A Predictive Model for Taste Taint Accumulation in Recirculating Aquaculture Systems (RAS) Farmed-Fish – Demonstrated With

Ecological Modelling 291 (2014) 242–249

Contents lists available at ScienceDirect

Ecological Modelling

j ournal homepage: www.elsevier.com/locate/ecolmodel

A predictive model for taste taint accumulation in Recirculating

Aquaculture Systems (RAS) farmed-ﬁsh – demonstrated with geosmin

(GSM) and 2-methylisoborneol (MIB)

∗

Priyantha I. Hathurusingha, Kenneth R. Davey

School of Chemical Engineering, The University of Adelaide, 5005, Australia

a r t i c l e i n f o a b s t r a c t

Article history: The accumulation of “earthy” or “muddy” off-ﬂavours due to taste taint accumulation as geosmin (GSM)

Received 9 May 2014

or 2-methylisoborneol (MIB) in the ﬂesh of ﬁsh from Recirculated Aquaculture Systems (RAS) is a major

Received in revised form 6 August 2014

concern globally. To aid RAS farm management a time dependent concentration predictive model was

Accepted 7 August 2014

developed. The model is a sum of two exponential terms with time that simulate simultaneous taint

uptake and elimination. Illustrative simulations for RAS barramundi (Lates calcarifer) a premium ﬁsh

Keywords: ◦ −1

grown at a water temperature of 28 C show that the threshold for consumer rejection of 0.70 ␮g kg

2-Methylisoborneol (MIB)

MIB will be reached at 225 days. At a typical RAS harvest of 240 days the concentration of MIB is predicted

Geosmin (GSM)

to be four (4) times that for GSM. Because model predictions showed good agreement with independent

Recirculating Aquaculture System (RAS)

data for both RAS barramundi and rainbow trout (Oncorhynchus mykiss) it was concluded the model was

Taste taint in ﬁsh

Taste taint prediction free of programming and computational errors and of a generalized form. Model simulations revealed a

◦

Time dependent concentration modelling 5 C variance in RAS growth temperature did not meaningfully impact taint accumulation as either GSM

or MIB. A major beneﬁt to the RAS industry is that model simulations can be used to investigate a range of

growth protocols in RAS farming to limit taint. An advantage is the model can be conveniently simulated

in standard spread-sheeting tools.

−1

1. Introduction and 0.072 ␮g kg in the ﬁsh-ﬂesh (Howgate, 2004). Consumers can

readily detect taint as “earthy” or “muddy” off-ﬂavour and unpleas-

Fish farmed in Recirculating Aquaculture Systems (RAS) is ant odour at these levels and there is strong buyer resistance.

a globally important alternative to capture of wild-fish. RAS is Taste taint in fish-flesh due to GSM and/or MIB in RAS has been

increasingly popular due to a higher production per unit area, less reported for barramundi (Lates calcarifer) (Percival et al., 2008),

water and land usage, year-round production, and; better control Murray cod (Maccullochella peelii peelii) (Palmeri et al., 2008), rain-

of the ﬁsh-rearing environment (Ebeling and Timmons, 2012). bow trout (Oncorhynchus mykiss) (Robertson et al., 2006), arctic

A drawback however is the potential for accumulation in the charr (Salvelinus alpinus) (Houle et al., 2011), largemouth bass

RAS growth water, and consequently ﬁsh-ﬂesh, of unwanted taint (Micropterus salmoides), and; white sturgeon (Acipenser transmon-

as off-ﬂavours and unpleasant odours. Of particular interest are tanus) (Schrader et al., 2005). The dynamics of the RAS growth and

geosmin (GSM) and 2-methylisoborneol (MIB). These semi-volatile, taint environment are complex, with the quantity of GSM/MIB in

secondary metabolites are produced by planktonic and benthic the water and ﬁsh-ﬂesh varying with micro-organism, system loca-

cyanobacteria and actinomycetes (Wood et al., 2001; Guttman and tion, water nutrient(s), ﬁsh species and size, and; portion of the ﬁsh

van Rijn, 2009; Tucker, 2000). The use of high nutrient load and high which is assayed (Howgate, 2004; Percival et al., 2008).

ﬁsh-stocking densities in RAS appear to promote these taste taint Effective husbandry practices to control taste taint in farmed

producing micro-organisms. Taint at very low concentration in RAS ﬁsh have not been established (Howgate, 2004). At present, purg-

−1 −1

␮ ␮

water, for example 0.015 g L GSM or 0.018 g L MIB (Persson ing post-growth in clean water of RAS ﬁsh prior to marketing is

and York, 1978; Persson, 1980), can result in, respectively, 0.056 widely used to leach taint (Tucker and van der Ploeg, 1999); for

example, seven (7) days purge for farmed barramundi (South-

ern Barramundi Farmer’s Association, Clarendon, Australia, pers.

