Assessing the Depletion Status and Sustainability of Catfish (Clarias gariepinus) Fisheries in the Southeast Arm of Lake Malawi

Abstract

Catfish is a major commercial and subsistence species in Malawi, making its sustainability vital for local livelihoods and food security. However, limited evidence exists on the long-term biological and economic depletion of commercial catfish stocks. This study assessed the depletion status of the catfish fishery in the southeast arm of Lake Malawi using secondary catch and effort data from 2000 to 2023 obtained from the Malawi Department of Fisheries, and price and cost data obtained from the field study. Applying the bioeconomic Gordon–Schaefer model, the study estimated biological depletion and economic depreciation to quantify resource losses and evaluate the fishery’s sustainability. Constant and periodic harvesting strategies were examined to determine sustainable harvest thresholds. Results show that depletion occurred in 15 of the 24 years analysed, with a cumulative biomass loss of 446.1 tonnes and an estimated total depreciation of about MK 1.5 billion. These findings indicate exploitation beyond sustainable levels both biologically and economically, threatening stock recovery, long-term productivity, and economic viability. The study highlights the value of bioeconomic modelling in fishery assessment and underscores the urgent need for improved management, including strengthened monitoring, effort regulation, and enhanced enforcement, to ensure sustainable utilisation of catfish resources and protect dependent livelihoods.

1. Introduction

Sustainable fisheries are critical for food security, livelihoods, and ecosystem health worldwide [1]. Inland fisheries, in particular, provide protein, income, and employment to millions of people in developing countries [2]. However, many fish populations are declining due to overexploitation, poor management, and environmental change [1,2,3,4]. Maintaining sustainable fishery levels requires effective monitoring and management of fishery resources, including the assessment of stock depletion [3] and the implementation of sustainable harvesting strategies [2].

In Malawi, the fish sector is a vital component of the national economy, contributing to food security, income, and employment [5]. The sector supplies about 40% of the country’s protein needs [6] and provides both direct employment through fishing and indirect employment through activities such as boat building, fish processing, net making, and engine repairs [5]. Fish exports generate over USD 24 million annually, and the sector contributes approximately 4% of Malawi’s GDP [7]. Lake Malawi, the largest lake in the country and the ninth largest globally, harbours extraordinary biodiversity, with over 1000 estimated fish species, most of which are endemic [8,9]. The lake accounts for more fish landings than any other in Malawi [10], making it a critical region for fishery management. Geographically, Lake Malawi is divided into three main zones: the southeast arm, the southwest arm, and the upper Shire system, which includes Lake Malombe and the upper Shire River [11]. Among these, the southeast arm is the most productive fishery region, extending across the southern portion of the lake and linking to Lake Malombe [4,11].

The Malawian fishery sector comprises capture fisheries and aquaculture [12]. Capture fisheries, which are divided into artisanal and commercial subsectors, contribute over 90% of national fish landings [4]. While artisanal fisheries dominate the sector, commercial fishing activities have increased in recent years [4,7]. As a result of this growth, there are increasing concerns regarding the sustainability of fish populations in Malawi [11], reflecting global trends [3]. Overfishing, exacerbated by open-access regimes and poor management strategies, has led to declining fish stocks, reduced catch rates, and potential ecosystem disruptions [1,2,3,4]. Indicators such as declining catch per unit effort (CPUE) and rising prices of commercially important fish species, resulting from market scarcity, support the notion of overfishing in Malawi [4]. Increased fishing pressure has led to the overexploitation of most fish species [13], including Engraulicypris sardella (usipa) [11] and Oreochromis species (chambo) [4]. Effective management strategies are therefore essential to rebuild and maintain fish stocks.

Among the commercially important fish species in Malawi, catfish (Clarias gariepinus) plays a key role in both domestic consumption and export markets [13]. Demand for catfish is particularly high among high-income households in Malawi and neighbouring countries [14,15]. Catfish is also important to local communities, providing food security, nutrition, and income through fishing, processing, and selling [7]. Despite its economic significance, no empirical assessment of the depletion status of the commercial catfish fishery in the southeast arm of Lake Malawi exists, creating a critical knowledge gap for fishery management and policy formulation. Without such information, the fishery remains at risk of overexploitation, which could ultimately lead to the collapse of the catfish stock.

The Gordon–Schaefer (GS) model, a bioeconomic surplus production model based on the logistic equation, integrates biological and economic parameters to assess fish population stocks, estimate sustainable catch levels, and calculate the depletion and economic depreciation of fishery resources [2,7,11,16,17,18]. Advantages of the GS model include its simplicity, cost-effectiveness, and reliance on readily available catch and effort data, making it suitable for data-limited contexts such as Malawi [7]. Previous applications of the GS model in Malawi focused on species such as Oreochromis species (chambo) and Engraulicypris sardella (usipa) [4,11,19,20], but no study has assessed catfish fisheries. Furthermore, prior studies did not quantify biological depletion or economic depreciation of fish resources, nor did they evaluate sustainable harvesting strategies using a bioeconomic framework. As a result, information on the depletion and depreciation of catfish resources in Malawi remains unknown.

Depletion refers to the reduction in fish population abundance or biomass to levels that hinder natural replenishment [16]. In this study, depreciation is defined as a consequence of depletion, whereby the loss of fish biomass (natural capital) is expressed in monetary terms [3,16]. High fishing rates can reduce populations below sustainable capacity, resulting in declining stock biomass, reduced catches, and ecosystem disruption [3,16]. Understanding depletion and depreciation is essential for preventing overexploitation and biodiversity loss, as highlighted by studies in other regions [1,3].

