Holt Model Research Articles

A stochastic modified Beverton–Holt model with the Allee effect

In this paper, we consider a discrete stochastic Beverton–Holt model with the Allee effect. We study the effects of demographic and environmental fluctuations on the dynamics of the model. Moreover, we investigate the potential function, the attainment time and quasi-stationary distributions of the system.

Interplay between strong Allee effect, harvesting and hydra effect of a single population discrete-time system

The dynamics of a single population with non-overlapping generations can be described deterministically by a scalar difference equation in this study. A discrete-time Beverton–Holt stock recruitment model with Allee effect, harvesting and hydra effect is proposed and studied. Model with strong Allee effect results from incorporating mate limitation in the Beverton–Holt model. We show that these simple models exhibit some interesting (and sometimes unexpected) phenomena such as the hydra effect, sudden collapses and essential extinction. Along with this, harvesting is a socio-economic issue to continue any system generation after generation. Different dynamical behaviors for these situations have been illustrated numerically also. The biological implications of our analytical and numerical findings are discussed critically.

Can Conservation Stocking Enhance Juvenile Emigrant Production in Wild Atlantic Salmon?

AbstractConservation stocking is frequently used by fishery managers to stabilize or increase production of depleted fish stocks. However, in the case of salmonids the benefits are increasingly questioned and generally poorly quantified. We investigated the effects of ova stocking on freshwater emigrant production in a declining Scottish population of “spring” Atlantic Salmon Salmo salar. The stocking program was designed to minimize risks, maximize expected benefits, and bypass population bottlenecks between the ova and fry stages. Long‐term data (33 cohorts over 42 years, including 8 years of stocking) on numbers of ova and juvenile emigrant production were used to investigate whether the ova–emigrant stock–recruitment relationship differed between conditions of natural spawning and stocking. We considered Ricker and Beverton–Holt models that included terms for the effects of stocking, intercohort competition, and changes in trap efficiency on emigrant production. The “best model” was considered to be that with the lowest corrected Akaike information criterion (AICc). The strength of evidence for competing models was provided by smooth AICc weights. There was strong support for intercohort competition whereby large cohorts reduced survival rates of subsequent cohorts. There was little support for a stocking effect, and the best model did not include stocking. Changes in juvenile emigrant production could have been detected with 80% power if those changes had increased by an average of around 24% over the eight stocked years, indicating relatively high power to detect stocking effects. Although focused on a particular river system and set of ova stocking protocols, this study suggests that stocking fails to increase Atlantic Salmon production where wild fish populations and suitable habitat remain.

Prediction of Cholera Incidence by Using the Comparison of Four Models: Autoregressive Integrated Moving Average Model, Holt Model, Brown Model and Simple Regression Model

Prediction of Cholera Incidence by Using the Comparison of Four Models: Autoregressive Integrated Moving Average Model, Holt Model, Brown Model and Simple Regression Model

Stock assessment of Japanese eels using Japanese abundance indices

The paper compiles a catch history of Japanese eels Anguilla japonica in East Asia and some Japanese relative abundance series. Maximum likelihood estimates of stock abundance of eels have been obtained using the abundance series and various biological parameters, such as growth, maturity and natural mortality. Age- and sex-structured models have been used to express the dynamics of stock abundance, and the Beverton and Holt model has been used to express the relationship between stock and recruitment. Data for estimations are standardized catch per unit effort of commercial fishery for exploitable stock (1954–2006 and 1968–2008) and for glass eel (1954–2010, 1972–2004, and 1973–1997). From the results of the base case scenario of estimations, the estimated stock size of individuals aged ≥1 year was 18.7 thousand tons in 2010, which was 24 % of the carrying capacity. The estimated stock size has recovered since 1990. Maximum sustainable yield was 4,180 tons if only the exploitable stock were utilized, and 266 tons if only the glass eel were utilized. These results and issues relating to estimation and management for reducing the fishery impact on stock are discussed.