∗ comm.). In addition, copper sulphate is a widely used as an algae-

Corresponding author. Tel.: +61 8 8313 5457; fax: +61 8 8313 4373.

E-mail address: [email protected] (K.R. Davey). cide in RAS production tanks, but effective treatment protocols are

http://dx.doi.org/10.1016/j.ecolmodel.2014.08.009

P.I. Hathurusingha, K.R. Davey / Ecological Modelling 291 (2014) 242–249 243

costly and time-consuming, taint assessment at present is largely

Nomenclature dependent on sensory evaluation by industry “experts” (Percival

et al., 2008).

The equation given in parentheses after description refers to that

Quantitative mathematical models, widely used in the chem-

in which the symbol is ﬁrst used or deﬁned.

−1 ical engineering and process foods industries, offer the potential

a taint elimination coefﬁcient, day (Eq. (5))

−1 −1 for insight, management, and ultimately control of taint in RAS

b taint accumulation coefﬁcient, ␮g kg day (Eq.

farmed-ﬁsh. Bio-magniﬁcation, bio-concentration and food-web

(4))

−1 models have been used based on steady-state assumptions where

COX concentration of dissolved oxygen, mg L (Eq. (11))

−1 the flux of the chemicals into and from the fish-flesh is zero (Clark

CW taint concentration (as GSM or MIB) in water, ␮g L

et al., 1990). However, it is questionable to us whether equilibrium

d exponent of length–mass relationship for VBGF

assumptions can be reasonably made for practical RAS systems: it

equation, dimensionless (Eq. (22))

−1 −1 is apparent there is no empirical evidence that the net chemical

dy/dt rate of change of taint in ﬁsh ﬂesh, ␮g kg day

exchange rate is zero between the RAS water and ﬁsh-ﬂesh phases.

(Eq. (1))

Against this background, a new quantitative process model to

e lipid mass ratio, dimensionless fraction (Eq. (16))

predict concentration of taint, as either GSM or MIB, was developed

EW chemical uptake efﬁciency across the gill, dimen-

to aid RAS management. The aim was to produce a quantitative

sionless fraction (Eq. (9))

guide for RAS farming practice that could be applied to minimize

GSM geosmin

−1 taint in ﬁsh-ﬂesh.

GV gill ventilation rate, L day (Eq. (9))

−1 −1 The model is developed from a whole-of-process perspec-

k1 taint accumulation through gills, L kg day (Eq.

tive and is based on conservation of mass and energy principles

(2))

−1 (Foust et al., 1980) and thermodynamic processes established in

k2 taint elimination through gills, day (Eq. (2))

(bio)chemical engineering (Bailey and Ollis, 1986). It is illustrated

kg growth dilution plus metabolic transformation,

−1 with independent data for farmed barramundi (L. calcarifer), an

day (Eqs. (2) and (17))

−1 important RAS ﬁsh in Australia and globally. The applicability of a

kG rate constant for growth dilution, day (Eq. (17))

−1 generalized form of the model for prediction for other aquaculture

km rate constant for metabolic transformation, day

species, in particular rainbow trout (O. mykiss), is also assessed with

(Eq. (17))

−1 independent data. Model trends are shown to agree well with the

K growth co-efﬁcient for VBGF equation, day (Eq.

(necessarily fragmented) published data from the wider literature.

(22))

The beneﬁt of a model for taint in assessing a range of farm growth

KOW octanol–water partition coefﬁcient, dimensionless

protocols and the longer term need for an extensive experimental

(Eq. (10))

evaluation is discussed.

mf mass of the ﬁsh at t, kg (Eq. (2))

mf∞ mass the ﬁsh will grow indeﬁnitely, kg (Eq. (22))

2. Materials and methods

MIB 2-methylisoborneol

n number of (independent) data

2.1. Predictive model development

QW rate of chemical transport in the aqueous phase,

−1

L day (Eq. (13))

−1 The controlling route for chemical uptake into ﬁsh-ﬂesh is

QL rate of chemical transport in the lipid phase, L day

widely assumed to be the gills (Persson, 1984); ingestion of taint

(Eq. (13))

2 through the skin or via feed is considered negligible (McKim et al.,

R correlation coefﬁcient

1996; Nichols et al., 1996). Elimination of taint from the ﬁsh-ﬂesh

RAS Recirculating Aquaculture System

◦ is assumed to occur through the gills and with both reduced con-

T temperature, C (Eq. (12))

centration of taint molecules in the fish-flesh with fish growth plus

t growth time, day (Eq. (1))

metabolic transformations within the fish-flesh. Because RAS fish

to scaling constant, day (Eq. (22))

are harvested before egestion or reproduction any taint loss due

VBGF von Bertalanffy Growth Function, (Eq. (22))

to these can be reasonably ignored. Typically the RAS system is

VL lipid mass (weight), kg (Eq. (13))

−1 uniform in temperature. For example, for farmed barramundi in

y taint (as GSM or MIB) concentration, ␮g kg (Eq.

