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Invasive Species

Invasive Species. Species occasionally invade new habitat, irrespective of whether intentional or unintentional result of human activities If the population becomes successfully established, the population will grow and eventually need to expand its range. Invasive Species.

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Invasive Species

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  1. Invasive Species • Species occasionally invade new habitat, irrespective of whether intentional or unintentional result of human activities • If the population becomes successfully established, the population will grow and eventually need to expand its range

  2. Invasive Species • Considering the potential negative impact of invasive species, it is important we better understand the how’s and why’s of species range expansion • What are the two factors that influence range expansion (or contraction) rate? Population Growth Emigration (or Dispersal) Rate

  3. Invasive Species • In this exercise, you will treat each cell in the spreadsheet as a patch of habitat, which may house a local population • Each population may grow or shrink according to its birth and death rates and it may exchange members with neighboring local populations through immigration or emigration • The number of cells occupied by local populations is the range of the population

  4. Invasive Species • We begin by assuming that the local population in each cell grows according to a logistic model: b’ and d’ represent per capita rates when populations are small and uncrowded • However, this model does not take into account any I or E Nt+1 = Nt + (b+ b’Nt)Nt – (d + d’Nt)Nt

  5. Invasive Species • We could either add more terms to the model, or simply the model • If we insert Rmax to represent the population’s maximum geometric rate of growth and Rdd for the density-dependent reduction in population growth rate Nt+1 = Nt + (b+ b’Nt)Nt – (d + d’Nt)Nt Nt+1 = Nt + bNt – dNt + b’Nt2+ d’Nt2 Nt+1 = Nt + (b - d)Nt – (b’ - d’)Nt2

  6. Invasive Species Nt+1 = Nt + (b - d)Nt + (b’ - d’)Nt2 • Let Rmax = b-d and Rdd = b’-d’ • This is the same as the logistic model earlier • Let’s add E Nt+1 = Nt + Rmax*Nt + Rdd*Nt2 Nt+1 = Nt + (Rmax* RddNt)Nt

  7. Invasive Species Here Eminrepresent the minimum emigration rate and Edd the density-dependent increase in emigration Emigrants have to go somewhere and this model assumes equal likelihood to any adjacent cell Nt+1 = Nt + (Rmax* RddNt)Nt – (Emin + EddNt)Nt

  8. Invasive Species • From the perspective of the ‘target’ cell, immigrants move in from neighboring cells at rates determined by the sizes of the populations in those neighboring cells (L & R) • The population of each cell grows by reproduction in its own cell and loses members by emigration. It does receive some members from L or R Nt+1 = Nt + (Rmax* RddNt)Nt – (Emin + EddNt)Nt + 0.5(Emin + EddLt)Lt + 0.5(Emin+EddRt)Rt

  9. Invasive Species • This model can be adjusted to represent geometric population growth as well

  10. Invasive Species • Objectives • Build a spatially explicit model of range expansion (or invasion) by a logistically growing population • Model the expansion of a species’ range in one and two dimensions • Determine how the rate of range expansion relates to population growth and emigration

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