Subscribe Now Subscribe Today
Research Article

Techniques to Assess Fish Productivity in Aquaculture Farms and Small Fisheries: An Overview of Algebraic Methods

O. Alatorre-Jacome, F. Garcia Trejo, G.M. Soto-Zarazua and E. Rico-Garcia
Facebook Twitter Digg Reddit Linkedin StumbleUpon E-mail

The main goal of aquaculture and small fisheries is the bioaccumulation of chemical elements in edible tissue. Fish, shellfish, decapods and/or algae are commonly cultivated organisms in marine and freshwater aquaculture systems. Total biomass is the best indicator of production system performance. However, due to the high variation of technologies and methods used in aquaculture, special techniques are required to make thorough studies. The present study is a summary of algebraic fish biometric techniques to assess fish biomass production. Numerical computations were carried out for didactical purposes.

Related Articles in ASCI
Similar Articles in this Journal
Search in Google Scholar
View Citation
Report Citation

  How to cite this article:

O. Alatorre-Jacome, F. Garcia Trejo, G.M. Soto-Zarazua and E. Rico-Garcia, 2012. Techniques to Assess Fish Productivity in Aquaculture Farms and Small Fisheries: An Overview of Algebraic Methods. Journal of Applied Sciences, 12: 888-892.

DOI: 10.3923/jas.2012.888.892

Received: November 05, 2011; Accepted: March 16, 2012; Published: June 27, 2012


Fisheries and aquaculture both involve the production of high quality fish protein (Obaroh and Achionye-Nzeh, 2011; Bozoglu et al., 2006; Huda et al., 2002). Fisheries are based on the extraction of living resources in water bodies (Bostock et al., 2010; Akca et al., 2006). Aquaculture is the farming of aquatic plants and animals (Iwama, 1991). Both disciplines provide most of the world’s aquatic edible resources (Food and Agriculture Organization of the United Nations (FAO, 2010).

Aquaculture productivity is commonly measure as total biomass. However, in many cases additional parameters are required to make thorough studies (Alagaraja, 1991). Simple algebraic models can be used to make important decisions in farm (Roomian and Jamili, 2011). These methods are relative easy to carry out and their implementation requires basic mathematical background. In scientific research they can be used to compare similar experimental procedures (Alatorre-Jacome et al., 2011).

In the case of fisheries, direct and indirect methods to assess productivity have been extensively developed (Cochrane, 2002; Sparre and Venema, 1998; Pauly, 1983). But as for inland, small-scale aquaculture systems, the application of large and complex fisheries analysis could be far to be done.

The purpose of the present study was to propose a synthetic methodology in order to assess small-scale fish productivity. Formulae for collective and individual fish growth determination are presented. A case study in aquaculture is analyzed for collective growth performance indexes. A small-fisheries study case is analyzed to explain the procedure for individual fish growth determination.


Data measurement: For the following parameters, there were required four types of response variables: Fish total length (mm), fish wet weight (g), time (days) and number of fish measured. The correct techniques for accurate measures can be found in the literature (Sparre and Venema, 1998; Brander, 1975). For explicative purposes, examples on calculations were analyzed on results.

Total biomass production: According to Ricker (1971) biomass is the amount of substance in a population expressed in material units, such as living or wet weight, dry weight, ash-free weight, nitrogen contents, etc. It is also termed as standing crop.

For the total biomass wet weight (Wt) we use:


where, Wi is the weight of the ith fish in the system.

Because the aquacultural systems are very heterogeneous about its size and capacity, is useful apply the term relative density (prel) per volumetric unit (kg m-3) to compare among them:


where, Wt is the total biomass on the system and V is its volume. In extensive systems if often used the area instead volume.

Akinwole and Faturoti (2007) use the next equations as useful indicators for the system productivity. The Total Weight Gain (TWG) function indicated the gain of biomass in a given time:


where, Mf is the final mass of the fish and Mi is the initial mass.

The Average Daily Growth Rate (ADGR) indicate the average weight gained each day:


where, TWG is the total weight gain (from Eq. 3) and D are the culture day (Shnel et al., 2002).

According to Bwala and Omoregie (2009), the Specific Growth Rate (SGR) is:


where, Mf is the final weight of the fish, Mi is the initial mass of the fish, ln is the natural logarithm and D are the culture.

Metabolic Growth Rate (MGR) and the Feed Conversion Efficiency (FCE) can been computed with the methodology exposed on the work of Frei and Becker (2005):


where, Mf is the final mass of the fish, Mi is the initial mass of the fish and D are the interval time (in days). For FCE:


where, Mf is the final mass of the fish, Mi is the initial mass of the fish and F is the dry weight of the feed.

