Effect of Linear and Non-Linear Estimation of Fish Mortality on Feed Conversion Rate and Economic Profitability of Oreochromis shiranus in Cages
Phiri Francis1,2*, Singini Wales2, Kapute Fanuel2 and Jere Bob2
1Department of Fisheries, Chisitu Fisheries Research Station, Africa
2Department of Fisheries and Aquatic Sciences, Mzuzu University, Africa
Submission: July 27, 2018; Published: August 24, 2018
*Corresponding author: Phiri Francis, Department of Fisheries, Chisitu Fisheries Research Station, Chisitu, Mulanje, Malawi, Africa, Po Box: 105, Tel: +265888358737/+265999606727, Email: email@example.com
How to cite this article: Phiri F, Singini W, Kapute F, Jere B. Effect of Linear and Non-Linear Estimation of Fish Mortality on Feed Conversion Rate and
Economic Profitability of Oreochromis shiranus In Cages . Ann Rev Resear. 2018; 3(2): 555606. DOI: 10.19080/ARR.2018.03.555606
This study was conducted to investigate the effect of linear and non-linear methods of estimating fish mortality on feed conversion ratio (FCR) and profitability of cage cultured Oreochromis shiranus (Makumba). Two treatments were used, designated as T1 and T2 and were replicated three times. In each cage, 105000 fish were stocked at an initial average body weight of 1.59±0.04g and cultured for 365 days. The fish was fed twice a day with formulated feed (36% Crude Protein) at 4-1% body weight with feed adjustments based on standing biomass from linear and non-linear estimated mortality. The results showed that there were significant differences between the two treatments on FCR
. Final mean weight was 179.41±7.71g and feed conversion ratio was 1.64±0.15 for T1 and 177.56±8.27g and 1.54±0.14 respectively for T2. Profitability of the two treatments was calculated by enterprise budgeting. There were significant effects on gross margin between the two treatments Gross margin values were K302,523,924.30 for T1 and K356,065,320.29 for T2. The study concludes that use of non-linear method of estimating fish mortality affect feed conversion ratio and economic profitability of Oreochromis shiranus cultured in cages. It is therefore recommended to use non-linear method of estimating fish mortality if farmers are to reduce FCR and maximize profits from the cage culture of Oreochromis shiranus as feed wastage due to feed overestimation resulting from miscalculation of mortality, can be minimized by 15.77%.
Fish catches in Malawi’s natural waters have experienced a sharp decline over the past decades, and as reported by Morgan in  sustainability of the fish stocks is not likely, given the demand for fish in the country. This development contributed to the increased emphasis on developing aquaculture as a major source of fish and rural income. Aquaculture now occupies a strategic position in the fisheries sector in Malawi. Development of a viable and sustainable cage aquaculture industry has therefore been identified by the Government of Malawi (GoM) as a flagship programme . According to Balarin & Haller as reported  fish growth in aquaculture is a result of several factors such as proper doses of fertilizer application, regular feeding, optimum stocking density, maintenance of physico-chemical factors, disease prevention and various control measures. The success of cage culture production as in all forms of aquaculture systems is therefore dependent on fish survival rate and how fast the fish grows to table size with reduced production inputs. Fish like any other living organism undergo several life series events among which growth and risks to life are. Fish in its lifetime is exposed to and must overcome several risks including: predation, starvation, disease and theft, all of which result into fish mortality . Fish losses in cage culture come
about due to death (mortality) escapes and theft. According to  fish can die at any time within the culture period, but small fish are more vulnerable to cannibalism, bird predation, water quality imbalance, and disease than larger fish. This means that majority of the mortality occurs in small fish as compared to bigger fish. Fish mortality rate (MR) is often established using the estimated numbers method by use of historic records . This can be expressed as linear and non-linear method of estimating mortality. In Malawi, like with most farmers in the region, fish mortality is estimated using linear method, where it is assumed that fish die at a constant rate along the production cycle. However, in non-linear estimation method, mortality is high at juvenile stage and almost insignificant at adult stage/table size. As reported by  feed requirements are calculated based on estimated standing biomass in the cage. This biomass is determined taking into account mortality levels along the production period. Most Malawian farmers using the estimated numbers method, experience a 30% mortality rate in their cages.
