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Change in schedule

Change in schedule. Lecture Mon 6th feb Moved to Tue 7th feb 10.15-12. Subjects Chapters in the book. Basic about models Discrete Processes Deterministic models Stochastic models Continous processes Deterministic models ( Stochastic models – excluded ). Discrete stochasticity.

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Change in schedule

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  1. Change in schedule • Lecture Mon 6th feb Moved to Tue 7th feb 10.15-12

  2. SubjectsChapters in the book • Basic aboutmodels • DiscreteProcesses • Deterministicmodels • Stochasticmodels • Continousprocesses • Deterministicmodels • (Stochasticmodels –excluded)

  3. Discrete stochasticity chance is a component How to interpret data with noise? data into the model (empirical) data out of the model (theoretical results) How to construct models with stochastic components?

  4. Measures of centrality and variability/central tendency and dispersion • mean • variance • Mean square distance to the mean • Standard deviation square root of variance

  5. Box whisker plot • A picture of the variability • median • Upper to lower quartile – half of all values • min and max values

  6. Create stochastic models • distributions • Not page 62-65 • Environmental – vs demographic stochasticity • Environmental -external effects • variation between individuals • Test the model • chi-2 test

  7. Distributions • normaldistributionmean och standard deviation • binomialdistributionn number of trials, p probabilitycompare with tossing coin 100times: n = 100 p = 0.5 for headthe distribution tells you probability for different amounts of head given 100 times tossing a coin

  8. Distributions (matlab) • normaldistributionR = normrnd(MU,SIGMA) generates normal random numbers with mean, MU, and standard deviation, SIGMA R = normrnd(5,0.2,[1 1000]),hist(R) • Also randn(5) • binomialdistributionR = binornd(N,P) generates binomial random numbers with parameters N and P.R=binornd(100,0.2,[1 1000]),hist(R)

  9. Normal distribution • 68.27% of all values is within one standard deviation from the mean 95% ….. within two standard deviations 99%…… within three standard deviations

  10. Matlabs • R = binornd(N,P) generates binomial random numbers with parameters N and P.R=binornd(100,0.2,[1 100]),hist(R)Binomial probability density functionbinopdf(0,200,0.02) • Binomial cumulative distribution functionbinocdf(X,N,P) • Mean and variance for the binomial distribution.[M,V] = binostat(N,P) • Random numbers from a specified distribution.rn = random('Normal',0,1,2,4)rp = random('Poisson',1:6,1,6) • RAND Uniformly distributed pseudo-random numbers • RANDN normal distributed pseudo-random numbers

  11. The book has erronous definitions Environmental- vsdemographic stochasticitet • Environmental ecology: climate, weather, other populations • demographic the effect of small numbers, you can’t use the mean of the population mean of birth is 2 with variance 0.5 – what about a population of 10 individuals – how many newborns? It will vary!

  12. Environmental stochasticity • Continous • Every single time is effected by the stochasticy. Common factors:temperatureother populationsfor every time step you have to calculate a new growth rate or dispersal or (depends on if the environemtalvaraition has effect on it or not. • Catastrophic: few events • Seldom but drastic. The whole or parts of population is wiped out. You have to consider how often the catastrophe occurs.

  13. Demographic stochasticity • The effect of few individuals • with few individuals the variation between them have an effect • with many individuals their differences evens out : one can use the mean • Example: 5 individuals – meanbirthrate= 3, variance 2. compareif 1000 individuals. What per capita birth rate for different years of the two? And environmetnalstochmay alter meanbirtratebetweenyears

  14. Stochasticity Number of individuals Startpopulation100, meangrowth1.2 standard deviation 0.15 Demographic: variation between individuals /initially 100 Tid Environmental : larger effect – the effect is on the mean. Always apparent

  15. Stochasticity Antal individer Startpopulation5, mean growth 1.2 with standard deviation 0.15 Demographic: variation between individuals /initially, Larger effect when fewer individuals –compare previous slide Tid Environmental : larger effect – the effect is on the mean. Always apparent

  16. Environmental stochasticitymatlab see hints Number of individulas [y,stdev,medel]=environmentstoch(1.2,0.15,50,20,100); Tid Log(Number of individuals) frequency Number of individuals

  17. Demografisk stokasticitet Number of individulas [y,stdev,medel]=environmentstoch(1.2,0.15,50,20,100); Tid Log(Number of individuals) frequency Number of individuals

  18. Test the modelChi-2 test – model out data vs empirical data • X2 is large if observed values are far from expected, alos note that is increase with numvber of obervations • Use table to correct for number of observations, degrees of freedom – n-1 • Determine, by table, if X2 is large enough to reject the model /result . Not on percentage!

  19. Summary • Distributions • normal • Binomial • Uniform • Environmental stochasticity • Continous • Catastrophic • Demgraphicstochasticity • chi-2 test of model data vsemperical

  20. Bloom’s TaxanomyA Hierarcical Knowledge Taxonomy

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