A new model for simulating growth in fish

A real dynamic population model calculates change in population sizes independent of time. The Beverton & Holt (B&H) model commonly used in fish assessment includes the von Bertalanffy growth function which has age or accumulated time as an independent variable. As a result the B&H model has to assume constant fish growth. However, growth in fish is highly variable depending on food availability and environmental conditions. We propose a new growth model where the length increment of fish living under constant conditions and unlimited food supply, decreases linearly with increasing fish length until it reaches zero at a maximal fish length. The model is independent of time and includes a term which accounts for the environmental variation. In the present study, the model was validated in zebrafish held at constant conditions. There was a good fit of the model to data on observed growth in Norwegian spring spawning herring, capelin from the Barents Sea, North Sea herring and in farmed coastal cod. Growth data from Walleye Pollock from the Eastern Bering Sea and blue whiting from the Norwegian Sea also fitted reasonably well to the model, whereas data from cod from the North Sea showed a good fit to the model only above a length of 70 cm. Cod from the Barents Sea did not grow according to the model. The last results can be explained by environmental factors and variable food availability in the time under study. The model implicates that the efficiency of energy conversion from food decreases as the individual animal approaches its maximal length and is postulated to represent a natural law of fish growth.

Resonance in Beverton–Holt population models with periodic and random coefficients

An increase in the mean population density in a fluctuating environment is known as resonance. Resonance has been observed in laboratory experiments and has been studied in discrete-time population models. We investigate this phenomenon in the Beverton–Holt model with either periodic or random variables for two biologically relevant coefficients: the intrinsic growth rate and the carrying capacity. Three types of resonance are defined: arithmetic, geometric and harmonic. Conditions are derived for each type of resonance in the case of period-2 coefficients and some results for period p>2. For period 2, regions in parameter space where each type of resonance occurs are shown to be subsets of each other. For the case of random coefficients with constant intrinsic growth rate, it is shown that the three types of resonance do not occur. Numerical examples illustrate resonance and attenuance (decrease in the mean population density) in the Beverton–Holt model when the coefficients are discrete random variables.

Dynamics of a discontinuous discrete Beverton–Holt model

Our aim is to investigate the global asymptotic behaviour, oscillation, periodicity and bifurcation in discontinuous Beverton–Holt type difference equationwhere x0>0, functions k and r are discontinuous piecewise constant functionssatisfyingand h is Heaviside function.

Sustainable Exploitation of Fish Stocks by Long-Term Profit Maximization with Special Regards to Cod in the Baltic Sea

An important aim of fishery management is the conservation and sustainable exploitation of fish stocks whereas maximization of profit is the aim of fishermen. At first view this seems to be contradictory. The main management tools for stock exploitation are fishing effort (summarizing all effort limitations) and the so called technical measures (mesh size). The presented new model, using these control variables, is intended to replace the Gordon Schaefer model and based on the Beverton and Holt yield-per-recruit model. The Beverton and Holt model, however, do not take into account the feedback of stock-size changes on recruitment and therefore also on yield. Overcoming this disadvantage is one finding in this paper. For the computation of optimal exploitation pattern the Shepherd approach for construction of sustainable yield curves was extended by incorporating the control of mesh size along with the current exclusive control of fishing effort. This extension turns all fishing mortality reference points into reference functions of the age at first capture. The sole economic important demersal stock in the western Baltic Sea is the cod stock of that area. This paper describes an equilibrium model for the computation of long-term harvesting strategies for that stock including the control of mesh size into the well-established exploitation models. It was shown that the stock is more reliably protected against collapsing by economic considerations rather than by measures chosen according to the precautionary approach. If the Baltic cod stock is exploited according to the suggested approach with an optimized, much larger mesh size in the steady-state, a larger profit is ensured simultaneously with improved stock conservation. This model can also be applied for the maximization of the overall profit within mixed-species management by overlaying the single-species results. Here, however, it is only possible to find an overall optimum which generally differs from the single species optimum. An economic reasonable limit of exploitation is given by the FMSY-curve – the fishing mortality resulting for a given age at first capture in the maximum yield for this age while the Fpa-curve according to precautionary approach has to be considered as the final line of defense against stock collapse. The precautionary approach only calls for changes in effort limitations or technical measures if a violation of its principles has occurred in a multi-species fishery due to ecological reasons. Apart from stock protection the main objective of this paper is to find at the same time appropriate values for the management control variables defining an equilibrium maximizing the profit (maximum economic yield – MEY) of the fishery.

