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Performance of small populations

Performance of small populations. Number of cases. Population size. Distribution of population sizes. Scorzonera hispanica. Processes in small populations. Deterministic Loss of pollinators, problems with finding mates Stochastic Effect of random fluctuations. Deterministic effects.

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Performance of small populations

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  1. Performance of small populations

  2. Number of cases Population size Distribution of population sizes Scorzonera hispanica

  3. Processes in small populations • Deterministic Loss of pollinators, problems with finding mates • Stochastic Effect of random fluctuations

  4. Deterministic effects • Demographic – effects directly on population dynamics • Genetic – effects via genetic diversity

  5. Demographic effects • Allee effect

  6. Allee effect • Limited possibility to find a partner due to low population density

  7. Limitation by number of pollinators Ågren, J. (1996), Lythrum salicaria

  8. Limitation by pollen availability • Testing limitations by pollen availability • Separation from plant vitality and habitat quality

  9. Ågren, J. (1996), Lythrum salicaria

  10. Stochastic effect • Demographic • Environmental • Disturbance

  11. Demographic stochasticity

  12. Demographic stochasticity • Application of probabilities to limited sample (mortality, reproduction….) • Problem only in small populations

  13. 50% survival probability

  14. 4 0.5 0.9 0.3 Data • Probabilities of transitions in the life-cycle

  15. Lathyrus vernus

  16. Data Killer whale

  17. Population transition matrix Seedling vegetative flowering Seedling Vegetative Flowering • Population growth rate • Stable stage distribution

  18. Modeling demographic stochasticity? • Matrix multiplication

  19. Average Good luck Bad luck Application of probabilities to each individuals Ineffective calculation

  20. Alternative • Use knowledge on distribution of the probabilities • Transition probability – multinomialdistribution • Reproduction – binomial or Poisson distribution

  21. Poisson distribution

  22. Killer whales 1: yearling 2: juvenile 3: mature females 4: post reproductive females Demographic stochasticity or changing condition?

  23. Killer whale • Only 1 offspring per female, number has binomial distribution • Other multinomial distribution

  24. Killer whale Populations with 4 individuals

  25. Population size Killer whale

  26. Projection of population size in time

  27. Demographic or environmental stochasticity? • How probable it is that there is no reproduction over 5 years? Time without reproduction – killer whale

  28. Extinction of lineages • Branching process models

  29. Environmental stochasticity

  30. Environmental stochasticity • Variation of demography in time • Combination of good and bad year

  31. Data • Variability in transition probabilities over time • Combination of spatial and temporal variation

  32. Models of environmental stochasticity • Independent between years • Markov chains – dependencies between years • Autoregressive techniques – continuous changes in quality

  33. Independent performance between years • Random combination of different qualities

  34. Variation in transition probabilities • Whole matrices vs. single transitions • Covariance

  35. Scorzonera hispanica

  36. Thomas 1990, simulace

  37. Variation vs. mean • Variation– probability of survival in small populations • Mean – long-term trends

  38. Population growth rate in changing environment • Not possible to average – depends on stable stage distribution • Simulation – multiple combinations of all matrices

  39. Long term population growth rate

  40. Demo. and env. stochasticity

  41. Extinction • Demo. stochasticity – integer numbers • Env. stochasticita – fractions

  42. Disturbance

  43. Effect ofdisturbance • Relationship between disturbance size and frequency • Problems with quantification

  44. Disturbance Song et al. 2001

  45. Without disturbance With disturbance Mangel & Tier 1994, simul

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