Australia, RAS water is carefully maintained at all times and sea-

(1)) ◦

sons at a bulk temperature of 28 C through heated and insulated

growth-tanks (Southern Barramundi Farmer’s Association, Claren-

Greek symbols

ˇ don, Australia, pers. comm.).

pre-exponential growth constant (Eqs. (3) and (22))

Consider the uptake and elimination of taint molecules (as GSM

exponential growth constant (Eq. (3) and (22))

and MIB) in RAS farmed-ﬁsh as illustrated schematically in Fig. 1.

(All symbols used are carefully deﬁned in the Nomenclature at the

beginning of this paper.)

−1

not understood. This has led to excessive use of copper sulphate and Let y (␮g kg ) = the concentration of taint as either GSM or

−1

ineffective application (Rimando and Schrader, 2003). Repetitive MIB in the ﬁsh-ﬂesh and CW = the concentration (␮g L ) of taint

application seems to have resulted in developing copper-resistance as either GSM or MIB in the RAS water at any time, t. The rate of

within cyanobacteria (Garcia-Villada´ et al., 2004; Shavyrina et al., change of taint (y) in the ﬁsh-ﬂesh with time (t) is therefore given

2001). Guttman and van Rijn (2009) report that aerobic bio-ﬁlters by:

in RAS have not been successful in controlling taint. Other methods

that have been tried to restrict taint, include: control of nutrients = uptake rate − elimination rate (1)

in tanks, use of organic-rich beds or absorbents (activated carbon),

oxidizing agents (potassium permanganate, ozone), and; UV irra- The uptake rate of either GSM or MIB will be a function of the

−1 −1

diation of the water. These have however not proved practicable rate constant for uptake (k1, L kg day ), the ﬁsh mass (mf, kg) and

(S. Poole, Department of Primary Industries, Brisbane Australia, the taint concentration in the RAS water (CW). The elimination rate

unpublished data). Because chemical analyses of ﬁsh-ﬂesh are of GSM or MIB will be a function of the rate constant for elimination

244 P.I. Hathurusingha, K.R. Davey / Ecological Modelling 291 (2014) 242–249

where EW is the gill chemical uptake efﬁciency (dimensionless frac-

−1

tion) and GV is the gill ventilation rate (L day ). The chemical

uptake efﬁciency was, reasonably, assumed by Gobas (1998) to be

a function of an octanol–water partition coefﬁcient (KOW) of the

chemical of interest that can be expressed through the following relationship:

−1

EW = (1.85 + 155/KOW) (10)

A relationship between gill ventilation rate and oxygen con-

sumption rate of the ﬁsh species based on empirical data is given

by Arnot and Gobas (2004), namely:

m0.5

Fig. 1. Schematic of a generalized ﬁsh with uptake (k1CW) and elimination (k2y + kgy) 1400 f

GV = (11)

of taint molecules (as GSM or MIB). COX

−1

−1 where COX is the concentration of dissolved oxygen (mg L ). This

through the gills (k2, day ), the rate constant for growth dilution

−1 is considered to be a function of temperature and can be computed

plus metabolic transformation (kg, day ) and the instantaneous

from the equation given by Neely (1979):

value of y at time, t. Substitution of these parameters into Eq. (1)

gives: COX = 14.45 − 0.413T + 0.00556T (12)

where T = RAS growth water temperature in degree Celsius. The

= k m C − (k + k )y (2)

dt 1 f W 2 g

assumption of saturated growth water is justiﬁed in RAS because,

where (dy/dt) is the rate of change of taint in ﬁsh-ﬂesh in conjunction with temperature control, aerator-mixers are

−1 −1

␮

( g kg day ). continuously employed to ensure optimum ﬁsh growth (South-

The mass of ﬁsh (mf) grown for harvest is known to be a function ern Barramundi Farmer’s Association, Clarendon, Australia, pers.

of growth time in the RAS tank. Published growth data as mass comm.).

of ﬁsh (kg) vs growth time (day) is generally highly exponentially The chemical elimination rate from the ﬁsh gills to the water

correlated (Glenn et al., 2007; dos Santos et al., 2008, 2013) (see (k2) is correlated with the chemical transport rate in aqueous and

below Eq. (19) for barramundi) and fish mass is therefore given by: lipid phases of the fish, lipid content of the fish and octanol water

t partition coefﬁcient of the taint chemical. The relationship can be m = ˇ

f exp (3)

expressed (Gobas, 1993) as: Let: 1 VL VL = KOW + (13)

k2 QW QL

b = ˇk1CW (4)

where QW is rate of chemical transport in the aqueous phase (L day

and −1 −1

), QL is the rate of chemical transport in the lipid phase (L day )

a =

( 2 + kg) (5) and VL is lipid weight (mass). Gobas and Mackay (1987) derived a

relationship between QW and mf using experimental data to give:

Substitution for b and a into Eq. (2) and rearranging gives:

