Prediction of bio-economically sustainable yield and optimum fishing effort for the Nile tilapia (Oreochromis niloticus L.) of Hawassa,

The Nile tilapia ( Oreochromis niloticus , L. 1758) stock of Lake Hawassa, Ethiopia, was assessed to estimate bio-economically sustainable yield (MSY and MEY) and optimum fishing effort (f opt ) using length-based analytical models (Jone’s Cohort Analysis and Thompson and Bell). Pertinent data (length, weight, catch, effort, etc.) were collected on a daily basis between May 2012 and June 2013 from the two landing sites, where fishermen at the northern and the southern part of the lake land their catch for retail. The assessment revealed an estimated current yield of 240.23 t/year and 216.33 t/year for the southern and northern part of the fishery of the lake, re -spectively. The predicted biologically maximum sustainable yield (MSY) was 240.2 t/year and 218.7 t/year for the southern and northern fishery, respectively, which were obtained at an F-factor of 1 and 1.5, respectively. On the other hand, the maximum economic return was generated from the southern and northern fishery at an F- factor of 0.8 and 1.4, respectively. Therefore, the level of effort at the time of sampling (F-current) should be reduced by 20 % for the southern fishery while the current effort of the northern fishery can be expanded by 40% in order to obtain the max imum economically sustainable yield. Accordingly, the optimum level of fishing effort (f opt ) to be exerted at the lake level was estimated at about 650 nets per day in order to exploit O. niloticus stock of Lake Hawassa sustainably.


INTRODUCTION
The commercial fishery of Lake Hawassa primarily rests on Oreochromis. niloticus that contributes about 90% of the total annual catch (LFDP, 1997;Elias Dadebo, 2000;Tadesse Fetahi and Seyoum Mengistou, 2007). Since the last two Consequently, Lake Hawassa is one of the most abused lakes in the country. Starting from the early 1990's, the fishery of Lake Hawassa has been continuously expanding with a rise in the number of fishermen and fishing gears. Following this progressive increment of fishing effort, the annual fish yield in the early 1990's reached its peak at about 900 t/year (LFDP, 1997). The fishery has, however, undergone drastic changes in recent years. The yield has been continuously declining and reached about 50% of the maximum record, indicative of a dwindling fish population size probably resulting from overexploitation in the last two decades (LFDP, 1997;Reyntjens and Tesfaye Wudneh, 1998). *Corresponding author: yosef.teklegiorgis@yahoo.com statistical data collection system practiced in Lake Hawassa (also in other lakes of the country as well) has not been geared towards generating age and/or length structured catch data. Hence lack of such data has mainly limited the application of analytical type models. As a result, little is known about the potential yield of the exploited fish species, even the limited information available on potential yield estimates are derived from empirical models. Therefore, in this study analytical stock assessment models have been used to estimate the maximum bio-economically sustainable yield of the most fished stock, O. niloticus, as well as the biologically and economically optimum fishing pressure to be exerted on the stock. Hawassa city, which is located 275 km south of Addis Ababa, the capital city of the country. It has an altitude of 1,680 m above sea level, a surface area of 90 km 2 , a mean depth of 11 m, a volume of 1.036x10 9 m 3 and a drainage area of 1,250 km 2 (LFDP, 1997). It is a terminal lake with no surface outflow and receives surface inflow through Tikur Wuha River (LFDP, 1997).