This study aims to estimate the depletion of the commercial catfish fishery in the southeast arm of Lake Malawi using catch and effort data from 2000 to 2023. Employing the GS model, the study calculates annual depletion by comparing actual catches with sustainable yields and derives economic depreciation to quantify monetary losses. Additionally, the study examines constant and periodic harvesting strategies to identify sustainable catch levels. By applying the GS bioeconomic model to catfish fisheries for the first time in Malawi, this study provides critical insights into the ecological and economic impacts of overfishing, management inefficiencies, and environmental change. The findings inform evidence-based management policies and support sustainable harvesting practices, thereby promoting both conservation and economic benefits.

2. Materials and Methods

2.1. Study Area

The data used in this study pertain to catfish from the southeast arm of Lake Malawi, which encompasses the southern portion of the lake and connects to Lake Malombe via the Upper Shire River. Among the three major regions of Lake Malawi, the southeast arm is the most productive. For monitoring and management purposes, this area is divided into six strata: Southeast Boadzulu, Southwest Boadzulu, Northeast Boadzulu, Northwest Boadzulu, Fort Maguire, and Makanjira [11]. Data were collected and analysed across all six strata. Figure 1 is the map of the southeast arm of Lake Malawi.

Figure 1. Map of the southeast arm of Lake Malawi.

2.2. Data Sources

This study utilised both secondary and field data. The secondary data consisted of time-series records of catch (tonnes) and effort (trips) for the commercial catfish fishery in the southeast arm of Lake Malawi from 2000 to 2023. Effort values represent the total number of fishing trips by commercial fishers in a given year, while catch values correspond to the aggregated landings from all six strata of the southeast arm. These data were obtained from the Malawi Department of Fisheries, located in Mangochi District.

Price and cost data were collected through a field study conducted in the southeast arm of Lake Malawi between June and December 2023. A total of 142 commercial fishers participated by completing a structured questionnaire. Written informed consent was obtained from all participants. Participation was voluntary and followed an explanation of the study’s objectives, including participants’ right to withdraw at any time. To ensure confidentiality, no personal identifiers were recorded during data collection.

The snowball sampling technique was used to recruit participants. Although non-random sampling may introduce bias by overrepresenting certain categories of fishers, this approach allowed the researchers to identify and engage experienced commercial fishers who were actively operating in the study area [11].

The price value used in this study represents the average price, in Malawi Kwacha (MK) per tonne, of catfish (Clarias gariepinus) in 2023. The total cost was determined by summing up fixed, variable, and opportunity costs associated with the fishing activity. Fixed costs refer to expenses that remain constant regardless of the quantity of fish caught; they are not influenced by day-to-day fishing operations. For commercial fishers in the southeast arm of Lake Malawi, these include the cost of purchasing trawlers, fishing licenses, and depreciation. Variable costs, on the other hand, fluctuate with fishing effort and include expenses for fuel, food, and crew labour during fishing trips. Opportunity costs represent the potential benefits or income fishers forego when they engage in fishing instead of pursuing alternative economic activities. All these cost components are essential to consider when estimating the total cost of fishing [21,22]. All cost values are expressed in Malawi Kwacha (MK).

2.3. The Gordon–Schaefer Model

The Gordon–Schaefer (GS) model was selected for this study to analyse the depletion status of the catfish fishery in the southeast arm of Lake Malawi. The GS model is represented by the differential equation

$${\displaystyle \frac{d}{dt}}\left[x\left(t\right)\right]=rx\left(t\right)\left(1-{\displaystyle \frac{x\left(t\right)}{K}}\right)-qE\left(t\right)x\left(t\right),x\left(0\right)=x_0$$

(1)

where $x\left(t\right)$ represents the stock biomass or the size of the fish population, $x_0$ denotes the initial population size, r is the intrinsic growth rate of the fish biomass, q is the catchability coefficient, E is the fishing effort, and K is the carrying capacity, which is the maximum number of fish that the environment can sustain without adversely affecting the population [18,23,24]. The harvest or yield is expressed as

$$H\left(t\right)=qE\left(t\right)x\left(t\right).$$

(2)

The GS model assumes logistic population growth and a closed population, thereby ignoring species interactions such as competition and predation [25]. It further assumes that both biological parameters, namely the intrinsic growth rate, carrying capacity, and catchability coefficient, and economic parameters, including price and cost, remain constant over time [21]. Additional assumptions include that catch per unit of effort (CPUE) is proportional to biomass, there is no immigration or emigration, gear efficiency is constant, environmental variability does not affect the fish population, and fishing and natural mortality occur simultaneously [7,22].

In this study, catch and effort data were available for a 24-year period, whereas historical price and cost data were not available. Economic data were therefore obtained from a field survey conducted in 2023. The use of single-year economic data is consistent with the GS model’s assumption that prices and costs remain constant over time. Accordingly, the 2023 price and cost values were assumed to be representative of the entire study period and were applied uniformly across the analysis.

Parameter Estimation

Biological parameters were estimated using the Walters–Hilborn method, which involves regressing catch per unit effort (CPUE) [7]. Following [26], the dependent variable was $\left({\displaystyle \frac{U_{t+1}}{U_t}}-1\right)$, defined as the ratio of catch per unit effort in the subsequent year $\left(U_{t+1}\right)$ to that in the current year $\left(U_t\right)$, minus one. The independent variables were catch per unit effort in the current year $\left(U_t\right)$ and total fishing effort in the current year $\left(E_t\right)$. The multiple linear equation takes the form

$$\left({\displaystyle \frac{U_{t+1}}{U_t}}-1\right)=r-{\displaystyle \frac{r}{qK}}{U}_t-q{E}_t.$$

(3)

To obtain parameter estimates, Equation (3) was compared with the general multiple linear equation

$$y=a\pm b{x}_1\pm c{x}_2,$$

(4)

and the biological parameters were derived as follows:

$$r=a,q=c,\mathrm{and}K={\displaystyle \frac{a}{cb}}.$$

(5)

The multiple linear regression analysis was performed using JASP version 0.95.4. The Walters–Hilborn method was preferred due to its illustrative potential [20].