Q 0.6(±0.2) = . m dy W 88 3 (14)

+ t f

ay =

bexp (6)

Gobas and Mackay (1987) reported that the chemical transport

∼

Eq. (6) can be integrated by parts (Evans, 2010) to give: rate in the aqueous phase is 100 times higher than in the lipid

phase; therefore it can be assumed that: b t b y = exp −

at (7)

Q = . Q

(a + ) (a + )exp L 0 01 W (15)

Eq. (7) can be rearranged to conveniently give: Lipid mass (V ) of the ﬁsh is correlated to the lipid mass ratio (e)

b (dimensionless) and can be conveniently expressed as:

y t −at

= [exp − exp ] (8)

a + V = em

L f (16)

The model for taste taint in ﬁsh-ﬂesh of Eq. (8) shows that the

The rate constant for growth dilution plus metabolic transfor-

predicted level is the sum of two exponential terms with time in

mation of the taint chemical (kg) is given by:

the RAS growth tanks, namely, uptake and elimination.

k = k + k

There are generally however no published data for k1 and k2 or g ( G m) (17)

kg in the refereed literature (for example for barramundi ﬁsh) for

The rate constant for growth dilution (kG) can be computed

immediate simulation of taint. For model development these rate

using the equation given in Thomann et al. (1992) as:

constants need to be deﬁned mathematically.

−0.2 k = . m

G 0 00251 f (18)

2.2. Rate constants k1, k2 and kg

The rate constant for metabolic transformation of the taint chemical

(km) is available in the refereed literature (Gobas, 1993) to cover a

Arnot and Gobas (2004) found the gill uptake rate constant (k )

1 −1

range of ﬁsh species of km = 0.00063 day .

is a combination of two processes: gill ventilation, and chemical

Eqs. (1)–(18) plus the general value for km, deﬁnes the model

uptake efﬁciency across the gills. Accordingly, the chemical uptake

for taste taint in RAS ﬁsh.

rate was expressed as:

The model can be conveniently set-up and solved as a Microsoft

E G TM

k = W V (9) Excel spread sheet. The widespread use of these tools means that

1 m

f model communication can be streamlined.

P.I. Hathurusingha, K.R. Davey / Ecological Modelling 291 (2014) 242–249 245

Fig. 3. Predicted taste taint as GSM (- -) and MIB ( ) in barramundi-ﬂesh with RAS

◦

Fig. 2. Fit of growth data ( ) of Glenn et al. (2007) for barramundi ﬁsh farmed in growth time at a growth water temperature 28 C with CW, respectively, 0.0004 and

◦ 0.0133t 2 −1

␮

ponds at a water temperature 28 C (mf = 0.0519 exp , R = 0.9623). 0.003 g L .

day in RAS tanks. The table shows that k1, k2 and kg values decrease

2.3. Illustrative simulations for GSM in barramundi (L. calcarifer)

ﬁsh-ﬂesh with increasing growth time. For example, the level of taint as GSM

−1

ranges from 0.0115 to 0.2166 ␮g kg , respectively, with growth

time, 30–240 days. The bold text in the table at 150 days of growth

Barramundi (L. calcarifer) has a high demand as a premium pro-

is the simulation illustrated in Table 1.

tein in the seafood market and is becoming globally popular as an

To visualize these taint data, a continuous plot with growth time

RAS farmed-ﬁsh. Interest is due to a relatively fast growth, toler-

in the RAS tanks is presented as Fig. 3. The data for MIB are super-

ability to production handling and adaptability for high stocking

imposed and compared with those for GSM in the ﬁgure to permit a

densities. In Australia, RAS farmed barramundi that are grown in

◦ direct visual comparison of the predicted accumulation of the two

28 C water are harvested at 0.80 kg live mass after a 240 day growth

taint molecules. These data highlight accumulation of taste taint in

cycle, unless there is a special buyer requirement (Southern Barra-

ﬁsh-ﬂesh as an exponential pattern.

mundi Farmer’s Association, Clarendon, Australia, pers. comm.). A

From the ﬁgure, it can be seen for example there is a predicted

typical, detailed growth curve (n = 9) for barramundi is presented

rapid accumulation of GSM in the barramundi ﬁsh-ﬂesh in the

by Glenn et al. (2007) and is reproduced as Fig. 2.

period following 100 days of growth.

