the 
cases of the American lobster ( Homa - 
rus americanus) (Chen and Wilson, 
2002), green sea urchin ( Strotigylo - 
centrotus droebachiensis ) (Grabowski 
and Chen, 2004), Atlantic cod ( Gadus 
morliua ) (Jiao et ah, 2005), prong- 
horn spiny lobster (Panulirus penicil- 
latus) (Chang et al., 2009), and Japa- 
nese eel ( Anguilla japonica ) (Lin et 
al., 2010a). 
Estimation of natural mortality 
(M) is challenging (Vetter, 1988) be- 
cause both its mean and variance 
are prone to considerable uncertain- 
ty. For example, the estimates of M 
have varied among different empiri- 
cal methods (Pascual and Iribarne, 
1993; Lin and Sun, 2013). The vari- 
ances of M estimates also have dif- 
fered among approaches (e.g., Cubil- 
los et al., 1999, versus Hall et al., 
2004; Lin et al., 2012). It is easier to 
obtain growth information. The von 
Bertalanffy growth function is an 
