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Lecture 8: Population Growth

Lecture 8: Population Growth. EEES 3050. Population growth. Predicting the growth of populations Problems? Populations are not always growing Ecosystems change Sometime hard to know how many currently exist Or, the birth/death rates. Can we quantify?

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Lecture 8: Population Growth

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  1. Lecture 8: Population Growth EEES 3050

  2. Population growth • Predicting the growth of populations • Problems? • Populations are not always growing • Ecosystems change • Sometime hard to know how many currently exist • Or, the birth/death rates. • Can we quantify? • Based on the ideas of the life tables discussed last time.

  3. Population growth • Two ways to think about population growth • 1) With discrete generations. • Single breeding season, live for 1 year. • Each female produces an average number of female offspring each year • = R0 = net reproductive rate. • 2) With overlapping generations. • Prolonged breeding or continuous breeding season. • Growth depends on the conditions at the current moment. • =r = per-capita rate of population growth.

  4. Population growth with discrete generations.

  5. Population growth • What is the problem with this model? • Populations do not grow forever. • What can we do to alter this equation?

  6. (R0 )

  7. Growth rate dependent upon population size. • Population growth is density dependent. , where B is the slope of the line.

  8. Growth rate dependent upon population size. • What does this look like if we add a limit?

  9. Allee Effect • Definition: • A positive relation between population density and the per capita growth rate. • In other words, for smaller populations, the reproduction and survival of individuals decreases.

  10. Allee Effect

  11. Population growth with overlapping generations • Multiplication rate constant. • r = instantaneous rate of population growth • = b – d, where b and d are the instantaneous birth and death rates.

  12. Use geometric growth model to get: Nt = N0ert

  13. Populations do not show geometric growth curves. • What can be added to the geometric equation? • K = Carrying capacity • Called the logistic growth curve

  14. Logistic growth curve • Simple • Need 2 parameters • r = potential rate of population increase per capita • K = Density at which space is saturated

  15. Model of growth • Do populations actually grow this way? • In Lab • Paramecium by Gause 1934 • Drosophila melangaster by Pearl 1927 • Tribolium by Chapman 1928

  16. Model of growth • Do populations actually grow this way? • In Lab • Paramecium by Gause 1934 • Drosophila melangaster by Pearl 1927 • Tribolium by Chapman 1928 • Populations sometimes showed this, so is there a problem with these models? • All these were conducted in the lab in stable conditions. • For short periods of time.

  17. Still, over long time periods no species has maintained a population at the original asymptote.

  18. Does logistic model hold in the field? • What situation would be required for a population ecologist to test the logistic model? • How can this be done in the field? • Introduced species • Reindeer introduced on purpose • Natural increases • Geese in N.A. and Europe. • Recovery of endangered species.

  19. Daphnia rosea

  20. Again the logistic model is often wrong… • Should it be used? • Why use models? • All models are wrong. • But is the model useful? • Predictions with limits.

  21. When is it right and useful? • In early growth stages. • Harvesting fish or game. • When is the most efficient time to harvest. • Determining carrying capacity. • Stable populations • What happens when resources are changed?

  22. Importance of stochastic events • Define stochastic: • Something based on probabilities. • In a stochastic model, the results will be different every time the model is run. • Why is it important to add stochasticity to a model of population growth? • Abiotic factors • Biotic factors • Are never constant!

  23. Stochastic Example • With a deterministic model, if R0 = 2 and N0 = 6 • How many in generation 1? • What if R0 is stochastic? • If the probability of 1 female is 0.5 and • The probability of 3 female is 0.5 than…

  24. Trail 1 Trial 2 N1 = 14 N1 =

  25. Exam • Friday Seminar: • Ken Kilbert: Natural Resource Damages • University of Toledo, Law School • Remember there is a test Thursday… • Approx 40 questions. • Will consist of approx. 50% multiple choice, short answer, and 50% written questions. • You can help write the exam… • Send me a question via e-mail by noon tomorrow (preferably earlier). • Can be multiple choice, T/F, short answer, essay, etc. • Questions?

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