Use of enough feeds that can be fully ingested and utilized by the fish is of paramount importance in commercial as well as small scale aquaculture. Feed wastage through application of excess feed based on poor stock assessment or cage biomass projections has contributed to loss of feed and consequently high
production costs. The key challenge has been, and continue to be
poor estimation of fish feed, which is caused by miscalculation
of mortality or fish loss which in turn affect feed conversion
ratios as well as farm economic performance. Over-estimation
of feed emanating from underestimation of fish mortality can
result in higher FCR values, while under-estimation of feed
from overestimation of fish mortality results into unrealistic
FCR values. Most farmers in Malawi use linear estimation of fish
mortality, where mortality is believed to occur throughout the
culture period at a constant loss-rate. Use of linear estimation
method can bring over-estimation of the standing-crop biomass
hence an over-estimation of feed during calculation of feed
rations, resulting into high feed conversion ratios. This is
counterproductive and can lead to abandonment of fish culture
due to high economic losses. The present study used FCR in
analysing productivity due to its direct linkage and capacity to
estimate feed (input) potential in attaining fish growth (output).
The study also used gross margin analysis to assess profitability
potential of the mortality estimation methods since gross
margin use variable costs to estimate the profitability prospect
of an enterprise against its revenues by looking at whether an
enterprise will cover its production costs. Therefore, the aim of
the study was to investigate the effect of linear and non-linear
estimation of fish mortality on feed utilisation and economic
performance of Oreochromis shiranus in cages.
The study was conducted between December 2011,
and January 2013 at the Malawi Development Corporation
(MALDECO) Aquaculture Ltd in Mangochi District, Southern
Malawi Figure 1. MALDECO lies at a latitude of 19º19.982΄S, and
a longitude of 35º09.149΄E.
The study used secondary data collected by MALDECO
Aquaculture Limited. Six floating cages of 14.7m diameter and
approximately 6m depth were stocked, each with 105,000
Oreochromis shiranus fingerlings of 1.59±0.04g average body
weight (ABW) placed in Lake Malawi. The fish was subjected to
two treatments where in T1 fish mortality was estimated using
linear method, while in T2 fish mortality was estimated using non-linear method. Standing fish biomass was used to calculate
approximate feed requirements in each of the respective cages.
The treatments were replicated three times, and the fish was
cultured for a period of 365 days.
The fish was fed in the morning and afternoon at 9:00hrs
and 14:00hrs respectively, with formulated feed of 36% crude
protein (CP) from MALDECO Aquaculture’s Feed Milling Section.
Feeding rate was adjusted from 4% of total body weight during
the first and second month, to 3% of total body weight for the
third and fourth month, and 2% of total body weight for the fifth,
sixth and seventh month and finally 1% of total body weight for
the remainder of the culture period. Feed was administered by
broadcasting and was presented as dry pellets.
MALDECO collected data on fish mortality, weight of fish feed
used, fish growth, production costs and fish sales. Data on fish
mortality and feed was collected on daily basis, while data on
growth and production costs was collected on monthly basis.
Data on fish sales was collected at the end of the production
cycle. Fish mortality was monitored twice every day during
feeding trips and divers were monitoring fish carcasses that
sunk to the bottom of the cage once every week. The initial total
body weight of the fish (kg) was recorded at the time of stocking,
and the fish was sampled to monitor fish growth every last day of
the month. Fish growth data was used as a mechanism to dictate
adjustments in feeding rates respective of average body weight.
To avoid biasness, fish samples were collected by random
sampling. Numbers of fish dying were recorded on daily basis
throughout the research period and this assisted in adjusting
feed requirements in the cages respective of standing biomass.
The sampling exercise was conducted early in the morning
between 6.00hrs and 9.00hrs. A seine net was used to seine fish
from the cages to get a representative sample, while a scoop net
was used to get fish samples from the seined fish which was
batch-weighed using a standard weighing scale. A sample size of
500 fish from each cage was used at every sampling interval, and
batch weights were used to calculate average body weight. After
365 days of culture, all the fish in the cages was harvested. The
fish was counted to calculate total mortality figures, and final
body weight was measured to determine fish growth.
Growth indices were estimated using the following formulas:
Mean weight gain (MWG)
Where: WT2 is final mean weight of fish at time T2, WT1 is
initial mean weight of fish at time T1.
Mortality Rate (MR) %
Where: M is natural mortality, N is number of fishes stocked.
Feed Conversion Ratio (FCR)
Where: F is amount of feed used (g), MWG is Mean Weight
Economic indicators were calculated using the following: -
Gross Margin (GM)
Where: TR is Total Revenue, TVC is Total Variable Cost.
Return to Variable Cost (RVC)
Where: GM is Gross Margin, TVC is Total Variable Cost.
Break-even Yield (BEY)
Where: TVC is Total Variable Cost, P is Price of product
Break-even Price (BEP)
Where: TVC is Total Variable Cost, Y is Yield (output).
