Summary: Biological Modeling Of Populations 2020

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  • 1 Math reader

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  • Linear systems only have solutions when?

    The determinant is not equal to 0
  • A stable node when?

    Both lambda 1 and 2 < 0
  • Imaginary eigenvalues when?

    The discriminant is negative 
  • 3 Density dependence

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  • Negative density dependence 

    At high population densities the availability of essential resources is typically low, and this is expected to result in a lower fecundity and/or higher death rates.
  • Density dependent birth, replicating population

    Where K is the population size N of which the birth rate is 0
  • Positive density dependence

    When the population growth is regulated by an increased population density. This allows for multiple steady states.
  • A Hill-function is a convenient tool for?

    Defining increasing or decreasing non-linear functions.
  • 4 Stability and return time

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  • To determine whether or not a steady state is stable

    Take derivative/slope of N bar. If the slope is negative -> stable
  • Unsteady stable states form the borders of?

    Basins of attractions
  • Steady states with a small basin of attractions are not resilient because?

    Disturbances that breach the basin of attraction bring the population to an alternative attractor.
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