These data are from pond growth systems. However in the

absence of speciﬁc information for RAS, these data were correlated

with growth time to give ˇ = 0.0519 and = 0.0133 respectively. 4. Discussion

The high correlation coefﬁcient (R = 0.96) indicates a very good ﬁt

(Snedecor and Cochran, 1989). For the purpose of model illustra-

It can be seen from Fig. 3 that the predicted level of GSM in barra-

tion it is assumed the growth of barramundi in RAS will be very

mundi ﬁsh-ﬂesh is much less than that for MIB at any growth time

similar. Therefore Eq. (3) becomes:

over the period 30–240 days. Both curves are however exponential

. t

0 0133 with growth time in the RAS tanks. m = .

f 0 0519exp (19)

Generally, the reported sensory threshold for GSM in barra-

A detailed, step-wise simulation of the model can now be made. mundi fish-flesh that can make the fish taste earthy and muddy is

−1

The steps are conveniently summarized as Table 1. For example, considered to be 0.74 ␮g kg (Jones et al., 2013). As can be seen

Lines 1–6 of the table are the input parameters and correspond- in Fig. 3 this concentration is predicted to be reached at about

ing check on units. Lines 7–20 are the calculations, results and the 225 days growth in the RAS tanks. At harvest at 240 days the

−1

relevant equations used. Line 21 is the level of predicted taint. The concentration of MIB is predicted to be 0.8912 ␮g kg (Table 2).

particular simulations in the table, columns 4 and 5 are respectively Signiﬁcantly, this is four (4) times the predicted concentration of

simulation of taint taste as GSM and MIB, in barramundi fish-flesh GSM in the barramundi fish-flesh. This difference can be attributed

−1

at 150 day of growth in the RAS tanks. to the initial lower CW for GSM (0.0004 ␮g L ) at about 1/10 that

−1

The predicted level of taint taste in the barramundi ﬁsh-ﬂesh for MIB (0.003 ␮g L ) (Glencross et al., 2007) used in the simula-

at 150 days of growth is seen from the table to be for GSM, tions. Possible reasons for the difference in values for CW for the two

−1 −1

␮ ␮

y = 0.0618 g kg and that for MIB, y = 0.2514 g kg . molecules include the diversity of taint causing micro-organisms

To complete the simulation of RAS growth of barramundi and involved and the different aqueous solubility of the taint off-ﬂavour

accumulation of GSM and MIB in the ﬁsh-ﬂesh these calculations molecules (Jüttner and Watson, 2007; Pirbazari et al., 1992). In

≤ ≤

are repeated for a range of values, 30 t 240 day. This covers the general, cyanobacteria and actinomyctes are considered to be the

growth period from ﬁngerling at 30 day to harvest of the ﬁsh at 240 major contributors to taste taint and they are able to produce either

day. GSM or MIB. Interestingly, certain species are capable of produc-

ing both molecules (Jüttner and Watson, 2007). Additionally, the

3. Results aqueous solubility of GSM is less than that for MIB (respectively,

−1

150 and 194.5 mg L ) (Pirbazari et al., 1992) that would lead to

Table 2 summarizes the model predictions for taste taint as GSM higher levels of MIB in growth water when both molecules are

and MIB in RAS barramundi ﬁsh-ﬂesh for the growth period 30–240 produced.

246 P.I. Hathurusingha, K.R. Davey / Ecological Modelling 291 (2014) 242–249

Table 1

Model simulation procedure showing inputs, calculations and output for predicted taste taint as both GSM and MIB in barramundi ﬁsh-ﬂesh at 150 day of growth in RAS

tanks.

Parameter and units Taint taste as:

GSM MIB

Inputs

Line

1 t day 150 150

2 kOW dimensionless 3.57 3.31

−1

3 km day 0.00063 0.00063

−1

4 CW ␮g L 0.0004 0.0003

◦

5 T C 28 28

6 e dimensionless 0.1 0.1 Calculations

−1

7 COX mg L 7.24 (Eq. (12)) 7.24 (Eq. (12))

−1

8 GV L day 100.73 (Eq. (11)) 100.73 (Eq. (11))

9 EW dimensionless 0.528 (Eq. (10)) 0.519 (Eq. (10))

−1 −1

10 k1 L kg day 140.13 (Eq. (9)) 137.51 (Eq. (9))

−1

11 QW day 49.41 (Eq. (14)) 49.41 (Eq. (14))

−1

12 QL day 0.49 (Eq. (15)) 0.49 (Eq. (15))

13 VL kg 0.038 (Eq. (16)) 0.038 (Eq. (16))

−1

14 k2 day 0.34 (Eq. (13)) 0.60 (Eq. (13))

−1

15 kG day 0.00304 (Eq. (18)) 0.00304 (Eq. (18))

−1

16 kg day 0.00367 (Eq. (17)) 0.00367 (Eq. (17))

17 mf kg 0.381 (Eq. (19)) 0.381 (Eq. (19))

−1

18 a day 0.3436 (Eq. (5)) 0.3436 (Eq. (5))

−1 −1

19 b ␮g kg day 0.0029 (Eq. (4)) 0.0029 (Eq. (4))

20 dimensionless 0.0133 (Eq. (19)) 0.0133 (Eq. (19)) Output

−1

21 y ␮g kg 0.0618 (Eq. (8)) 0.2514 (Eq. (8))

Although for MIB there is no reported consumer sensory thresh- 4.1. Impact of varying GSM concentration in growth water (CW)

old for barramundi fish-flesh, it can be reasonably assumed this will on accumulation in fish-flesh

