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The maximum sustainable yield is the largest yield that can be taken from a population at equilibrium. In figure 3, if H {\displaystyle H} is higher than H 2 {\displaystyle H_{2}} , the harvesting would exceed the population's capacity to replace itself at any population size ( H 3 {\displaystyle H_{3}} in figure 3).
Standard method like Gauss elimination can be used to solve the matrix equation for .A more numerically stable method is provided by QR decomposition method. Since the matrix is a symmetric positive definite matrix, can be solved twice as fast with the Cholesky decomposition, while for large sparse systems conjugate gradient method is more effective.
In population ecology and economics, the maximum sustainable yield or MSY is, theoretically, the largest catch that can be taken from a fishery stock over an indefinite period. [ 8 ] [ 9 ] Under the assumption of logistic growth, the MSY will be exactly at half the carrying capacity of a species, as this is the stage at when population growth ...
Biologists use the concept of maximum sustainable yield (MSY) or mean annual increment (MAI), to determine the optimal harvest age of timber. MSY can be defined as “the largest yield that can be harvested which does not deplete the resource (timber) irreparably and which leaves the resource in good shape for future uses”.
The concept of maximum sustainable yield (MSY) has been used in fisheries science and fisheries management for more than a century. Originally developed and popularized by Fedor Baranov early in the 1900s as the "theory of fishing," it is often credited with laying the foundation for the modern understanding of the population dynamics of fisheries. [1]
The Beverton–Holt model is a classic discrete-time population model which gives the expected number n t+1 (or density) of individuals in generation t + 1 as a function of the number of individuals in the previous generation, + = + /.
The MSE either assesses the quality of a predictor (i.e., a function mapping arbitrary inputs to a sample of values of some random variable), or of an estimator (i.e., a mathematical function mapping a sample of data to an estimate of a parameter of the population from which the data is sampled).
Sustainable yield is the amount of a resource that humans can harvest without over-harvesting or damaging a potentially renewable resource. [1]In more formal terms, the sustainable yield of natural capital is the ecological yield that can be extracted without reducing the base of capital itself, i.e. the surplus required to maintain ecosystem services at the same or increasing level over time. [2]