2.4. Annual Sustainable Production, Depletion and Depreciation

Annual sustainable production for a fishery resource is the maximum quantity of fish that can be harvested from a stock each year without causing depletion of the population. In other words, it is the level of annual catch that allows the fish population to replenish itself naturally through growth and reproduction, ensuring that future generations can be harvested at the same rate. Mathematically, annual sustainable production corresponds to the maximum sustainable yield (MSY), which is the equilibrium point at which the natural growth of the fish population equals the annual fish catch.

For the GS model, the annual sustainable production function is given by the following equation [1,18]:

$$H\left(E\right)=qEK\left(1-{\displaystyle \frac{qE}{r}}\right).$$

(6)

Annual sustainable production for each year was calculated by substituting that year’s fishing effort and the estimated biological parameters (r, q, and K) into Equation (6). The resulting sustainable production estimates were then compared with the corresponding actual production values to assess whether annual catch levels were within sustainable limits. In this context, actual production, also referred to as actual catch, denotes the total annual landings from all strata of the southeast arm of Lake Malawi.

Depletion refers to the reduction in fish population due to overfishing. The following equation is used to calculate depletion of the fishery resource [7]:

$$\mathrm{Depletion}=\mathrm{Actual}\mathrm{Catch}-\mathrm{Sustainable}\mathrm{Catch}.$$

(7)

At equilibrium, resource rent, measured in Malawi Kwacha, is given by the following equation [23]:

$$\mathrm{Rent}=TR\left(E\right)-TC\left(E\right)$$

(8)

where $TR$ is the total revenue $(TR=\mathrm{price}(p)\times \mathrm{harvest}(h\left)\right)$ and $TC$ is the total cost ($TC=\mathrm{cost}\left(c\right)\times \mathrm{effort}E$). Resource rent for each year was calculated using the corresponding price, cost, fishing effort, and catch (harvest) data. The unit rent was then obtained by dividing resource rent by the actual catch:

$$\mathrm{Unit}\mathrm{Rent}={\displaystyle \frac{\mathrm{Resource}\mathrm{Rent}}{\mathrm{Actual}\mathrm{Catch}}}.$$

(9)

In this context, depreciation of fish resources is defined as the decrease in the total economic value of fish that can be sustainably harvested as a direct consequence of depletion. Economically, depreciation is viewed as a decline in the natural capital stock of a fishery resource. Depreciation is calculated from the depletion of fish resources using the following equation [3,16]:

$$\mathrm{Depreciation}=\mathrm{Average}\mathrm{Unit}\mathrm{Rent}\times \mathrm{Depletion}.$$

(10)

Using Equations (7) and (10), depletion and depreciation were calculated, respectively, to determine the extent of loss in the catfish fishery resource in the southeast arm of Lake Malawi.

2.5. Constant and Periodic Harvesting GS Models

The Gordon–Schaefer model without fishing is given by the following equation [23]:

$${\displaystyle \frac{dx}{dt}}=rx\left(1-{\displaystyle \frac{x}{K}}\right)$$

(11)

where x is the biomass level or fish population, r is intrinsic growth rate, and K is the carrying capacity. Equating the right hand side of Equation (11) to 0 gives two equilibrium points $x=0$ and $x=K$. This means that if the population starts at 0, it remains at the same point. Similarly, if the population starts at K it will also remain at K.

2.5.1. Constant Harvesting GS Model

Constant harvesting removes a fixed number of fish each year [27]. The Gordon–Schaefer model with constant harvesting is given by

$${\displaystyle \frac{dx}{dt}}=rx\left(1-{\displaystyle \frac{x}{K}}\right)-H$$

(12)

where H is a constant.

To determine equilibrium points we equate the right hand side of Equation (12) to 0:

$$rx\left(1-{\displaystyle \frac{x}{K}}\right)-H=0\Rightarrow rx-{\displaystyle \frac{r{x}^2}{K}}-H=0\Rightarrow {\displaystyle \frac{r{x}^2}{K}}-rx+H=0.$$

Comparing this with the general quadratic equation $a{x}^2+bx+c=0$, we have $a={\displaystyle \frac{r}{K}}$, $b=-r$, and $c=H$. Solving for x yields

$$x={\displaystyle \frac{r\pm \sqrt{r^2-4(r/K)H}}{2(r/K)}}={\displaystyle \frac{K}{2}}\left(1\pm \sqrt{1-{\displaystyle \frac{4H}{rK}}}\right).$$

(13)

Thus, there are two equilibrium points associated with the system in Equation (12) when the rate of harvesting is less than the bifurcation point:

$$x_1^{*}={\displaystyle \frac{K}{2}}\left(1+\sqrt{1-{\displaystyle \frac{4H}{rK}}}\right), x_2^{*}={\displaystyle \frac{K}{2}}\left(1-\sqrt{1-{\displaystyle \frac{4H}{rK}}}\right).$$

To find the maximum sustainable harvesting rate, we set the expression under the radical equal to zero, giving

$$H={\displaystyle \frac{rK}{4}}.$$

(14)

This value represents the birfucation point. At this point, we consider three scenarios for harvesting: $H={\displaystyle \frac{rK}{4}}$, $H>{\displaystyle \frac{rK}{4}}$ and $H<{\displaystyle \frac{rK}{4}}$. Solution curves were plotted for each harvesting level to identify equilibrium points, if present, and assess their stability. The solution curves were generated using Python version 3.14.0.