The Beverton–Holt q-difference equation

The Beverton–Holt model is a classical population model which has been considered in the literature for the discrete-time case. Its continuous-time analogue is the well-known logistic model. In this paper, we consider a quantum calculus analogue of the Beverton–Holt equation. We use a recently introduced concept of periodic functions in quantum calculus in order to study the existence of periodic solutions of the Beverton–Holt q-difference equation. Moreover, we present proofs of quantum calculus versions of two so-called Cushing–Henson conjectures.

Maximum survival of eggs as the key parameter of stock–recruit meta-analysis: accounting for parameter and structural uncertainty

Despite their name, hierarchical stock–recruit meta-analyses are often parameterized in terms of steepness, which depends not only on the assumed stock–recruitment relationship but also on the recruit–spawner relationship. This parameterization requires assumptions about the reproductive potential of the recruit that are not desirable if the focus of the study is limited to the spawning–recruitment phase instead of the full life cycle. Thus, usage of steepness should be avoided in studies that aim to produce informative priors for the stock–recruit relationship for use in studies of other salmon stocks. An alternative key parameter for stock–recruit models is the maximum survival of eggs, which is the slope at the origin of the stock–recruitment curve when spawning stock size is defined in terms of the number of eggs. Furthermore, the current widely used practices in stock–recruit modeling could be improved by taking into account the stock-specific model uncertainty. We use the method of Bayesian model averaging to build a hierarchical stock–recruit model that allows stock-specific model structures with Beverton–Holt, Ricker, and hockey stick models as alternatives, all of which can be parameterized with the maximum survival of eggs. We illustrate our approach by analyzing nine previously published datasets for Atlantic salmon (Salmo salar).

A recruitment-mortality model in the precautionary management toolkit of African tropical inland, single-species fisheries

A recruitment-mortality model and a Beverton–Holt or Ricker stock-recruitment model are combined to derive stock performance metrics. A composite (age-aggregated) yield-per-recruit (CYPR) emerges from these derivations. Upon a balanced equilibrium (e.g., recruitment>yield), the CYPR maximizes at an asymptote (Asy) beyond which CYPR cannot drop whatever the age-at-harvest. F0.5Asy, the fishing mortality corresponding to 0.5Asy, may form the basis of a conservative feedback-policy rule. The approach aims to complement the management tools for inland single-species fisheries in tropical Africa, but can be applied for any single-species fishery. It is illustrated using data for the Zambian Bukabuka (Lates stappersii) fishery of Lake Tanganyika.

Performance Reliability Modeling Based on ARIMA Model

Performance reliability method (PRM) has great advantages on modeling with few failure data by using the performance degradation data. The purpose of this paper is to find the defects of PRM based on HOLT model, and PRM method based on ARIMA model was proposed by introducing the product fleet real-time performance reliability information to the measuring points. Finally, an example applying on the aero-engine remaining life prediction was taken to validate that PRM method based on ARIMA model can avoid variances errors derived from the formula, compared with the PRM model based on HOLT model. The relative error of the improved method has 11.765% lower. So we can draw a conclusion that this method is effective and feasible.

Performance Reliability Modeling Based on ARIMA Model

Performance reliability method (PRM) has great advantages on modeling with few failure data by using the performance degradation data. The purpose of this paper is to find the defects of PRM based on HOLT model, and PRM method based on ARIMA model was proposed by introducing the product fleet real-time performance reliability information to the measuring points. Finally, an example applying on the aero-engine remaining life prediction was taken to validate that PRM method based on ARIMA model can avoid variances errors derived from the formula, compared with the PRM model based on HOLT model. The relative error of the improved method has 11.765% lower. So we can draw a conclusion that this method is effective and feasible.

Optimal timing of interventions in fishery resource and pest management

Assuming that a fish population follows the continuous logistic growth or the discrete Beverton–Holt model, several optimal impulsive harvesting policies for the maximum stock level of the fish at the end of a fishing season are investigated under the condition of fixed intensity and frequency of impulsive harvesting. The optimal impulsive harvesting moments for all cases considered are given analytically and the related numerical simulations are also provided. Furthermore, the methods employed can also be used to investigate the optimal timing of chemical control in pest management. Our results confirm that the optimal timing of pesticide applications such that the density of the pest population is minimal at any time during a planting season or the average of density of the pest population over the planting season is minimal is the beginning of the planting season. In practice, the results can be used to guide the fisherman to manage fisheries and guide farmers to control pests.

