Surface Temperature Influences the Population of <i>Limnothrissa miodon</i> in Lake Kariba

Mutasa, Farikayi K.; Jones, Brian; Tendaupenyu, Itai H.; Nhiwatiwa, Tamuka; Ndebele-Murisa, Mzime R.

doi:https://doi.org/10.1155/2023/1457714

International Journal of Ecology

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Abstract Introduction Materials and Methods Model Formulation Discussion Conclusions Data Availability Conflicts of Interest Acknowledgments References Copyright Related Articles

Research Article | Open Access

Volume 2023 | Article ID 1457714 | https://doi.org/10.1155/2023/1457714

Surface Temperature Influences the Population of Limnothrissa miodon in Lake Kariba

Farikayi K. Mutasa,¹Brian Jones,²Itai H. Tendaupenyu,^3,4Tamuka Nhiwatiwa,⁵and Mzime R. Ndebele-Murisa⁶

Academic Editor: Ram Chander Sihag

Received12 Aug 2022

Revised20 Mar 2023

Accepted20 Apr 2023

Published10 May 2023

Abstract

Global warming is a serious world problem where earth’s temperature has been reported to increase over the years; the aquatic ecosystems are also not the exceptions. But, the effects of this phenomenon on the aquatic ecosystems are not well understood. This study aims to understand the influence of surface temperature on the population density of Limnothrissa miodon in Lake Kariba. We constructed a mathematical model on the population dynamics of Limnothrissa miodon with nutrients, phytoplankton, zooplankton, and Hydrocynus vittatus. Lake surface water temperature was modelled by a cosine function, and the parameters were estimated from data fitting. Numerical simulations were used to determine the stability of the nonautonomous model. Numerical simulation results of the nonautonomous model showed a stable periodic orbit for varying initial conditions, and therefore, instability. Numerical techniques were used to investigate the influence of surface water temperature on Limnothrissa miodon. Results from the model with fitted lake surface water temperature data showed that a shift in the optimal temperature for phytoplankton growth from C to C, corresponding to dominance of Cyanophyceae over Chlorophyceae, resulted in a decline in the population density of Limnothrissa miodon. Numerical results showed that the population density of Limnothrissa miodon declines after an optimum temperature of C for phytoplankton growth. Numerical simulation results suggested that warming of the lake may lead to a decline in Limnothrissa miodon population density in Lake Kariba.

1. Introduction

Global warming is one of the major issues confronting the modern civilization [1]. The major concern is the increasing temperature of the biosphere; the aquatic ecosystems are not an exception. Major concern of the aquatic biologists is to understand the adverse effects of this phenomenon on the aquatic communities [2]. With this purpose, this study was conducted to determine the influence of lake surface water temperature on the population density of Limnothrissa miodon in Lake Kariba. The Lake Kariba fishery which is shared by both Zimbabwe and Zambia is of paramount importance for the continued survival of the small pelagic clupeid, Limnothrissa miodon [3]. Limnothrissa miodon (Boulenger, 1906), also referred to as kapenta, is a major source of protein and income for fishing cooperatives, wholesalers, retailers, and the local community [4]. Reports that the kapenta catches are in decline are a cause of concern to many stakeholders in the kapenta fishery and academia. The decline in the catches in kapenta has been attributed to overfishing, predation by Hydrocynus vittatus, climate change, and the reduction of nutrient inflow into Lake Kariba. According to Nhambura [5], several cooperatives and companies which make up the Kariba kapenta industry are struggling and facing collapse since the amounts of kapenta in Lake Kariba are dwindling because of the changing climate. The depletion of kapenta may also have a negative effect on the levels of Hydrocynus vittatus (tigerfish), which feeds on kapenta and contributes immensely to the economy of Kariba. Therefore, it is important that we formulate and analyse a mathematical model in order to understand the effects of temperature on the population density of kapenta in Lake Kariba.