−1

be about 0.70 ␮g kg ; this is because this is the concentration also

reported for similar ﬁsh species, e.g. both channel catﬁsh (Ictalurus The impact of varying taint concentration in the growth water

punctatus) and rainbow trout (O. mykiss) (Robertson et al., 2005). (CW) on accumulation in the ﬁsh-ﬂesh for both taint molecules can

It is interesting therefore that the concentration registered for off- readily be modelled as a function of growth time, t, in the tanks.

flavour for both taint molecules in the fish-flesh is nearly identical. A suitable form is likely to be increasing CW with time in either a

This may be attributed to the similar physical and chemical proper- linear, or, a moderate-exponential form.

ties of these two molecules. For instance, both these molecules are To illustrate this for GSM, it is assumed there is a linear depen-

tertiary alcohols with the octanol–water partition coefﬁcient less dence with a reasonable estimate for 30 ≤ t ≤ 240 day given by:

than 6. The octanol–water partition coefﬁcient is considered to be

C −6

W = 0.0002 + 2 × 10 t (20)

the major criterion which predominantly determines the chemical

uptake route (Clark et al., 1990). Moreover, their molecular densi-

Eq. (20) has been ﬁtted to predict, respectively, a mean value of

−

ties (∼0.9) and refractive indices of reference (∼1.4) are also similar 1

CW = 0.0004, a minimum, 0.0002 and maximum, 0.0006 ␮g L at

(Pirbazari et al., 1992).

each of 30, 120 and 240 days growth.

The simulation results have been predicated on a constant value

Fig. 4 summarizes the impact of varying CW. The ﬁgure reveals

C for taint concentration in the growth water with growth time

W that the taint concentration in barramundi ﬁsh-ﬂesh at 240 day is

−

(t). This may not always be the case and C may vary with growth ∼ 1

W 49 times greater than that for 30 days (0.0075 ␮g kg ) growth

time in the tanks (Department of Agriculture Fisheries and Forestry,

for GSM.

Brisbane, Australia (DAFF) S. Poole, pers. comm.). The impact of

Results are compared in Fig. 4 with the predictions for constant

−

changing C with time was therefore investigated using simula- 1

W CW = 0.0004 ␮g L GSM. It can be seen that at harvest at 240 days

tions of the model.

growth there would be expected to be a greater taint concentration

Table 2

−1

Predicted taste taint (y) as GSM and MIB in barramundi ﬁsh-ﬂesh with growth time (t) in RAS tanks at (Glencross et al., 2007) constant CW = 0.0004 ␮g L for GSM and

−1

CW = 0.003 ␮g L for MIB. (The bold text for 150 day is the detailed illustrative simulation presented in Table 1).

−1 −1 −1 −1 −1

t (day) mf (kg) kg (day ) k1 (L kg day ) k2 (day ) y (␮g kg )

GSM MIB GSM MIB GSM MIB

30 0.077 0.0048 245.0 240.6 0.645 1.148 0.0115 0.0470

60 0.115 0.0044 212.9 209.1 0.549 0.977 0.0176 0.0714

90 0.171 0.0042 185.3 182.0 0.464 0.833 0.0270 0.1085

120 0.256 0.0039 160.9 158.0 0.399 0.708 0.0406 0.1651

150 0.381 0.0036 140.1 137.5 0.340 0.602 0.0618 0.2514

180 0.568 0.0034 121.7 119.6 0.290 0.512 0.0937 0.3827

210 0.847 0.0032 105.8 104.0 0.247 0.434 0.1423 0.5841

225 1.034 0.0031 98.7 97.0 0.228 0.400 0.1755 0.7209

240 1.263 0.003 92.0 90.4 0.210 0.368 0.2166 0.8912

P.I. Hathurusingha, K.R. Davey / Ecological Modelling 291 (2014) 242–249 247

Fig. 4. Comparison of predicted taste taint (y) as GSM in barramundi ﬁsh-ﬂesh

−1

with growth time with constant (0.0004 ␮g L ) CW ( ) and CW varying (- -)

−1 Fig. 5. Predicted taint (y) as GSM in barramundi ﬁsh-ﬂesh with RAS growth time at

␮

(0.00026–0.00068 g L ) with growth time (t). ◦ ◦

two (2) different growth water temperature: 28 C ( ) and 18 C (- -).

in the ﬁsh-ﬂesh of GSM for RAS growth with varying CW. The ratio

is 1:1.75. e.g. Denmark, UK and France (Petersen et al., 2011; Robertson et al.,

The ﬂexibility of the new model for taint accumulation also 2006; Zimba et al., 2012).

permits study of the impact of changes in the RAS growth water To illustrate the generalized form for rainbow trout, it is neces-

temperature. sary to ﬁnd a suitable growth equation for this species. A graph

between the mass of the ﬁsh and the growth time (n = 11) was

4.2. Impact of varying growth water temperature (T) on taint obtained (Anon., 2012) and correlated to give:

accumulation in ﬁsh-ﬂesh

0.0138t m = .