2.5.2. Periodic Harvesting GS Model

Periodic harvesting is a sequence of periodic closure and openings of different fishing grounds [27]. The Gordon–Schaefer model with periodic harvesting is given by the following equation [28,29]:

$${\displaystyle \frac{dx}{dt}}=rx\left(1-{\displaystyle \frac{x}{K}}\right)-H\left(t\right)$$

(15)

where

$$H\left(t\right)=H(1+asin(2\pi t).$$

The term $H\left(t\right)=H(1+asin(2\pi t)$ represents the contribution of the sine wave to the periodic function. In other words, it is the coefficient that dictates the total rate of periodic harvesting with the period of one year [27,30,31]. Note that the mean harvesting rate of the periodic harvesting function $H\left(t\right)=H(1+asin(2\pi t\left)\right)$ is H.

The presence of the time-dependent function $H\left(t\right)=H(1+asin(2\pi t\left)\right)$ in Equation (15) makes this a non-autonomous differential equation. Technically, such systems do not have fixed equilibrium points. However, by setting the right-hand side of Equation (15) to 0 and solving for x, we obtain

$$x={\displaystyle \frac{K}{2}}\left(1\pm \sqrt{1-{\displaystyle \frac{4H(1+asin(2\pi t\left)\right)}{rK}}}\right),$$

(16)

which are time-dependent quasi-equilibrium points representing biomass levels where growth temporarily balances harvesting. For harvesting rates below the bifurcation point, there are two quasi-equilibrium points associated with the model in Equation (15):

$$x_1^{*}={\displaystyle \frac{K}{2}}\left(1+\sqrt{1-{\displaystyle \frac{4H(1+asin(2\pi t\left)\right)}{rK}}}\right) \mathrm{and} x_2^{*}={\displaystyle \frac{K}{2}}\left(1-\sqrt{1-{\displaystyle \frac{4H(1+asin(2\pi t\left)\right)}{rK}}}\right).$$

The bifurcation point is found by setting the expression under the radical to 0, giving

$$H={\displaystyle \frac{rK}{4(1+asin(2\pi t\left)\right)}}.$$

Note that when $a=0$, the quasi-equilibrium and bifurcation points reduce to the classical equilibrium points of the autonomous model in Equation (12).

The model in (15) is a non-autonomous differential equation, and its solutions are therefore periodic and follow the same general trend as those of the model in (12). Consequently, the stability analysis for periodic harvesting can also be assessed graphically. In the logistic growth model with constant harvesting, we previously concluded that $H={\displaystyle \frac{rK}{4}}$ represents a bifurcation point. For the function in (15), we can only infer that a bifurcation is likely to occur at a value close to $H={\displaystyle \frac{rK}{4}}$ [31]. To explore this, we plotted solution curves for $H={\displaystyle \frac{rK}{4}}$, $H>{\displaystyle \frac{rK}{4}}$ and $H<{\displaystyle \frac{rK}{4}}$ to examine whether the population persists or converges relative to the equilibrium points at each harvesting level. Python version 3.14.0 was used to generate the solution curves.

3. Results

3.1. Estimated Biological and Economic Parameters

Table 1 presents the biological data used in this study. These consist of time-series catch and effort data for the catfish fishery in the southeast arm of Lake Malawi from 2000 to 2023.

Table 1. Catch and effort of the commercial catfish (Clarias gariepinus) fishery.

Year	Catch (Tons)	Effort (Trips)
2000	149.8	3420
2001	141.3	2874
2002	119.7	1285
2003	122.5	1691
2004	94.4	1702
2005	55.2	1361
2006	89.2	1492
2007	86.0	1434
2008	119.1	2027
2009	112.7	2594
2010	91.0	2380
2011	62.1	1432
2012	49.2	1569
2013	78.1	2646
2014	75.3	2076
2015	67.5	1635
2016	113.0	4738
2017	132.1	3331
2018	93.7	3717
2019	20.2	2902
2020	32.9	2057
2021	48.9	1962
2022	67.5	1532
2023	49.8	1207

Based on the data presented in Table 1, the biological parameters were estimated using the Walters–Hilborn method. Results of the regression analysis are presented in Table 2.

Table 2. Regression Analysis Results.

Coefficient	Estimate	Standard Error	t	${\mathit{R}}^2$
Constant	0.658	0.452	1.457	0.24
CPUE ($U_t$)	−12.727	5.708	−2.230
Effort ($E_t$)	−0.00008783	0.000	−0.73

The multiple linear regression analysis yielded the following equation:

$$y=0.658-12.727U_t-0.00008783E_t.$$

(17)

The estimated values of the biological parameters r, q and K are presented in Table 3.

Table 3. Estimated Parameters.

Parameter	Description	Value	Unit
r	Growth rate	0.658	year−1
q	Catchability coefficient	0.000088	trip−1year−1
K	Carrying capacity	587.5	Tonne
p	Price per tonne	7,000,000	MK
c	Cost per trip per year	351,548	MK

Table 3 also presents the economic price and cost data. The price represents the average price of catfish in the southeast arm of Lake Malawi in 2023 (in Malawi Kwacha, MK). The cost corresponds to the total of fixed, variable, and opportunity costs associated with the catfish fishery in the same region, also expressed in Malawi Kwacha.

3.2. Annual Sustainable Production

Using the biological parameters in Table 3, the annual sustainable production function in Equation (6) becomes

$$H\left(E\right)=0.051699E-0.00000691E^2.$$

(18)

By substituting the fishing effort values for each year from Table 1 into Equation (18), the corresponding annual sustainable production values were calculated and are presented in Table 4.

Table 4. Sustainable catch of the commercial catfish (Clarias gariepinus) fishery.

