Read the summary and the most important questions on Biological Modeling of Populations 2020

• 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.