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Related Concept Videos

Routh-Hurwitz Criterion II01:19

Routh-Hurwitz Criterion II

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In the application of the Routh-Hurwitz criterion, two specific scenarios can arise that complicate stability analysis.
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first...
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Euler's Formula for Pin-Ended Columns01:21

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In structural engineering, the stability of columns under compressive axial loads is a critical consideration, described as buckling. A typical example involves a column PQ, which is pin-connected at both ends and subjected to a centric axial load F applied at one end, with a reaction force of F' = -F at the other end. Here, it is crucial to understand that when an applied load exceeds the critical load, buckling occurs as the system becomes unstable.
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Inverse z-Transform by Partial Fraction Expansion01:20

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The inverse z-transform is a crucial technique for converting a function from its z-domain representation back to the time domain. One effective method for finding the inverse z-transform is the Partial Fraction Method, which involves decomposing a function into simpler fractions with distinct coefficients. These fractions correspond to known z-transform pairs, facilitating the inverse transformation process.
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Cartesian Form for Vector Formulation01:26

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The Cartesian form for vector formulation is a process to calculate  the moment of force using the position and force vectors. The moment of force is defined as the cross-product of these vectors, making it a vector quantity. The Cartesian form of the position and force vectors involves unit vectors, which can be used to express the cross-product in determinant form.
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Euler Equations of Motion01:19

Euler Equations of Motion

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Imagine a rigid body that is rotating at an angular velocity of ω within an inertial frame of reference. Along with this, picture a second rotating frame that is attached to the body itself. This frame moves along with the body and possesses an angular velocity of Ω. The total moment about the center of mass is calculated by adding the rate of change of angular momentum about the center of mass in relation to the rotating frame and the cross-product of the body's angular velocity...
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Routh-Hurwitz Criterion I01:15

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Consider an electrical power grid, where stability is essential to prevent blackouts. The Routh-Hurwitz criterion is a valuable tool for assessing system stability under varying load conditions or faults. By analyzing the closed-loop transfer function, the Routh-Hurwitz criterion helps determine whether the system remains stable.
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Square root identities for harvested Beverton-Holt models.

Jerzy Filar1, Sabrina Streipert2

  • 1University of Queensland, Department of Mathematics and Statistics, St Lucia 4072, Australia.

Journal of Theoretical Biology
|June 18, 2022
PubMed
Summary

This study introduces a new net-proliferation rate for harvested species, finding that a square root harvest strategy can be a practical rule-of-thumb for sustainable fisheries management.

Keywords:
BarramundiBeverton–HoltFisheriesMaximum sustainable yieldPella–TomlinsonSingle speciesSquare root identityThreshold-risk

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Area of Science:

  • Fisheries Science
  • Population Dynamics
  • Ecology

Background:

  • Harvesting models often simplify the impact of fishing on population survival.
  • Maximum Sustainable Yield (MSY) is a key concept in fisheries management.
  • Understanding population dynamics is crucial for sustainable resource exploitation.

Purpose of the Study:

  • Introduce and define the 'net-proliferation rate' for harvested single-species models.
  • Establish analytically derived 'square root identities' relating proliferation and net-proliferation.
  • Evaluate the practical application of these identities in fisheries management.

Main Methods:

  • Analytically derived square root identities for Beverton-Holt recurrence.
  • Compared square root results with the Pella-Tomlinson model's optimal survival rate.
  • Fitted a stochastic Pella-Tomlinson model to Barramundi fishery data.

Main Results:

  • Square root identities were analytically derived for harvested single-species models.
  • The square root harvest strategy showed similar equilibrium biomass levels to MSY harvest for Barramundi data.
  • Risk sensitivity analysis indicated the utility of square root harvest as a rule-of-thumb.

Conclusions:

  • The square root harvest strategy offers a potentially robust and practical alternative to MSY.
  • Understanding population risk sensitivity is vital for mitigating overfishing.
  • This research contributes to developing more effective and sustainable fisheries management practices.