Year	Actual Catch (Tonnes)	Effort (Trips)	Sustainable Catch (Tonnes)
2000	149.8	3420	95.9
2001	141.3	2874	91.5
2002	119.7	1285	55.0
2003	122.5	1691	67.7
2004	94.4	1702	67.9
2005	55.2	1361	57.6
2006	89.2	1492	61.8
2007	86.0	1434	59.9
2008	119.1	2027	76.4
2009	112.7	2594	87.6
2010	91.0	2380	83.9
2011	62.1	1432	59.9
2012	49.2	1569	64.1
2013	78.1	2646	88.4
2014	75.3	2076	77.4
2015	67.5	1635	66.1
2016	113.0	4738	89.8
2017	132.1	3331	95.5
2018	93.7	3717	96.7
2019	20.2	2902	91.8
2020	32.9	2057	76.6
2021	48.9	1962	74.8
2022	67.5	1532	62.9
2023	49.8	1207	52.3

According to Table 4, the total actual catch of the commercial catfish fishery from 2000 to 2023 was 2071 tonnes, whereas the total sustainable catch over the same period was 1801.5 tonnes. The highest actual catch during the study period was 149.8 tonnes, recorded in 2000. Other years in which actual catch exceeded 100 tonnes include 2001, 2002, 2003, 2008, 2009, 2016, and 2017; in contrast, sustainable catch values remained below 100 tonnes in all years. The average actual and sustainable catches were 86.3 tonnes and 75.1 tonnes, respectively.

Figure 2 shows both the actual and sustainable catches for the commercial catfish fishery in the southeast arm of Lake Malawi from 2000 to 2023. The figure indicates that actual catch values were generally higher than sustainable catch values throughout most of the period.

Figure 2. Actual and sustainable catch of the commercial catfish fishery from the southeast arm of Lake Malawi.

3.3. Depletion and Depreciation

Table 5 shows that depletion occurred in 15 out of 24 years studied. Depletion did not occur in 9 years out of 24 years (2005, 2012, 2013, 2014, 2018, 2019, 2020, 2021 and 2023). The highest depletion occurred in 2002 with a depletion value of 64.7 tonnes. Total depletion over the study period is 446.1 tonnes.

Table 5. Depletion of the commercial catfish (Clarias gariepinus) fishery.

Year	Actual Catch (Tonnes)	Sustainable Catch (Tonnes)	Depletion
2000	149.8	95.9	−53.9
2001	141.3	91.5	−49.8
2002	119.7	55.0	−64.7
2003	122.5	67.7	−54.8
2004	94.4	67.9	−26.5
2005	55.2	57.6	2.4
2006	89.2	61.8	−27.4
2007	86.0	59.9	−26.1
2008	119.1	76.4	−42.7
2009	112.7	87.6	−25.1
2010	91.0	83.9	−7.1
2011	62.1	59.9	−2.2
2012	49.2	64.1	14.9
2013	78.1	88.4	10.8
2014	75.3	77.4	2.1
2015	67.5	66.1	−1.4
2016	113.0	89.8	−23.2
2017	132.1	95.5	−36.6
2018	93.7	96.7	3.4
2019	20.2	91.8	71.6
2020	32.9	76.6	43.7
2021	48.9	74.8	25.9
2022	67.5	62.9	−4.6
2023	49.8	52.3	2.5

Table 6 presents the resource rent and unit rent for the commercial catfish fishery in the southeast arm of Lake Malawi from 2000 to 2023. For each observed effort level (E), the corresponding catch, total revenue, total cost, and resulting rent values are reported. It is evident that negative resource rent occurred in 18 of the 24 years analysed.

Table 6. Resource rent of the commercial catfish (Clarias gariepinus) fishery.

Year	A. Catch	Effort	TR	TC	Rent	Unit Rent
2000	149.8	3420	1,048,600,000	1,202,294,160	−153,694,160	−1,025,995.73
2001	141.3	2874	989,100,000	1,010,348,952	−21,248,952	−150,381.83
2002	119.7	1285	837,900,000	451,739,180	386,160,820	3,226,072.01
2003	122.5	1691	857,500,000	594,467,668	263,032,332	2,147,202.71
2004	94.4	1702	660,800,000	598,334,696	62,465,304	661,708.73
2005	55.2	1361	386,400,000	478,456,828	−92,056,828	−1,667,696.16
2006	89.2	1492	624,400,000	524,509,616	99,890,384	1,119,847.35
2007	86.0	1434	602,000,000	504,119,832	97,880,168	1,138,141.49
2008	119.1	2027	833,700,000	712,587,796	121,112,204	1,016,895.08
2009	112.7	2594	788,900,000	911,915,512	−123,015,512	−1,091,530.72
2010	91.0	2380	637,000,000	836,684,240	−199,684,240	−2,194,332.31
2011	62.1	1432	434,700,000	503,416,736	−68,716,736	−1,106,549.69
2012	49.2	1569	344,400,000	551,578,812	−207,178,812	−4,210,951.46
2013	78.1	2646	546,700,000	930,196,008	−383,496,008	−4,910,320.20
2014	75.3	2076	527,100,000	729,813,648	−202,713,648	−2,692,080.32
2015	67.5	1635	472,500,000	574,780,980	−102,280,980	−1,515,273.78
2016	113.0	4738	791,000,000	1,665,634,424	−874,634,424	−7,740,127.65
2017	132.1	3331	924,700,000	1,171,006,388	−246,306,388	−1,864,544.95
2018	93.7	3717	655,900,000	1,306,703,916	−650,803,916	−6,945,612.76
2019	20.2	2902	141,400,000	1,020,192,296	−878,792,296	−43,504,569.11
2020	32.9	2057	230,300,000	723,134,236	−492,834,236	−14,979,764.01
2021	48.9	1962	342,300,000	689,737,176	−347,437,176	−7,105,054.72
2022	67.5	1532	472,500,000	538,571,536	−66,071,536	−978,837.57
2023	49.8	1207	348,600,000	424,318,436	−75,718,436	−1,520,450.52

Table 7 presents the depreciation for the commercial catfish fishery in the southeast arm of Lake Malawi. Since depreciation is derived from depletion, it has been calculated for the 15 years in which depletion occurred. The total estimated depreciation amounts to MK 1.5 billion.

Table 7. Depreciation of the commercial catfish (Clarias gariepinus) fishery.