Data was entered and analysed using Statistical Package for
Social Scientists (SPSS) version 16.0. Microsoft (Ms) excel 2007
was used to generate graphs. Hypothesis testing was done by
Chi-Square test at 95% confidence interval.
To assess feed efficiency in the two treatments, various
production characteristics were calculated using Equations 1-3,
and presented in Table 1. Fish growth over the experimental
period was not different despite fish being subjected to different
treatments in estimation of mortality.
To assess effect of linear and non-linear estimation
of mortality on the profitability of O. shiranus, economic
performance parameters for the 53 cages were estimated
and calculated using Equation 4-7 as presented in Table 2.
Profitability analysis results through enterprise budgeting
showed that feed for linear treated cages accounted to 77.73% of
total variable costs, while for non-linear cages feed contributed
74.62% to total variable costs. Linear treatment produced a yield
of 10.47kg/m3 and to break even, the harvested biomass needed
to exceed 6.54kg/m3 for linear, against 5.74kg/m3 for nonlinear
treated cages which produced a yield of 10.36kg/m3. T2
registered a bigger Gross Margin of MK356,065.29 for a return to
total variable cost of 80% and return to feed of 108% on a realised
revenue of MK799,130,178.09, compared to a Gross Margin of
MK302,523,924.30 for a return to total variable cost of 60%, and
a return to feed of 77% on revenues of MK807,532,281.70 for T1.
Chi-Square results showed significant effects of linear and nonlinear
mortality estimation on gross margin,
Results from effect of mortality estimation methods on FCR
showed that there were significant differences between use of
linear and non-linear methods . This demonstrates that
mortality estimation methods affect feed conversion ratios of
fish in cages. These results suggest that use of non-linear fish
mortality estimation methods result into significant changes
in the calculated feed conversion ratio in cage cultured O.
shiranus. Specifically, the results suggest that when adjusting fish feed based on non-linear method of estimating fish mortality
which on average reduces fish feed by 15.77%, the fish used
statistically lower amount of feed to grow 1kg of fish muscles.
This agrees with  who suggested that overfeeding wastes feed
and result into higher FCR. The differences in feed between the
two treatments, can be attributed to overestimation of biomass
during the first three months of culture in linear treated cages
where mortality rate was higher in non-linear (28.37%) than
in linear (7.5%). This agrees with  who also found that FCR
is affected by miscalculation of mortality estimates. However,
the yielding of lower FCR by non-linear method, as reported
by Bhijkajee & Gobin in  suggests efficient food utilization
through the extraction of more nutrients from the food and
converting it into flesh. The recorded FCR agrees with what was
earlier reported that FCR for Tilapia in cages range from 1.4 to
The results from effect of mortality estimation methods
on profitability showed that there were significant differences
between use of linear and non-linear methods
demonstrates that mortality estimation methods affect
profitability of fish in cage culture. Use of non-linear estimation
of fish mortality ensures that more profits are realized as
opposed to the use of linear fish mortality estimation. This can
be attributed to differences in feed estimates between the two
methods in which non-linear used slightly less feed by 15.77%.
The results agree with  who suggested that feeding and feed
costs represent the single largest component of operating costs
and the quality of feed and the way it is used are significant
determinants of profitability. The differences in feed between
the two treatments can be credited to overestimation of biomass
during the first three months of culture in linear treated cages
where mortality rate was higher in non-linear (28.37%) than
in linear (7.5%). This means that use of linear method overfed
the fish by 20.73% during the period. This result agrees with
 who reported that accurate, detailed and complete records
can help fish farmers to provide control over the business and
improve the management and efficiency of the farm, provide
a basis for farm credit and financing, determine the relative
profitability of various production techniques or systems, and
provide information for government programs. Farmers using
linear method of estimating fish mortality therefore lose 17.70%
of their potential profits than those using non-linear method
of estimating fish mortality, translating into 10.60% of total
From this study, “the effect of linear and non-linear
estimation of mortality on feed conversion rate and profitability
of Oreochromis shiranus cultured in cages”, which was to
investigate on the lack of efficient fish mortality estimation
method, it can be suggested that use of non-linear method, has
significant effect on feed conversion ratio by yielding lower FCR
than linear method. On the objective of assessing profitability
calculated based on linear and non-linear mortality estimation
methods in cage cultured O. shiranus, the study also concludes
that non-linear method has significant effect on profitability
by yielding more profits than linear method. Therefore, for the
attainment of profit-oriented cage culture, farmers must aim at
lowering feed conversion ratios and reducing production costs to
bring about increased profits by ensuring conscious estimation
of fish mortality to reduce miscalculation of feed.