Ndebele-Murisa [6], recorded the relative cellular concentration of phytoplankton classes in the Sanyati basin of Lake Kariba. The highest concentration was in the less palatable Cyanophyceae , followed by Chlorophyceae , Dinophyceae , Bacillariophyceae , Euglenophyceae , Chrysophyceae , and Xanthophyceae . The species with the highest relative concentration of was Cylindrospermopsis raciborskii, followed by Microcystis aeruginosa from the Cyanophyceae class. From the Chlorophyceae class, Staurastrum johnsonii had the highest relative concentration, followed by Coelastrummicroponum and Oedogonium sp. . Ndebele-Murisa [6] also recorded the relative concentrations of the Chlorophyceae species Staurastrum johnsonii, Coelastrum microponum, and Oedogonium sp. in the Sanyati basin. Cynaphytes are associated with the production of toxins [7, 8] and are often unigestible, indigestible, or nutritionally poor [9, 10]. Many species of Chlorophytes are less palatable due to long splines and long processes [11]. In Lake Kariba, Limnothrissa miodon mainly feeds on zooplankton, especially the Cladoceran species Bosmina longirostris [12, 13]. Machena [14] found out that of the diet composition of Limnothrissa miodon is zooplankton. According to Mhlanga [15], Limnothrissa miodon is a major prey species of Hydrocynus vittatus. Kenmuir [16] found out that of the diet of Hydrocynus vittatus consisted of Limnothrissa miodon. Environmental factors play an important role in a fishery [17–19], and as a result, it is critical to investigate mathematically the role of temperature in the dynamics of Limnothrissa miodon in the Lake Kariba fishery. Chifamba [17] found that maximum temperature was the best predictor of catch per unit effort (CPUE) of kapenta for the period and suggested that kapenta catch cycles might be related to weather conditions. Magadza [18] estimated a warming of C for the Lake Kariba area, using data from the Kariba meteorological station for the period . The lake warmed by a mean of C between 1965 and 1990, corresponding to a warming rate of C per decade [18]. Magadza [18] used temperature data from and determined an air temperature and water temperature maximum turning point of C and C, respectively, around for Limnothrissa miodon in Lake Kariba. The kapenta catches increased exponentially prior to the turning point and then decreased linearly afterward. Regression analysis results from a study by Ndebele-Murisa et al. [19] showed that temperature is a major factor in kapenta catches from . Ndebele-Murisa et al. [20] found that maximum temperature contributed to of the variation in kapenta stocks, of kapenta CPUE, and of the change in lake water levels from 1974 to 2010 in Lake Kariba. Sibanda [21] compared the temperature responses of selected phytoplankton classes in laboratory cultures, focusing on Chlorophyceae and Cyanophyceae. According to her findings, the growth rate of Chlorophyceae decreased above C, while that of Cyanophyceae, on the other hand, increased almost exponentially up to C. Magadza [18] observed a transition from Chlorophyceae to Cyanophyceae in Lake Kariba and found out that Cyanophyceae, particularly Cylindrospermum raciborskii, now dominate the lake phytoplankton.

How the temperature describes and influences the dynamics of the kapenta population in Lake Kariba has not been studied. A deterministic model involving nutrients, phytoplankton, zooplankton, kapenta, and tigerfish, as well as temperature as an environmental factor, is yet to be developed and tested. The kapenta model will aid in our understanding of the aquatic ecosystem dynamics in the kapenta fishery in Lake Kariba and we will be able to explain the influence of lake surface water temperature on kapenta levels. We hypothesized that (i) a shift from Chlorophyceae to Cyanophyceae will lead to a decline in kapenta population density and (ii) warming of the lake has an adverse effect on the population density of kapenta. The objectives of the study were to (i) formulate and analyse a mathematical model with data fitting, (ii) determine the optimum temperature for phytoplankton growth for the fitted lake surface water temperature data, (iii) compare numerical results on kapenta population density for the mathematical models with the Chlorophyceae and Cyanophyceae phytoplankton classes, and (iv) determine the effect of lake warming on kapenta population density.

2. Materials and Methods

2.1. Study Area

Lake Kariba is located in a tropical area with seasonal rainfall on the Zambezi river between latitudes to S and longitudes to E [22], has a volume and surface area of 160 and 5364 , respectively, and has an average width of 19.4 km, with the widest section measuring 40 km [23]. The lake is 486 m above sea level, and the shoreline is about 2164 km long [3, 23]. The kapenta fishery in Lake Kariba is highly mechanised, licence-controlled, and is shared by Zimbabwe and Zambia [6]. A map of Lake Kariba and its fishing basins is shown in Figure 1.