Site description
Lake Hawassa has the most diversified phytoplankton community (i.e., over 70 species) in the rift system, amongst of which Cyanophytes (mainly Microcystis) makeup over 75 % of the total algal biomass (Elizabeth Kebede, 1996).
Lake Hawassa is one of the most fished lakes in the rift valley. There are six fish species in the lake of which O. niloticus is commercially the most important contributing about 90% of the annual catch (Reyntjens and Tesfaye Wudneh, 1998 (Gara quadrimaculata, Rüppell, 1835) (Elias Dadebo, 2000).
Two groups of fishermen cooperatives operate, one in the southern and the other in the northern part of the lake. The former land their catch at the southeastern shore at a place locally known as 'Amora-Gedel (Figure 1), which is also a fish market where the fishermen retail their catch. This cooperative has 270 fishermen and they have a long history of fishing experience. They have been fishing since commercial fishery was established some five decades ago (LFDP, 1997). The second groups of fishermen cooperative that operate at the northern part of the lake compose 37 fishermen and it is relatively recent, established less than a decade ago. They land their catch in the northern side of the lake at a place called 'Tikur-Wuha', which is the entry point of the Tikur-Wuha River (Figure 1).
Due to conflicting interest between the two groups of fishermen, the fishing grounds of the northern and southern fishery do not overlap, which in turn has left some free zone in between. In other words, the fishermen that operates in the southern side fish at the southern one-third of the lake while those in the north fish at about one-third of the northern part of the lake area. Thus the middle part of the lake is a kind of buffer zone.

Sampling regime and data collection
Data were collected on daily basis from both landing sites (Amora Gedel and Tikur-Wuha).  (Table 2).

Data summarization and analysis
The catch data were summarized in a manner useful for stock assessment using Jones length based cohort analysis model (Jones, 1984) and length-based Thompson and Bell yield prediction model (Thompson and Bell, 1934;Sparre and Venema, 1992 (Pauly, 1984;Sparre and Venema, 1992):

Preparing length frequency of the sample catch
Length measurements recorded daily were grouped into one centimeter length intervals to prepare a Likewise, the average daily data of the sampled major fasting days were used to estimate the corresponding data of the un-sampled major fasting days.

Estimating the annual total length composition of landed fish
This was done by multiplying the length frequency of the sampled days catch by an appropriate conversion factor which was equal to C/c, in which 'C' = the estimated total catch of fish during the whole year and 'c' = the total catch of fish during the sampled days (Sparre and Venema, 1992).

Estimating population size and fishing mortalities using Jones length based cohort analysis
The Jones length based cohort analysis model (Jones, 1984) was used to estimate the fish population abundance and fishing mortality coefficient by length group of O. niloticus. This was done in three steps as follows: Estimating the population number of the largest length group in the catch The following equation was employed (Jones, 1984;Sparre and Venema, 1992) Where:

Estimating the population numbers of consecutively younger length groups in the catch
This was done using the following equation: Where: N(L 1 ) and N(L 2 ) = the population of fish in the water that attained length L 1 and L 2 , respectively C(L 1 ,L 2 ) = the total annual catch in number of fish caught between lengths L 1 and L 2 H(L 1 ,L 2 ) = the fraction of N(L 1 ) fish that survived natural deaths as it grows from length L 1 to L 2, and it is computed by the following equation (Jones, 1984) Where: L ∞ = the asymptotic length (cm) of O. niloticus attained at mature size L 1 and L 2 = consecutive length groups of fish (cm) that contributed to the fishery K = Von Bertalanffy growth rate constant (yr -1 ) M = the rate of natural mortality coefficient for O.
niloticus stock of Lake Hawassa.
Estimating the fishing mortality rate for the respective length groups Fishing mortality values for each length group was estimated using the following equation.
Where F(L 1 ,L 2 ) = fishing mortality coeffecient pertaining to the respective length group N(L 1 ), N(L 2 ) and M are as defined above. ∆t = the time required for fish of length L 1 to grow to length L 2, and it is defined by the following equation (Jones, 1984;Pauly and Morgan, 1987;Gulland and Rosenberg, 1992).
The terms are as defined above.
To use equations 2, 3, 4 and 5, the following input data and parameters were prepared in advance.  (Pauly, 1984): Where values of L ∞ and K are as described above for O. niloticus stock and T is the mean annual surface water temperature of Lake Hawassa recorded during the study period, which was 21 o C.