Individual fish growth: In hatchery or nursery system is also important the length of the fish. Both variables (weight and length) are related by the next equation (Sparre and Venema, 1998):


where, W(i) is the weight for the ith fish, L(i) is the total length of the fish and the letters a and b are the growth parameters obtained by linearization.

In many cases is useful to predict the increment of the length and weight of the fish in a given time. It can be achieve using potential growth model. A very popular model among fish researchers is the von Bertalanffy’s growth function:


where, Lt is the total length of the fish on time t, Ll is the maximum total length at infinite time, k is the growth constant, to is the initial time to growth and t is time. In the case of weigh, the equation is the following:


where, Wt is the total weight of the fish on time t, Wl is the maximum total weight at infinite time, k is the growth constant, to is the initial time to growth and t is time (Pauly, 1983).


Total biomass production: Soto-Zarazua et al. (2010) cultivated 1,200 tilapia fish fingerlings on circular tanks with a capacity of 20 m3. The average initial weight was 20 g and after 180 days the weight of all the fishes was measured. Applying the formula 1, the total biomass production on one tank was 580.33 kg. For relative biomass production (Eq. 2):


The initial total weight gain assumed 1,200 fish and 20 g per fish was 24 kg. For Eq. 3:


And the average daily growth rate per tank, according to Eq. 4:


The Specific Growth Rate ( SGR) was:


Metabolic Growth Rate (MGR) and the feed conversion efficiency (FCE) can been computed with the methodology exposed on the work of Frei and Becker (2005):


In addition, there was reported 940.13 kg of feed consumed during the experiment, so the feed conversion efficiency was:


Individual fish growth: In 2006, Alatorre-Jacome measured the following data for length and weight on M. salmoides located in a small lake in center México (Table 1).

Fitting the data for an exponential model (r2 = 0.97) the specific length-weight relation was:


To obtain the parameter for Von Bertalanffy equation, K and Lo there are several methods. In this case we used the following. In literature, In literature, the propose value L = 358.4. With the data of age and length (Table 2), in a third column there was calculated:


Plotting the values of the first and the third column, there was obtained by linear regression (R2 = 0.9971) the parameters a = 0.33, which is the value x at y = 0 and b = 0.3255, the slope of the line. The value K = b and To was:


And the Von Bertalanffy’s weight equation for this population is:


Table 1: Length and weight measured on largemouth bass (M. salmoides) on Camecuaro Lake, 2006

Table 2: Linearization of time (age) and length values to parameter determination on von Bertalanffy’s equation

Calculating the fish weight at L, we obtain L = 652.07, so the Von Bertalanffy’s weight equation is:



There are many different values for productivity index on literature, which explained the global performance for one system. In this case, the value of 29 kg m-3 is obtained. Timmons et al. (2002) recommended less than 40 kg m-3 for systems with blower. However, Rakocy et al. (2006) reported densities of 60 kg m-3 for aquaponic systems. In extensive systems, Sarker et al. (2005) reported lower values (479 kg ha-1) even with strains of genetically improved farm tilapia. The principal causes of productivity are due to managing practices, temperature (Ghosh et al., 2008; Sarkar et al., 2007) and water quality factors in culture water (Hossain et al., 2007).

In ADGR, the index can be used to make more accurate feed management schedules. A variation can be made with the data, dividing ADGR by number of fishes. Then the average day growth rate per fish can be obtained. In this case, 2.57 g day-1 fish-1 is reported. Rezk et al. (2002) reported ADGR from 1.87 g day-1 fish-1 in O. aureus after 35 days of culture. This value is lower than the observed on Soto-Zarazua et al. (2010) but the main difference is than Rezk cultured fingerlings, who have a different metabolism than adults. In other hand, Liti et al. (2005) reported ADGR from 0.06 to 1.5 g day g day-1 fish-1 found on tilapia fed on two formulated diets with locally available feed in Kenia.

From SGR, Akinwole and Faturoti reported SGR from 2.656 to 2.86 measured on C. gariepinus cultivated in recirculating aquaculture system. Velazquez and Martinez (2005) reported 0.97 and 0.86 for C. auratus. Hlophe et al. (2011) reported SGR values lower than 1.7 in T. rendalli fed with kikuyu grass.

On the other hand, Cho and Bureau (2001) suggested the elimination of the parameter due to the non-realistic approaching of its calculation. In MGR, the index is used in nutritional studies. Richter et al. (2002) reported several index (From 1.76 to 5.04 g kg-1 day-1) in order to assess a more convenient maintenance diet formulations in red tilapia. At last, the feed conversion efficiency of 0.59 means that almost 60% of the mass provided for the tilapia was assimilated as tissue. This is very convenient, due the requirements of the fish to its energy for respiration and the balance of non-assimilated food.

