1 / 20

Logistic Equation

Logistic Equation. dN/dt = r m N (K-N) = r m N(1-N/K) K . What are the assumptions of the logistic equation?. 1) population started with a stable age distribution - already discussed

xiomara-lamorena
Télécharger la présentation

Logistic Equation

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Logistic Equation dN/dt = rmN(K-N) = rmN(1-N/K) K

  2. What are the assumptions of the logistic equation? 1) population started with a stable age distribution - already discussed 2) density is measured equally - i.e. how is density measured? This can be a problem when the biomass of different life stages are different, also size/individual is different under different conditions. 3) depressive effects of density on the rate of increase operates instantaneously without time lags.

  3. Time Lags dN/dt = rmN (K - Nt-tau) K

  4. Time Lags tau

  5. Time Lags Key point - oscillations can be intrinsic in the system and not driven by external environmental changes.

  6. Nicholson’s Blowflies

  7. Nicholson’s Blowflies

  8. Nicholson’s Blowflies

  9. Nicholson’s Blowflies The recruitment of new individuals into the population was determined at the egg-laying stage by the influence of food supply on per capita fecundity. As a result, fluctuations were significantly reduced. The time lag in density-dependent response was reduced.

  10. Daphnia

  11. Daphnia

  12. Population Projection N0,t N1,t Population Vector Nt = N2,t . . Nn,t

  13. Population Projection The number of new organisms (age 0) at time t+1 will be the contribution of fertility from all aged mothers. N0,t+1 = foN0 + f1N1 + f2N2 + f3N3 + … + fkNk The number of organisms age 1 at time t+1 = s0N0 The number of organisms age 2 at time t+1 = s1N1 The number of organisms age 3 at time t+1 = s2N2

  14. f0 f1 f2 f3 f4 …… fk-1 fk s0 0 0 0 0 …… 0 0 0 s1 0 0 0 …… 0 0 0 0 s3 0 0 …… 0 0 0 0 0 s4 0 …… 0 0 . . . . . . . . . . . . . . 0 0 0 0 0 sk-1 0

  15. See example in class MNt = Nt+1 M

  16. Stage Model

More Related