Predicting bio-economically sustainable fish yield and optimum fishing effort
The outputs of the above cohort analysis procedures were used as input data for the Thompson and Bell yield prediction model to predict sustainable fish yield at different levels of fishing mortalities (Thompson and Bell, 1934;Pauly and Morgan, 1987;Schnute, 1987;Sparre and Venema, 1992).
For the length based Thompson and Bell model, input data and sources comprised the following: i. Length composition of the annual total number of fish landed by the fishery. This was obtained from field data collection (catch statistics data) as described earlier. ii.
Estimates of population numbers of fish and fishing mortality coefficient (F) by length group. Source: results of the Jones length based cohort analysis described earlier.
iii  and Venema, 1992). Since there is a one-to-one correspondence between fishing mortality (F) and fishing effort (f), the value of F-factor chosen as optimum was used to recommend how much the current level of fishing effort need to be increased or decreased to get the maximum sustainable and bio-economical yield from the stock.

Status of O. niloticus fishery of Lake Hawassa
As noted above, the two cooperatives operating on the southern (Amora-Gedel landing site) and in the northern part (Tikur-Wuha landing site) of the lake have 270 and 37 fishermen, respectively ( times higher) compared to the total cost incurred per year at the northern part of the lake (Table 2).
Overall an estimated total cost of 960,340 Birr and 388,940 Birr per year was expended by the cooperatives at the southern and northern part of the Lake for fishing, respectively. These costs were used as inputs to make economic analysis of the fishing operation of the respective fishery (Table 2). Amora-Gedel landing site (Table 3).   based on data collected from the catch landed at the northern part of the lake, was over 1.6 million fish (Table 4 column 4, first row). Accordingly, these estimates were fairly comparable. Where, W is the average weight in grams of each length group and L is the average length of respective length groups in centimeters. The coefficient of determination (R 2 ) value for the relationship was 0.96 indicating that the estimated total weight for the respective length group is 96 %, which is related to the measured weight of each length group. Also the mean price of fish shown by column 3 is the average retail price of respective length group of fish.
Values in columns 4 and 7 (Table 5)  The reference F-array is shown in columns 3 and 5 of Table 4. It has been multiplied by each value of F-factor shown in column 1 of Tables 6 and 7 to produce the new fishing mortality coefficient for each length group. Then values of yield and revenue (columns 2 and 3, Tables 6 and 7) were predicted using the new F-array. Column 4 (Tables 6 and 7) shows total annual cost of fishing of the two fishery obtained by multiplying the current total cost of fishing obtained at the time of sampling (Table 2)  t/year is obtained from the fishery at the southern part of the lake at an F-factor of 1 (Table 6). On the other hand, a predicted maximum net annual profit of Birr 4,531,792 can be generated from the fishery at an F-factor of 0.8. This implies that a maximum return from the southern fishery can be obtained if the fishing pressure at the time of sampling (F-current) is reduced by 20%. Regarding the fishery at the northern part of the lake, the analysis showed that the predicted yield becomes maximum (MSY) at an F-factor of 1.5, but the profit becomes maximum (Birr 3,907,981) at an F-factor of 1.4 (Table 7). This indicates that the fishery at the Table 6. Predicted annual yield (t/year), gross revenue, cost and net profit (Birr) obtained from O.niloticus fishery at the southern part of Lake Hawassa.

Southern fishery
Yield (

Status of O. niloticus fishery of Lake Hawassa
Commercial fishery started in the 1950's in Lake Hawassa (LFDP, 1997). Until fishery at the northern part of the lake started eight years ago Amora-Gedel landing site, which is located at the south eastern shore of the lake, was the only landing site where fishermen retailed their catch. kg/net) is higher than the corresponding value (1.95 kg/net) at the southern fishery. This is because of the fact that the catch of the southern fishery is composed of smaller sized fish. Obviously, this is a response to intensive fishing (Bwanika, et al. 2004) conducted at the southern fishing grounds.
More than 90 % of the catch of the southern fishery