Global behavior of solutions of a periodically forced Sigmoid Beverton–Holt model

Our aim in this paper is to investigate the boundedness, the extreme stability, and the periodicity of positive solutions of the periodically forced Sigmoid Beverton–Holt model: where {a n } is a positive periodic sequence with period p and δ>0. In the special case when δ=1, the above equation reduces to the well-known periodic Pielou logistic equation which is known to be equivalent to the periodically forced Beverton–Holt model.

A Conceptional Analysis of Dynamics and Production in Bioeconomic Models

Harvesting functions and stock dynamic equations in age‐structured bioeconomic models are generalized in order to incorporate density dependence. Using this generalization, anything from completely uniformly distributed fish to extreme schooling can be analyzed. The classical Beverton–Holt model comes out as a special case of the generalized model. The generalization can be applied both for simulation as well as for optimization purposes given appropriate software. Conceptual analysis indicates that pulse fishing seems to become less and less economically profitable as we move from uniformly distributed fish to schooling species. This has important implications for how fish stocks ought to be managed.

A ACURACIDADE DOS MODELOS DE PREVISÃO DE DEMANDA COMO FATOR CRÍTICO PARA O DESEMPENHO FINANCEIRO NA INDÚSTRIA DE ALIMENTOS <br><strong>DOI:10.7444/fsrj.v2i2.58</strong>

Toda organização precisa saber dimensionar suas capacidades produtivas de modo que estas se encaixem perfeitamente com as demandas. O papel da previsão de demanda é fornecer subsídios para o planejamento estratégico da organização. Este processo permite que os administradores antecipem o futuro e planejem de forma mais conveniente as suas ações. Não basta, entretanto, ter um sistema de previsão de demanda. É a qualidade da informação obtida por este sistema que capacita a organização a obter melhor planejamento das operações. Dentro deste contexto, este trabalho apresenta um estudo de caso com os objetivos de: (a) definir o modelo quantitativo de previsão de demanda de maior grau de acurácia e (b) verificar a influência da acuracidade da previsão de demanda no desempenho financeiro da organização. Trata-se de uma pesquisa descritiva ex-post fact em que foram utilizados dados históricos de demanda de cinco grupos de produto, no período de 2004 a 2008. Os resultados demonstram que se a empresa empregasse o modelo ARIMA para os grupos A, B e E, o modelo de Holt para o grupo D e o modelo de Winter para o grupo C, o faturamento poderia ser aumentado em, aproximadamente, dois milhões e oitocentos mil reais anuais.

Spawning stock and recruitment in North Sea cod shaped by food and climate

In order to provide better fisheries management and conservation decisions, there is a need to discern the underlying relationship between the spawning stock and recruitment of marine fishes, a relationship which is influenced by the environmental conditions. Here, we demonstrate how the environmental conditions (temperature and the food availability for fish larvae) influence the stock–recruitment relationship and indeed what kind of stock–recruitment relationship we might see under different environmental conditions. Using unique zooplankton data from the Continuous Plankton Recorder, we find that food availability (i.e. zooplankton) in essence determines which model applies for the once large North Sea cod (Gadus morhua) stock. Further, we show that recruitment is strengthened during cold years and weakened during warm years. Our combined model explained 45 per cent of the total variance in cod recruitment, while the traditional Ricker and Beverton–Holt models only explained about 10 per cent. Specifically, our approach predicts that a full recovery of the North Sea cod stock might not be expected until the environment becomes more favourable.

Holt’s exponential smoothing and neural network models for forecasting interval-valued time series

Interval-valued time series are interval-valued data that are collected in a chronological sequence over time. This paper introduces three approaches to forecasting interval-valued time series. The first two approaches are based on multilayer perceptron (MLP) neural networks and Holt’s exponential smoothing methods, respectively. In Holt’s method for interval-valued time series, the smoothing parameters are estimated by using techniques for non-linear optimization problems with bound constraints. The third approach is based on a hybrid methodology that combines the MLP and Holt models. The practicality of the methods is demonstrated through simulation studies and applications using real interval-valued stock market time series.