2.2. Data Collection

The surface water temperature data for Lake Kariba were provided by the University of Zimbabwe Lake Kariba Research Station (UZLKRS), and the data were collected at Station 7, Sanyati mouth, 1st cross, Gachegache mouth, Charara, Nyaodza, and Nyenje for the period July 2014 to December 2017 [25].

3. Model Formulation

The model has 5 classes whose densities are functions of time: denoting the concentration of nutrients, is the population density of phytoplankton, is the zooplankton population density, is the density of the Limnothrissa miodon population, and is the density of the Hydrocynus vittatus population. The Limnothrissa miodon model [26] is developed to include the effect of temperature on growth of phytoplankton. The coefficient of temperature for the growth of phytoplankton [27] is assumed to bewhere is lake surface water temperature, is optimal temperature for phytoplankton growth, and is the minimum temperature for phytoplankton growth. The water temperature is modelled bywhere the parameters , , , and are estimated from data fitting. is the fitted temperature in , is the mean water temperature, is the amplitude, is the angular frequency , is time in months, and is a phase angle. The nonlinear dynamical system iswith initial conditionand defined as

To be the mathematically feasible region, nutrients enter the water body at the rate where is a constant; is an uptake rate; and , are the predation rate coefficients. The ’s for are depletion rate coefficients. The ’s for are the phytoplankton, zooplankton, Limnothrissa miodon, and Hydrocynus vittatus growth rate coefficients, respectively. The coefficient is a positive constant for the crowding of the Limnothrissa miodon population. Kapenta are harvested at a rate , where is the catchability coefficient and is the effort measured as boat nights. The growth rate of Hydrocynus vittatus is [28] and is the population density of kapenta at which specific growth rate becomes half of its saturation value. The tigerfish are harvested at a rate , where is the catchability coefficient and is the effort.

3.1. Positivity of Solutions

Theorem 1. Let the initial data be . Then, solutions of , , , , and of system (3) are positive .

Proof 1. It follows from the first equation of system (3) thatand we obtainFrom the second equation of system (3),By integrating (8), we obtainFrom the third equation of model (3),and integrating (10) results inConsidering the fourth equation of system (3),and integration of (12) results inAccording to the fifth equation of model (3),Integration of (14) yieldsWe therefore conclude that solutions of model (3) with initial conditions (4) remain positive .

3.2. Existence of Solutions

Theorem 2. A solution of model system (3) is feasible.

Proof 2. It is essential to demonstrate that all feasible solutions of model (3) are uniformly bounded in . Let be any solution of system (3) with non-negative initial conditions. Let , thenwhere . Thus,Equation (17) has the solutionas t, (18) becomesTherefore, all solutions of the system (3) enter the feasible region,This completes the proof of the theorem.

4. Data Fitting Results

A cosine function in equation (2) was fitted in MATLAB R2016a to the mean monthly surface water temperature data for the period July 2014 to December 2017 in order to estimate and describe the variation in the lake surface water temperature in Lake Kariba. The output obtained from MATLAB was

The estimates of parameters of equation (2) are shown in Table 1. The goodness of fit statistics for the fitted model (21) were sum of squared estimate of errors (SSE), , , and root mean square error (RMSE).

The actual and fitted surface water temperature plots are shown in Figure 2.

The fitted model has a very high indicating that the fit quality to the series of the temperature data points is good.

5. Numerical Simulations

For the coefficient of temperature for the growth of phytoplankton, , in (1) we assumed C [27], C for Chlorophyceae, and C for Cyanophyceae in Lake Kariba [18]. The plots of the temperature coefficient versus temperature for Chlorophyceae and Cyanophyceae are shown in Figures 3(a) and 3(b), respectively.

(a)

(b)

5.1. Chlorophyceae and Cyanophyceae

In this subsection, we compared numerical results on kapenta population density for the mathematical models with the Chlorophyceae and Cyanophyceae phytoplankton classes. We simulated model (3) using the fitted equation for in (21) and the default parameter values in (22) to illustrate the effect of on the dynamics of model (3).

The parameter values in equation (22) were obtained from published data, while the others were estimates. For the numerical simulations, a fourth-order Runge–Kutta numerical scheme written in Wolfram Mathematica 11 was used. The units of the variables , , , , and in the model system (3) are . Numerical simulation results in Figures 4–6 show a decline in the population density of phytoplankton, zooplankton, kapenta, and tigerfish as changes from C to C.