Year	A. Catch (Tonnes)	S. Catch (Tonnes)	Depletion	Depreciation
2000	149.8	95.9	−53.9	−181,720,351.35
2001	141.3	91.5	−49.8	−167,897,467.48
2002	119.7	55.0	−64.7	−218,131,850.32
2003	122.5	67.7	−54.8	−184,754,642.93
2004	94.4	67.9	−26.5	−89,343,029.89
2006	89.2	61.8	−27.4	−92,377,321.47
2007	86.0	59.9	−26.1	−87,994,455.85
2008	119.1	76.4	−42.7	−143,960,278.34
2009	112.7	87.6	−25.1	−84,623,020.76
2010	91.0	83.9	−7.1	−23,937,189.14
2011	62.1	59.9	−2.2	−7,417,157.19
2015	67.5	66.1	−1.4	−4,720,009.13
2016	113.0	89.8	−23.2	−78,217,294.09
2017	132.1	95.5	−36.6	−123,394,524.29
2022	67.5	62.9	−4.6	−15,508,601.00

3.4. Constant Harvesting

Using biological parameters in Table 3, the bifurcation point in Equation (14) is $96.6$ tonnes. Figure 3 shows solution curves for the case $H=60$ tonnes per year. It is observed that there are two equilibrium points $x_1^{*}=112.9$ and $x_2^{*}=474.6$. According to Figure 3, population size starting at any of these equilibrium points remains there forever. For any initial biomass level or population size greater than 474.6 tonnes, the population approaches the equilibrium value 474.6 tonnes in the long run. Similarly, for any initial population between 112.9 and 474.6 tonnes, the population asymptotically approaches 474.6 tonnes. However, any initial population less than 112.9 tonnes, the population goes into extinction in finite time. Therefore, the fixed point 112.9 is unstable while 474.6 is stable.

Figure 3. Solution curves for $H=60$. Each colored line represents a population trajectory corresponding to a different initial population size.

Figure 4 shows solution curves for the case $H=96.6$ tonnes, the bifurcation point. There is a single fixed point, $x^{*}=293.8$ tonnes. Population size starting at 293.8 tonnes remains there indefinitely. For any initial population size or biomass level greater than 293.8 tonnes the population approaches the equilibrium value 293.8 tonnes. However, for any initial population less than 293.8 tonnes, the population goes into extinction in finite time. Therefore the fixed point $x^{*}=293.8$ is semi-stable (making the system structurally stable). Hence, a harvest rate corresponding to $H=96.6$ tonnes triggers a long-term biomass level of exactly half the carrying capacity provided the initial population is less than 293.8 tonnes.

Figure 4. Solution curves for $H=96.6$. Each colored line represents a population trajectory arising from a distinct initial population size.

Figure 5 shows solution curves for the case $H=110$ tonnes per year. It is observed that there is no equilibrium point for this harvest rate. For any initial population size or biomass level, the population goes into extinction in finite time. Therefore, a harvest rate of $H=110$ tonnes per year sends the population into extinction in finite time, regardless of the initial population size or biomass.

Figure 5. Solution curves for $H=110$.

3.5. Periodic Harvesting

Figure 6 shows the periodic cycles for the case where $H=60$ tonnes per year. It is evident that there are two periodic solutions of period $P=1$ oscillating around the mean values: $x_1^{*}=112.9$ tonnes and $x_2^{*}=474.6$ tonnes. For any initial population starting at $x_1^{*}=112.9$ tonnes or at $x_2^{*}=474.6$ tonnes, the population remains there forever. For any initial population size above 474.6 tonnes, the population gradually converges toward the equilibrium mean level of 474.6 tonnes through sinusoidal oscillations. Similarly, for any initial population between 112.9 and 474.6 tonnes, the population asymptotically approaches 474.6 tonnes. However, for any initial population below 112.9 tonnes, the population goes extinct in a finite amount of time. Thus, the equilibrium point 112.9 is unstable while 474.6 is stable. Therefore, a harvest rate of $H=60$ tonnes per year results in a long-term biomass level that exceeds half of the carrying capacity provided the initial population is greater than 112.9 tonnes.

Figure 6. Periodic Cycles for $H=60$. Each colored line represents a population trajectory arising from a distinct initial population size.

Figure 7 shows periodic cycles for the case $H=96.6$, the bifurcation point. It is apparent that there is a single periodic solution, $x^{*}=293.8$ tonnes. Initial population or biomass levels starting from the equilibrium level $x^{*}=293.8$ tonnes, remain there indefinitely. For any initial population size above 293.8 tonnes, the population converges to the mean equilibrium level of 293.8 tonnes in the long run. However, for initial population size below 293.8, the population declines to extinction in finite time. Thus, the biomass level 293.8 tonnes is semi-stable. Hence, a harvest rate of 96.6 tonnes per year results in a long-term biomass equal to exactly half of the carrying capacity, provided the initial biomass is greater than 293.8 tonnes.

Figure 7. Periodic Cycles for $H=96.6$. Each colored line represents a population trajectory arising from a distinct initial population size.

Figure 8 illustrates the periodic dynamics for a harvest rate of $H=110$ tonnes per year. At this level of exploitation, the system has no equilibrium point, and the population declines to extinction within a finite time, regardless of the initial biomass level or population size. Consequently, a harvest rate corresponding to $H=110$ tonnes leads to population collapse.

Figure 8. Periodic Cycles for $H=110$. Each colored line represents a population trajectory arising from a distinct initial population size.

4. Discussion

Our analysis indicates that, overall, actual catches have consistently exceeded sustainable levels in the commercial catfish fishery of the southeast arm of Lake Malawi (Table 4 and Figure 2). Between 2000 and 2023, the cumulative actual catch surpassed the total sustainable catch, reflecting a sustained increase in fishing pressure. This pattern of overexploitation suggests that the fishery is currently operating beyond both its biological and economic limits, which may result in declining stock biomass, diminished long-term yields, and heightened risk of resource collapse. These findings underscore the urgent need for effective management interventions to ensure the sustainability of the catfish fishery and the livelihoods dependent upon it.