In the example presented for individual fish weight, it can be observed that in Eq. 16 the parameter b˜3.05. When the parameter b = 3, the growth is called isometric and if b<3 is called allometric negative and if b>3 is allometric positive (Pauly, 1983). So we can see that the fish measured have a good increment of weight. For the equations of von Bertalanffy’s equations, the parameter k is very important, because is the growth constant and is species specific (Lv and Pitchford, 2007). For this case, in the study of Guzman-Arroyo made 35 years earlier in the same place, the value was k = 0.56, so we can assume that the conditions were more favorable to a faster growth for M. salmoides.


Selected fish biometric indexes were presented in this work. The use of the parameters mentioned can bring more information for the intrinsic factors in the fish culture that influenced growth. They also allow the comparison between different populations in space and time. This paper can be used as a quick guide to measure fish productivity in small systems. The following parameters can be used by scientist or producers to compare different systems each other.


The Fondo de Investigación de la Facultad de Ingenieria (FIFI, 2011) of Queretaro State University sponsored this work, the financial support is greatly appreciated.

1:  Akinwole, A.O. and E. O. Faturoti, 2007. Biological performance of African catfish (Clarias gariepinus) cultured in recirculating system in Ibadan. Aquacult. Eng., 37: 18-23.
CrossRef  |  

2:  Alagaraja, K., 1991. Assessment of Fish Production in Aquaculture. In: Simposium on Aquaculture Productivity Held in December 1988 Under Aegis of Hindustan Lever Research Foundation, Sinha V.R.P and H.C. Srivatasva, (Eds.)., Oxford and IBH Publishing, USA.

3:  Alatorre-Jacome, O., E. Rico-Garcia, G.M. Soto-Zarazua, F. Garcia-Trejo and G. Herrera-Ruiz, 2011. A thermosolar nursery for tilapia (Orechromis niloticus L.). Sci. Res. Essays, 6: 4619-4626.
Direct Link  |  

4:  Bostock, J., B. Mcandrew, R. Richards, K. Jauncey and T. Telfer et al., 2010. Aquaculture: Global status and trends. Phil. Trans. R. Soc. B., 365: 2897-2912.
CrossRef  |  

5:  Brander, K., 1975. Guidelines for collection and compilation of fishery statistics. FAO Fisheries Technical Paper No. 148, pp: 46

6:  Bwala, R.L. and E. Omoregie, 2009. Organic enrichment of fish ponds: Application of pig dung vs. Tilapia yield. Pak. J. Nutr., 8: 1373-1379.
CrossRef  |  Direct Link  |  

7:  Cho, C.Y. and D.P. Bureau, 2001. A review of diet formulation strategies and feeding systems to reduce excretory and feed wastes in aquaculture. Aquacult. Res., 32: 349-360.
Direct Link  |  

8:  Cochrane, K.L., 2002. A fishery manager's guidebook. Management measures and their application. FAO Fisheries Technical Paper No. 424. Rome, FAO.

9:  Akca, H., M. Kayim and M. Sayili, 2006. SWOT analysis of fishery sector in Turkey. J. Applied Sci., 6: 1863-1867.
CrossRef  |  Direct Link  |  

10:  Hlophe, S.N., N.A.G. Moyo and J.R. Sara, 2011. Use of kikuyu grass as a fishmeal substitute in practical diets for Tilapia rendalli. Asian J. Anim. Vet. Adv., 6: 1076-1083.
CrossRef  |  

11:  Huda, F.A., M.M. Salehin and M.I. Khan, 2002. Economics of Periphyton-based aquaculture production in Bangladesh. J. Biol. Sci., 2: 518-519.
CrossRef  |  Direct Link  |  

12:  Frei, M. and K. Becker, 2005. A greenhouse experiment on growth and yield effects in integrated rice-fish culture. Aquaculture, 244: 119-128.
Direct Link  |  

13:  FAO, 2010. The state of world fisheries and aquaculture. Fisheries and Aquaculture Department, Food and Agriculture Organization of the United Nations, Rome,

14:  Ghosh, L., G.N. Tiwari, T. Das and B. Sarkar, 2008. Modeling the thermal performance of solar heated fish pond: An experimental validation. Asian J. Scientific Res., 1: 338-350.
CrossRef  |  Direct Link  |  

15:  Iwama, G. I., 1991. Interactions between aquaculture and the environment. Crit. Rev. Environ. Control, 21: 177-216.
CrossRef  |  