(a)

(b)

(c)

(d)

(a)

(b)

(a)

(b)

(c)

(d)

The time series plots and phase portraits in Figures 4–6 show oscillatory behaviour and a periodic orbit of period 1, respectively. Analysis results from the model (3) with the fitted surface water temperature (21) show that if shifts from C to C, which corresponds to the shift in dominance of Cyanophyceae to Chlorophyceae, then there will be a decline in the population density of kapenta. So, if the less palatable Cyanophyceae species become dominant in Lake Kariba, we expect a decrease in kapenta abundance in the lake. Pliński and Jóźwiak [29] found that phytoplankton progressed from Bacillariophycea to Chlorophyceae and then Cyanophyceae as water temperature rose. According to Solomon et al. [30], the decline in zooplankton production was due to a decrease in the more palatable Chlorophyceae as a result of rising water temperatures. Ndebele-Murisa [6] recorded a relative cellular concentration of and for Cyanophyceae and Chlorophyceae, respectively, in Lake Kariba, showing the dominance of Cyanophyceae over Chlorophyceae. Simulation results in Figures 4–6 are therefore in agreement with findings from Solomon et al. [30] and Magadza [18].

5.2. Temperature Changes in Lake Kariba

In order to determine the optimum temperature for phytoplankton growth for the fitted lake surface water temperature data which result in the maximum kapenta population density, in (2) varied from C to C using the fitted equation for in (21) for model (3) with C. The plot in magenta in Figure 7 shows the maximum and the curve in blue shows the minimum values of .

Figure 7 shows that the kapenta population density maximum curve had a maximum at about C and declined thereafter. Therefore, based on that result, it can be concluded that the optimal temperature for kapenta is approximately C. The result is not far off from the breakpoint of C for the kapenta catch obtained by Magadza [18].

In order to analyse model (3) for the warming of the lake water, we assumed that the lake warms by a rate of C per decade [18]. We added C to the mean surface water temperature data for the period to obtain an estimate of the mean surface water temperature after a decade. We projected further for the second decade by adding C to to get . We modelled the water temperatures and with (2), and the fitted models in (23) and (24) were

The fitted models were then substituted into (1). We simulated model (3) using some initial condition and compared numerical results from model (3) using the data, , and , with C and C in (1). Numerical results which illustrate the influence of lake warming on the concentration of nutrients and population density of phytoplankton, zooplankton, kapenta, and tigerfish are shown in Figures 8–10.

(a)

(b)

(c)

(d)

(a)

(b)

(a)

(b)

(c)

(d)

Results from Figures 8–10 show that as the lake warms, there is a corresponding decline in the population density of zooplankton, therefore resulting in a decline in the kapenta and tigerfish population density in the lake. Therefore, warming of the lake may have a negative effect on the population density of kapenta in the Lake Kariba fishery, and the environmental factor temperature may have a significant impact on kapenta abundance.

6. Discussion

In light of global warming, there is a knowledge gap regarding the effects of temperature increase on the density of Limnothrissa miodon in Lake Kariba. In this paper, we formulated and analysed a model that has nutrients, phytoplankton, zooplankton and Limnothrissa miodon, and temperature as an environmental factor. The phytoplankton growth rate, phytoplankton mortality, grazing on phytoplankton, zooplankton growth rate, zooplankton mortality, grazing on zooplankton, and Limnothrissa miodon mortality were assumed to be Holling type I forms. Feeding on Limnothrissa miodon and Hydrocynus vittatus growth was assumed to be Holling type II forms. Positivity and existence of solutions to model (3) were investigated. Numerical simulations were done for the model with default parameter values. Mathematical modelling provided an overall picture of the dynamics of the model variables. Assuming that existing trends in surface lake water temperature will continue, we used numerical simulations to demonstrate that global warming influences the Limnothrissa miodon population density in Lake Kariba. The thermal response of Limnothrissa miodon to global warming was considered in the context of thermal optima.

For the model with fitted lake surface water temperature data for the period , we used numerical simulations and investigated the effect of a shift in the optimal temperature for phytoplankton growth from C to , corresponding to dominance of Cyanophyceae over Chlorophyceae, and results showed a decline in the population density of Limnothrissa miodon.