Depletion refers to the rate at which the stock of natural resources (particularly non-renewable resources) is reduced. In this context, it indicates that the resource stock is declining faster than the sustainable rate, meaning that exploitation exceeds the level that can be maintained over time. A negative depletion value signifies that actual production surpasses sustainable production, potentially leading to economic losses, such as forgone rent, in the commercial catfish fishery of the southeast arm of Lake Malawi. According to our results, depletion occurred in 15 of the 24 years studied, suggesting that the catfish fishery is at risk of overexploitation and potential stock collapse. This finding underscores the need for effective management strategies, including monitoring of harvest levels and enforcement of sustainable catch limits, to safeguard the long-term productivity and economic viability of the fishery.

In this study, depreciation is defined as a direct consequence of biological depletion. Accordingly, depreciation is calculated directly from changes in fish population abundance or biomass. In a broader sense, depreciation may arise from several other factors, including market dynamics and changes in prices or costs. However, this study focuses on the bioeconomic linkage rather than the broader economic context. As a result, the applicability of the depreciation estimates presented here is limited to this bioeconomic framework.

Depreciation of fish resources refers to the loss of value or productivity of a fishery over time, typically due to overfishing, environmental degradation, or natural mortality. Thus, when a fishery is depleted, that is, when the biological stock declines, the resource’s future productivity and economic value also decrease, which constitutes depreciation. Our results indicate a total depreciation of slightly over MK 1.5 billion. This implies that the commercial catfish fishery in the southeast arm of Lake Malawi, from 2000 to 2023, has lost over MK 1.5 billion in economic value. Such significant losses highlight the urgent need for effective management strategies to ensure sustainable harvesting and to safeguard both the economic and ecological viability of the fishery.

The negative resource rent values observed in this study (Table 6) suggest that the fishery may be operating under economically inefficient conditions. Such outcomes are commonly associated with overfishing, excess fishing capacity, or ineffective management, all of which can reduce stock abundance and undermine long-term sustainability. When fish stocks are depleted, harvest levels decline while fishing costs tend to rise due to increased search time and effort, resulting in revenues that are insufficient to cover operating costs [32]. Consequently, negative resource rent is often interpreted as an indicator of economic overfishing. Addressing this situation may require management interventions.

Since the fisheries sector in Malawi is open-access and enforcement of regulations is challenging, measures such as implementing catch limits and rights-based management may not be feasible in the short term. More practical strategies under these constraints are community-based co-management approaches, which include voluntary reductions in fishing effort and participatory monitoring by local stakeholders. While catch limits and rights-based management remain important long-term goals, locally-driven interventions can help improve compliance in the short term, stabilise fish stocks, and reduce economic losses in the process.

However, negative resource rent does not necessarily arise solely from biological overexploitation. Market-related factors, including declining fish prices or increasing input costs, can also lead to negative rents even when stocks are not severely depleted [32]. In addition, subsidies are known to artificially lower fishing costs, encourage excessive effort, and accelerate rent dissipation, potentially resulting in negative resource rent. Although subsidies are not reported in the Malawian fishery sector, market inefficiencies, such as price volatility, limited market access, or rising fuel and input costs, may still play a role. Importantly, the negative resource rent values reported here are derived from the Gordon–Schaefer model, which assumes that prices and costs remain constant over the entire 24-year period. Thus, these values represent model-based economic signals of fishing pressure rather than observed profits. Overall, the observed negative resource rent likely reflects a combination of biological overexploitation and economic or market-related constraints, and should be interpreted cautiously as an indicator of economic overfishing.

Analysis of the harvesting models indicates that, to ensure sustainability, the commercial catfish fishery should be harvested at a rate lower than the bifurcation point of $H=96.6$ tonnes per year. Both the constant and periodic harvesting models demonstrate that harvesting above this threshold may lead to extinction of the resource. Results in Table 1 show that this value was exceeded in 8 of the 24 years studied. This pattern of excessive harvesting highlights a persistent risk to the long-term viability of the fishery.

However, the bifurcation threshold of $H=96.6$ tonnes should be interpreted as an approximate bioeconomic reference point rather than a precise biological limit or deterministic boundary. This threshold is derived from a stylised model based on estimated parameters that are subject to uncertainty. In practice, environmental variability, parameter uncertainty, changes in fishing efficiency, and behavioural responses of both fish and fishers may influence the location of the bifurcation point. Consequently, this threshold should be viewed as a precautionary guideline, above which the risk of stock collapse increases substantially. Maintaining annual harvests below this level would enhance the biological and economic sustainability of the commercial catfish fishery in the southeast arm of Lake Malawi. Strengthening monitoring, enforcement, and adaptive management will be essential to keep harvests within sustainable bounds.

Results from this study are consistent with previous studies in Malawi that used the Gordon–Schaefer model to assess the stock status of various fish species. For example, ref. [4] reported stock decline and overexploitation of chambo species in Lake Malombe. The observed economic overfishing was attributed not to economic factors such as price increases or decreases in costs, but to excessive fishing effort. The open-access nature of the fishery in Malawi was identified as the main driver of overexploitation. Similarly, ref. [11] concluded that Engraulicypris sardella (usipa) species in the southeast arm of Lake Malawi are also overexploited. Additionally, a study employing time series analysis suggested that overexploitation of the catfish fishery in the Mangochi district could not be ruled out [13].