16:  Liti, D., L. Cherop, J. Munguti and L. Chhron, 2005. Growth and economic performance of nile tilapia (Oreochromis niloticus L.) fed on two formulated diets and two locally available feeds in fertilized ponds. Aquacul. Res., 36: 746-752.
CrossRef  |  

17:  Bozoglu, M., V. Ceyhan, H.A. Cinemre, K. Demiryurek and O. Kilic, 2006. Evaluation of different trout farming systems and some policy issues in the black sea region, Turkey. J. Applied Sci., 6: 2882-2888.
CrossRef  |  Direct Link  |  

18:  Obaroh, I.O. and G.C. Achionye-Nzeh, 2011. Effects of crude extract of Azadirachta indica leaves at controlling profile breeding in Oreochromis niloticus (Linnaeus, 1758). Asia J. Agric. Res., 5: 277-282.
CrossRef  |  

19:  Pauly, D., 1983. Some simple methods for the assessment package of tropical fish stocks. FAO Fisheries Technical Paper 234, Food and Agriculture Organization of the United Nations, Rome, pp: 1-52.

20:  Lv, Q. and J.W. Pitchford, 2007. Stochastic von bertlanffy models, with applications to fish recruitment. J. Theor. Biol., 244: 640-655.
CrossRef  |  

21:  Rakocy, J.E., M.P. Masser and T.M. Losordo, 2006. Recirculating aquaculture tank production systems: Aquaponics-integrating fish and plant culture. SRAC Publication No. 454.

22:  Rezk, M.A., E.A. Kamel, A.A. Ramadan and R.A. Dunham, 2002. Comparative growth of Egyptian tilapias in response to declining water temperature. Aquaculture, 207: 239-247.
CrossRef  |  

23:  Ricker, W.E., 1971. Methods of Assessment of Fish Production in Fresh Waters. 2nd Edn., Blackwell, Oxford USA.

24:  Richter, H., G. Francis and K. Becker, 2002. A reassessment of the maintenance ration of red tilapia. Aquacult. Int. 10: 1-9.
CrossRef  |  

25:  Sarkar, B., B.C. Mohapatra, S.K. Singh, D. Majhi, N. Sarangi and G.N. Tiwari, 2007. Impact on energy consumption in greenhouse fish production. Asian J. Agric. Res., 1: 74-79.
CrossRef  |  Direct Link  |  

26:  Sarker, P.K., S.U. Ahmed, S. Rahman and D. Dey, 2005. Suitability and production performance of Oreochromis niloticus (GIFT) and Cyprinus carpio under mono and mixed culture system in coastal rice field. J. Biological Sci., 5: 289-291.
CrossRef  |  Direct Link  |  

27:  Shnel N., Y. Barak, T. Ezer, Z. Dafni and J. Van Rijn, 2002. Design and performance of a zero discharge tilapia recirculation system. Aquacult. Eng., 26: 191-203.
CrossRef  |  

28:  Soto-Zarazua M.G., G. Herrera-Ruiz, E. Rico-Garcia, M. Toledano-Ayala, R. Peniche-Vera, R. Ocampo-Velazquez and R.G. Guevara-Gonzalez, 2010. Development of efficient recirculation system for tilapia (Oreochromis niloticus) culture using low cost materials. Afr. J. Biotechnol., 9: 5203-5211.
Direct Link  |  

29:  Roomian, L. and S. Jamili, 2011. Population dynamics and stock assessment of hilsa shad, Tenualosa ilisha in Iran (Khuzestan province). J. Fish. Aquat. Sci., 6: 151-160.
CrossRef  |  Direct Link  |  

30:  Timmons, M.B., J.M. Ebeling, F.W. Wheaton, S.T. Summerfelt and B.J. Vinci, 2002. Recirculating Aquaculture Systems. 2nd Edn., Cayuga Aqua Ventures, New York.

31:  Velazquez, M. and F.J. Martinez, 2005. Design and testing of a faeces-collecting device for fish digestibility studies using demand or automatic feeding. Aquacult. Eng., 33: 126-134.
CrossRef  |  

32:  Hossain, M.Y., S. Jasmine, A.H.M. Ibrahim, Z.F. Ahmed and J. Ohtomi et al., 2007. A preliminary observation on water quality and plankton of an earthen fish pond in Bangladesh: Recommendations for future studies. Pak. J. Biol. Sci., 10: 868-873.
CrossRef  |  PubMed  |  Direct Link  |  

33:  Sparre, P. and S.C. Venema, 1998. Introduction to tropical fish stock assessment: Manual. FAO Fisheries Technical Paper No. 306/1, Rev. 2, Rome, pp: 407.

©  2021 Science Alert. All Rights Reserved