The optimum temperature for phytoplankton growth for the fitted lake surface water temperature data for the period varied from C to C, and simulation results showed a maximum kapenta population density at approximately C and the result is similar to the breakpoint of C for kapenta catch obtained by Magadza [18]. According to Abowei [31], a species’ existence is threatened if the water temperature exceeds its upper limit of toleration. Furthermore, according to McDonald et al. [32], lake warming to abovementioned optimum temperatures can result in a reduction in the production of species like lake trout.

In order to explore the influence of global warming on Limnothrissa miodon population density, we projected lake surface water temperature for the next two decades and used data fitting and numerical simulations to predict the population density of Limnothrissa miodon in Lake Kariba. Our findings show that the population density of Limnothrissa miodon declines as the lake warms and this is in agreement with Abdellaoui et al. [33], who used a time series analysis and modelling approach on assessing the impact of temperature and chlorophyll variations on the fluctuations of sardine abundance in Al-Hoceima. Their results showed an inverse relationship between fluctuations of sardine catch per unit effort and sea surface temperature and that sea surface temperature is the most important parameter affecting the abundance of small pelagic fish in the Moroccan Mediterranean Sea. Similarly, Lam et al. [34] used simulation models in their study and anticipated that climate change will decrease fish catches globally by by 2050. Our numerical simulation results are in agreement with findings of the European Environmental Agency’s research [35], which showed that lakes are impacted by climate change, mainly by temperature rises [35–37]. Our results are congruent with previous studies that have shown significant adverse effects of warming on freshwater ecosystems [38–41]. Our findings are also supported by Mohammed and Uraguchi [42], who suggested that climate change will have an adverse impact on the already strained fish resources in sub-Saharan African countries. The highlights of the study are as follows:(i)A cosine function was fitted to mean lake surface water temperature data and the accuracy of the fitted model was analysed(ii)Default parameter values and different initial conditions were used to run numerical simulations for a nutrient, plankton, kapenta, and tigerfish model with a temperature coefficient for phytoplankton growth(iii)Numerical simulation results of the nonautonomous model showed a stable periodic orbit for varying initial conditions, and therefore, instability(iv)Lake warming has a negative impact on the more palatable Chlorophyceae, thus leading to decline in kapenta density in Lake Kariba(v)Kapenta population density starts to decline after C(vi)A decadal warming rate of C results in a decline in zooplankton population density, which leads to a decline in the kapenta population density

7. Conclusions

Numerical results showed that the population density of kapenta declines after the lake surface water temperature surpasses C. Simulation results also showed that lake warming has a negative effect on the more palatable Chlorophyceae population density, resulting in a decline in the density of kapenta in Lake Kariba. Therefore, we conclude that lake surface water temperature influences the dynamics of Limnothrissa miodon since rising temperatures have been shown to have a negative impact on the kapenta population density in Lake Kariba. Lake surface water temperature influences the productivity in the water body, altering the mean and amplitude of plankton, kapenta, and tigerfish population density oscillations. Rising temperatures may lead to the disappearance of the more palatable Chlorophyceae and an abundance of the less palatable Cyanophyceae. This may result in a decline in zooplankton populations, and this may adversely affect the kapenta population. Therefore, lake warming may result in a decrease in the kapenta population and reduced kapenta catches in the lake, with the probable consequence of reducing the number of fishing vessels as the fishing will no longer be profitable. This can have adverse effects on the local communities and the local economy. In light of these findings, the governments of Zambia and Zimbabwe and all stakeholders are, therefore, encouraged to take action toward reducing the impacts of climate change in line with the Paris agreement, which was adopted in 2015.

For future studies, we intend to model the dynamics of Limnothrissa miodon with the invasive crayfish.

Data Availability

The data used to support the findings of this study are included within the article.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

The authors would like to express their gratitude to the Lake Kariba Fisheries Research Institute and the University of Zimbabwe Lake Kariba Research Station for providing the data used in this study. Dr. Nobuhle Ndlovu, Ms. Adroit T. Chakandinakira, and Ms. P Chirozva deserve special recognition. Research Board Grant number RDB/90/18 from the National University of Science and Technology supported this study.

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Copyright © 2023 Farikayi K. Mutasa et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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