f 0 0346exp (21)

In commercial RAS barramundi farming, a constant growth

with R = 0.94 (Snedecor and Cochran, 1989) indicating a very

water temperature might not be always be maintained, due to

good ﬁt. The effect of any temperature variation on ﬁsh

faulty maintenance or partial power failure etc. To illustrate the

◦ growth/growth physiology is assumed negligible for rainbow

impact of varying water temperature on taint taste, a 5 C decrease

trout also, and therefore ignored. The simulations can now be

and increase in water temperature is assumed practical. The effect

carried out using the procedure, Table 1 (with mf = 0.274 kg,

of this temperature variation on ﬁsh growth/growth physiology is

−1 −1

COX = 10.29 mg L (Robertson et al., 2006), GV = 58.62 L day ,

assumed negligible and is therefore ignored.

−1 −1

◦ EW = 0.519, k1 = 111.09 L kg day , e = 0.045 (Robertson et al.,

At the resulting two different temperatures of 23 and 33 C, k

1 −1 −1 −1

2006), k2 = 0.863 day , kG = 0.00325 day , km = 0.00063 day

values (Eqs. (9)–(12)) for GSM at, 150 day ﬁsh growth are, respec-

−1 −1

−1 −1 (Gobas, 1993), and; CW = 0.011 ␮g L (range 0.0–0.023 ␮g L ) for

tively, 131.60 and 151.14 L kg day . Substitution and simulation

−1

◦ GSM in growth ponds) to give, y = 0.5412 ␮g kg .

at 23 and 33 C showed, respectively, taint (y) as GSM of 0.0581

−1

and 0.0665 ␮g kg . Repeat calculations with the model gave simi-

lar results for taint as MIB. For example, simulation results for taste 4.4. Model validation with independent data

◦ −1

taint at 23 and 33 C were, respectively, 0.2350 and 0.2687 ␮g kg .

◦

The likely impact of a 5 C change in growth water temperature There are no extensive independent data published on taste

in RAS systems therefore did not meaningfully impact taint accu- taint accumulation as either GSM or MIB with RAS systems.

mulation in the ﬁsh-ﬂesh. For barramundi, limited data for taint as GSM from growth

Repeat simulations revealed however that a RAS temperature of ponds were however obtained (as growth time vs y) from

◦

18 C will give about a 16% reduction in taint accumulation for both the Department of Agriculture Fisheries and Forestry, Brisbane,

GSM and MIB. These simulations are presented in Fig. 5 for both Australia (DAFF) (S. Poole, pers. comm.). Assuming a barramundi

◦

18 and 28 C. Seen together with Fig. 4 it is apparent that the lower mass of about 1 kg at harvest, model simulations were carried out.

the RAS water temperature, the lower the taint accumulation in the A comparison between observed data and model predictions for

ﬁsh-ﬂesh. n = 14 values of taste taint is presented as Fig. 6.

−1

Repeat simulations for MIB revealed similar results; this might Given that the value of taint ranges from ∼2 to 20 ␮g kg , that

be expected given the very similar properties of the two taint is, one-order of magnitude the ﬁgure shows a moderately good ﬁt

molecules. of the model to these independent data. It is seen that there are

The generalized form of the model for taint accumulation in fish- five (5) residuals above the Y = X line, five (5) below it and four (4)

ﬂesh can be illustrated with application to other species. at (very nearly) Y = X.

For rainbow trout, model predictions were assessed against

4.3. Generalized model and simulations for rainbow trout (O. the independent data (n = 15) of Petersen et al. (2011) for growth

mykiss) in open recirculation aquaculture in Denmark. The growth water

◦

temperate was assumed to be 12 C for these data and the mean

Rainbow trout is a cold-water ﬁsh of salmonidae family. Trout mass of the ﬁsh 0.30 kg. (The data were digitized from the original

farming in RAS is a global practice, particularly in Europe, due to published plot.) A comparison of model predictions is presented

the cooler condition. Taint problems due to GSM or MIB in RAS in tabular form in Table 3 for values of observed taste taint as

−1

␮

rainbow trout have been reported in several European counties, GSM from 0.183 to 2.15 g kg that is, about a 12-fold range. The

248 P.I. Hathurusingha, K.R. Davey / Ecological Modelling 291 (2014) 242–249

maintained at a value, respectively, less than 0.0014 and

−1

0.0024 ␮g L . Clearly, a range of farming practices can be

investigated in this way without recourse to further unlimited

experimental trials.

Admittedly, for a more thorough model validation, extensive

data is needed to be collected throughout the growth period. A two-

year extensive study is now underway in a commercial-scale RAS

barramundi farm in South Australia. The costs can now be readily

justiﬁed based on the good ﬁt of predictions to independent data

for accumulation of taste taint in ﬁsh-ﬂesh.

