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Modelling in Ecology

Modelling in Ecology. Predictions in ecology rely on models. . Our program. What is a model? Matrix algebra Linear regression models More on regression Variance analysis Model selection techniques Classification techniques Eigenvector techniques More on eigenvectors

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Modelling in Ecology

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  1. Modelling in Ecology Predictions in ecology rely on models.

  2. Our program What is a model? Matrix algebra Linear regression models More on regression Variance analysis Model selection techniques Classification techniques Eigenvector techniques More on eigenvectors Species distribution modelling

  3. What is a model? A biological model is a formal representation of any biological process. Models serve to Simplify a process Make a process analytically tractable Identify basic patterns Identify basic variables (drivers) Make qualitative predictions Make quantitative predictions Derive testable hypotheses Provide guidelines for conservation and decision making There are many different types of models: Brain models, Cellular automata, Food web models, Species distribution models, infectious disease models, demographic models, ecosystem models … In general, there are two types of models: Analytical models Descriptive models Simulation models

  4. A simple analytical model A species – area relationship is modelled by two different analytical functions. These trend lines predict central tendencies (averages) around which the observed data scatter. The model predicts alpha, beta, and gamma diversities

  5. A descriptive (qualitative) model of slug carcass colonisation IdiotypanigricepsBasalysparva Hyperparasitoids Aspilota AAspilota B Aspilota C Aspilota COrthostigmasp KleridotomapsiloidesPentapleura sp. Aspilota AAspilota E Primary parasitoids Necrophagous flies Megaseliaruficornis Megaseliapulicaria Gymnophoraarcuata Limosina sp. ArionaterNecrophilus spp.Carabus spp. ConiceraschnittmaniFanniaimmuticaPsychodasp Time

  6. Modelling starts with a graphical representation The classical Silver Springs semi-quantitative model of ecosystem functioning by H. T. Odum (1971)

  7. Lower emmissions Trading credits with other firms The carbon credit system Industry Emmisions according to the credits Higher emmissions Carbon credits Trading for other permisions Local authorities permit emmisssions Payment

  8. Realism Modelling is essentially a trade-off (compromise) between 1. Generality 2. Realism 3. Precision Generality Trade-off Precision A good model does not only refer to a special case but allows for some generalisation. A model must be realistic with regard to its components and drivers. Predictive models must be sufficiently precise. A too precise model is rarely general. A too realistic model is rarely of general application (too case specific). A too general model is rarely precise.

  9. What is interesting: the prediction or the deviation? This quantitative model has low predictive power. It is not able to precisely predict species richness for a given area. The model might serve as a standard with which deviations (residuals) are compared. We are interested in patterns of deviation along the gradient for which the model is defined.

  10. Steps in model formulation Theory Derivation of questions from ecological theory Question Define the elements (drivers) of the models Do not overparameterise the model Provide a flowchart Validate the model with independent data sets. Assess the degree of imprecision. Assess predictive power Identify the necessary parameters to quantify the drivers Model validation Parameterisation

  11. Null models A null model is a pattern generating model that is based on randomization of ecological data or random sampling from a known or imagined distribution. The null model is designed with respect to some ecological or evolutionary process of interest ’ . (Gotelli and Graves 1996) Classical Person-Neyman hypothesis testing confronts a hypothesis with its counterpart, that is most often a random assumption. Does a IQ of 129 kg deviate from the average IQ of Europeans? We use a Z-test. A Z-test confronts the observation with a distribution ( normal distribution) that is linked to the Z-value. The null assumption refers to a random draw from a normal distribution If Z > 1.96 we accept the hypothesis at the two-sided 5% error level.

  12. Now we want to test whether couples are similar in IQ We have a precise starting hypothesis H0. There is no precisely defined null hypothesis with an associated null (random) distribution. We have to define a null model that simulates random draws of couples from the whole population. Null models often define simulations to obtain a desired random distribution with which the observed pattern is compared. We draw 1000 women and 1000 men at random from the observed distributions and calculate the average IQ difference and the associated standard deviation.

  13. A simple null model A normal random number : =200*(LOS()+LOS()+LOS()+LOS()+LOS()+LOS()+LOS()+LOS()+LOS()+LOS()+LOS()+LOS())/12

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