Modelling in EcologyPredictions in ecology rely on models.

1. What is a model?2. Matrix algebra3. Linear regression models4. More on regression5. Variance analysis6. Model selection techniques7. Classification techniques8. Eigenvector techniques9. More on eigenvectors10. Species distribution modelling

Our program

What is a model?

A biological model is a formal representation of any biological process.

Models serve to1. Simplify a process2. Make a process analytically tractable3. Identify basic patterns4. Identify basic variables (drivers)5. Make qualitative predictions6. Make quantitative predictions7. Derive testable hypotheses8. 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:1. Analytical models2. Descriptive models3. Simulation models

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

A descriptive (qualitative) model of slug carcass colonisation

HyperparasitoidsIdiotypa nigricepsBasalys parva

Aspilota AAspilota BAspilota C

Aspilota COrthostigma

sp

Megaselia ruficornis

Megaselia pulicaria

Arion aterNecrophilus

spp.Carabus spp.

Aspilota AAspilota E

Kleridotoma psiloides

Pentapleura sp.

Gymnophora arcuata Limosina sp.

Conicera schnittmani

Fannia immuticaPsychoda sp

Time

Primary parasitoids

Necrophagous flies

Modelling starts with a graphical representation

The classical Silver Springs semi-quantitative model of ecosystem functioning by H. T. Odum (1971)

Industry Emmisions according to the credits

Local authorities permit emmisssions

Carbon credits

Lower emmissionsTrading credits with

other firms

Higher emmissions

Payment

Trading for other

permisions

The carbon credit system

Modelling is essentially a trade-off (compromise) between

1. Generality

2. Realism 3. Precision

1. A good model does not only refer to a special case but allows for some generalisation.2. A model must be realistic with regard to its components and drivers.3. 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.

Generality

Precision

RealismTrade-off

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.

Steps in model formulation

Question

Define the elements (drivers)

of the models

Provide a flowchart

Identify the necessary parameters to quantify

the drivers

Parameterisation

Model validation

Derivation of questions from ecological theory

Theory

Validate the model with independent data sets.Assess the degree of imprecision.Assess predictive power

Do not overparameterise the model

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 andGraves 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

𝑍=𝐼𝑄𝑜𝑏𝑠−100

16

If Z > 1.96 we accept the hypothesis at the two-sided 5% error level.

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.

𝑍=∆ 𝐼𝑄𝑜𝑏𝑠−∆ 𝐼𝑄𝑒𝑥𝑝

𝜎𝑒𝑥𝑝

No Man Women Difference Mean StdDev Sorted difference

1 108.0663 100.8933 7.17302718 18.69119 14.33454 0.0561372 101.56 97.71983 3.84015654 0.1225293 113.0535 91.11541 21.9381392 0.1359074 112.5138 54.19814 58.3156358 0.1724035 108.824 133.0608 24.2368334 0.2081916 96.56909 81.69813 14.8709596 0.2343217 92.56258 85.86978 6.69279548 0.2378168 89.25959 104.8233 15.563699 0.2404579 116.8267 104.3472 12.479416 0.247577

10 91.39247 94.35775 2.9652841 0.26128311 115.4509 104.732 10.7189372 0.38798412 117.4005 90.29505 27.1054905 0.43461413 100.6308 100.6055 0.02535964 0.49097514 135.1346 112.7228 22.4118914 0.49212715 94.76996 102.7935 8.02354206 0.63451116 93.1209 128.9127 35.791814 0.64309417 91.30526 109.593 18.2877524 P 0.67198518 139.0272 111.6272 27.3999306 0.018 Observed 0.68962819 64.0826 95.93364 31.8510337 0.703756

A normal random number :=200*(LOS()+LOS()+LOS()+LOS()+LOS()+LOS()+LOS()+LOS()+LOS()+LOS()+LOS()+LOS())/12

A simple null model