Consistency of our results with previous studies using the Gordon–Schaefer model [2,4,11,20,33] likely reflects shared model assumptions and data structures rather than independent validation, highlighting a limitation due to potential methodological circularity. Nevertheless, our study makes distinct contributions by applying the Gordon–Schaefer model to a novel dataset spanning 2000 to 2023, providing updated estimates of biological depletion, economic resource rent, and depreciation. Additionally, the derivation of the bifurcation threshold offers an integrated biological and economic assessment of the fishery in Malawi, representing a conceptual advancement not addressed in prior evaluations.

These results underpin the challenges confronting the fishery sector in Malawi. Most fish species in the country are reported to be overexploited [13], which has contributed to a decline in the economic efficiency and benefits of the sector [4]. To address this, there is a need to review management options and strengthen weaker areas within the sector. Such measures appear to be the only way to prevent further depletion of fishery stocks.

Fish stocks in Malawi are managed through restrictions on fishing gears, fishing areas, and fishing periods. Catch statistics and annual frame surveys of fishing effort provide the input data for stock assessment studies that inform these management recommendations [8]. However, with several stocks reported to be declining [4,9,19,20], it is evident that the current management approach has not been fully effective. Implementation of these restrictions faces numerous challenges, including limited human capacity and inadequate financial resources. Strengthening monitoring, control, and surveillance systems on the lake, supported by additional funding, could play a crucial role in preventing further depletion of the commercial catfish fishery. Enhancing these systems would not only help conserve the resource but also reduce the substantial economic losses (depreciation) associated with ongoing depletion. Ultimately, improving management effectiveness is essential for ensuring the long-term sustainability and economic viability of fisheries in the southeast arm of Lake Malawi. However, the provision of additional funding depends on government allocations, donor support, and institutional priorities.

The regression analysis yielded a relatively low coefficient of determination ($R^2=0.24$ in Table 3), indicating that a limited proportion of the variability in the dependent variable is explained by the model. This may be partly attributable to fluctuations in the data arising from temporal instability in catch and fishing effort [19]. Similar low $R^2$ values have been reported in previous studies applying the Walters–Hilborn or Gordon–Schaefer framework [19,20,33,34]. In addition, the Gordon–Schaefer model assumes that fish population dynamics are not influenced by environmental variability. The exclusion of environmental covariates, such as rainfall and temperature, which can affect recruitment and stock productivity, may therefore have contributed to the low explanatory power of the model.

Despite the low $R^2$, which indicates that the model explains only a small portion of the variability in fish catch, the estimated parameters are biologically plausible and broadly consistent with previous assessments. However, downstream results, including sustainable catch, depletion, and depreciation, should be interpreted as approximate values rather than precise predictions. The low explanatory power of the model implies that these estimates carry considerable uncertainty, so they should be treated as indicative of general trends rather than exact targets. Conducting alternative model specifications and sensitivity analyses, as well as incorporating additional covariates such as environmental factors, could improve model fit and enhance confidence in the estimated parameters.

The bioeconomic Gordon–Schaefer (GS) model provided useful insights into the biological depletion and economic depreciation of the commercial catfish fishery in the southeast arm of Lake Malawi. However, the interpretation of the results should be made in light of the model’s underlying assumptions. It is important to note that, in practice, many of these assumptions may not hold under real fishery conditions. Despite these limitations, the Gordon–Schaefer model remains widely applied as a practical tool for guiding fishery management decisions [22,25,33,34,35]. In this study, estimates of sustainable catch levels were consistent with those reported in previous studies that also applied the Gordon–Schaefer framework [1,18], providing useful benchmarks for management. Similarly, the observed patterns of depletion, economic depreciation, and harvesting strategies are in agreement with findings from earlier studies [3,16,29,30,31].

There are several sources of uncertainty in parameter estimation using the Walters–Hilborn method. First, uncertainty may arise from measurement or reporting errors in catch and effort data. Second, the Gordon–Schaefer (GS) model assumption that CPUE is directly proportional to fish population size may be violated due to variations in environmental conditions and fishing gear effectiveness. Third, parameters in the Walters–Hilborn method are estimated indirectly from the coefficients of a linear regression. Even small estimation errors in the regression coefficients can propagate and result in substantial uncertainty in the derived parameter estimates. Despite these challenges, the Walters–Hilborn method remains a reliable approach for estimating parameters of the Gordon–Schaefer model [7,19,26].

The use of single-year price and cost data to calculate depletion, resource rent, and depreciation over the 24-year period was based on the Gordon–Schaefer (GS) model assumption that these economic parameters remain constant over time. However, in practice, the cost of fishing effort and the price of landed fish may be influenced by several factors. Fish prices may vary due to changes in consumer income, preferences, and market demand and supply conditions, while fishing costs may be affected by fluctuations in fuel prices, gear costs, wages, and technological change. Such factors may lead to violations of the constant price and cost assumption. Despite this limitation, the use of single-year economic data has been widely applied in previous bioeconomic studies [4,20,21,25].

5. Conclusions

Actual catches in the commercial catfish fishery of the southeast arm of Lake Malawi exceeded sustainable levels in 15 of the 24 years examined, indicating persistent biological overfishing. Moreover, negative resource rent was recorded in 18 of the 24 years, reflecting economic overfishing and the fishery’s inability to generate sufficient revenue to cover operational costs. The study recorded a total depletion of 446 tonnes and total depreciation of approximately MK 1.5 billion. This combined evidence of depletion and depreciation underscores the risk of continued overexploitation, which could ultimately threaten the long-term viability of the stock. Harvests exceeding the threshold of 96.6 tonnes per year further jeopardise the persistence of the commercial catfish population. To ensure the sustainability of this important resource, management and enforcement measures must be strengthened, including improving patrols to prevent fishing in restricted areas, during closed periods, and with illegal or destructive gears. Implementing effective and adaptive management strategies will be critical for safeguarding both the ecological integrity and economic value of the commercial catfish fishery. Without prompt intervention, catfish stocks risk collapse, jeopardising ecosystem stability and the livelihoods of local communities.