Finally, during model development a widely used exponential

curve for ﬁsh mass growth was used for the period to harvest of 240

day for barramundi and 270 days for rainbow trout for which inde-

pendent growth data showed a very good ﬁt for both (respectively,

2 2

R = 0.96, n = 9 and R = 0.94, n = 11). Present model predictions are

therefore adequate for these two species. More generally however,

if a ﬁsh is to grow for longer (indeﬁnite) periods then an S-curve

for growth with time might be used to make the model more uni-

versal and to generalize it for a range of other ﬁsh species. The von

Bertalanffy Growth Function (VBGF) for example could be used to

replace the present Eq. (3). The VBGF is given by (Hopkins, 1992):

−K(t−to) d

m = m −

f f∞(1 exp ) (22)

Fig. 6. Comparison between observed and predicted taste taint (y) as GSM in farmed

barramundi. Data (n = 14) supplied by Department of Agriculture Fisheries and

where mf∞ is the mean mass the ﬁsh will grow to indeﬁnitely, d is

Forestry, Brisbane, Australia, S. Poole, pers. comm.

an exponent of length-mass relationship, K is a growth co-efﬁcient,

and; to a scaling factor. It is important to note however that at max-

Table 3

imum mass, mf∞, the rate of elimination of taint through growth

Comparison of observed (Petersen et al., 2011) vs predicted taste taint as GSM in

◦ dilution, kG, is seen to become (Eq. (18)) constant (as it depends

rainbow trout (n = 15) grown in open RAS at 12 C for 9-months to a typical mass of

∼

308 (±72) g. only on the ﬁsh mass). A consequence is that kg kG (Eq. (17)),

simplifying the model.

−1 −1

CW (␮g L ) y (␮g kg )

Observed Predicted

a 5. Conclusions

0.005 0.183 (3) 0.22

0.006 0.25 (1) 0.26

0.0075 0.308 (3) 0.32 The accumulation of taste taint as either geosmin (GSM) or 2-

0.008 0.63 (4) 0.35

methylisoborneol (MIB) in the ﬂesh of RAS ﬁsh has been simulated

0.010 0.55 (4) 0.43

with a new transient-state model. The model is the sum of two

0.011 0.65 (2) 0.47

exponential terms of simultaneous taint uptake and elimination

0.012 0.96 (5) 0.51

0.013 0.5 (1) 0.55 with growth time. The model is generalized in form and applica-

0.014 0.275 (2) 0.59

ble to range of species of RAS ﬁsh including both barramundi (L.

0.015 0.60 (4) 0.63

calcarifer) and rainbow trout (O. mykiss).

0.017 0.89 (7) 0.70

Illustrative predictions for GSM in RAS barramundi ﬁsh-ﬂesh

0.018 0.72 (5) 0.74

0.026 0.95 (3) 1.02 revealed that at a typical harvest of 240 days the threshold for

−1

0.027 2.15 (7) 1.35 consumer rejection of 0.74 ␮g kg will not have been reached.

−

0.036 1.4 (3) 1.62 1

However for MIB taint the threshold (0.70 ␮g kg ) will be reached

a ◦

Number in parentheses is the mean of the number of ﬁsh sampled. at 225 days RAS growth. Simulations revealed that a 5 C variation

◦

in typical RAS water temperatures of 28 C did not meaningfully

impact taste taint accumulation as either GSM or MIB.

correlation coefﬁcient for these data was R = 0.66 (Snedecor and

Model predictions gave good agreement with independent

Cochran, 1989), indicating a moderately good ﬁt.

experimental values of taint as GSM in barramundi.

It is clear from both Fig. 6 and Table 3 that the model predictions

An advantage is the model can be conveniently simulated in

are on trend and give a good ﬁt over a meaningfully large range of

standard spread-sheeting tools for use by a range of users of differ- values of taint.

ent sophistication.

Because the predictions of the model show good agreement with

A major beneﬁt of this new model when fully experimentally

these independent data for barramundi and rainbow trout, it can

validated is that simulations will be used to investigate a range of

be concluded it is free of programming and computational errors

growth protocols in RAS farming to minimize taste taint in ﬁsh-

and is of a generalized form. ﬂesh.

4.5. Applying the model to investigate RAS growth protocols on

Acknowledgements

accumulated taste taint

We thank Ms. Sue Poole, Department of Primary Industries,

A signiﬁcant advantage of the validated model is that it can be

Brisbane, Australia for providing taint data for barramundi. PIH is

used to investigate growth protocols. For example, simulations

grateful to CRC Seafood, Australia, for providing ﬁnancial assistance

underscore consumer acceptance of RAS barramundi at harvest

and a scholarship to carry out this research.

of 240 day if the RAS water concentration CW of GSM and MIB is

P.I. Hathurusingha, K.R. Davey / Ecological Modelling 291 (2014) 242–249 249

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