A Generalized Logistic Regression Model of the ...

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Functional Distribution of Fin Whales. (Balaenoptera physalus) in Catalonian Coasts. Daniel Patón. Área de Ecología. Facultad de Ciencias. Campus de ...
A Generalized Logistic Regression Model of the Functional Distribution of Fin Whales (Balaenoptera physalus) physalus) in Catalonian Coasts

Daniel Patón Área de Ecología. Facultad de Ciencias. Campus de Badajoz. Universidad de Extremadura.

Natalia Amigó; Margarita Junza; Cristina Martín; Eduard Degollada Asociación EDMAKTUB, Barcelona

FIN-WHALE PROJECT This research project is focused towards the analysis of the environmental factors that affect the distribution and movement of Fin Whales in Catalonian coasts.

The project has a duration of five years and includes different interdisciplinary areas of research: identification by drones, GPS Sampling, chlorophyll measurements and

STATISTICAL MODELLING (my small contribution)

The first question: What is the size of the sampling unit?

Scale

Variogram analysis

Gyre

Scale

CONCLUSIONS: 1) The most appropriate unit size is 350 divisions (~46 km2) 2) Anisometry

The second: Models of Kernel density (XY)

Latitude

46 km2 of resolution (~350 divisions)

KernSmooth y Lattice Longitude

Latitude

18 km2 of resolution (~895 divisions)

Longitude

ANNUAL

Latitude

MARCH

Longitude

Latitude

APRIL

Longitude

Latitude

MAY

Longitude

8.0

Logarithm of Density

7.5

March

7.0 6.5 6.0

May

483 m

5.5 5.0

April

4.5 4.0 0.0

0.5

1.0

1.5

Logarithm of Scale

2.0

2

The third: Multifractal analysis of densities

Fractal dimension (Dq)

2.2

2.0

1.8

1.6

1.4

1.2

Global Data -10.0

-8.0

-6.0

-4.0

-2.0

1.0 0.0

2.0

4.0

6.0

8.0

Q momments (Relative densities of whales)

10.0

SAMPLING AREA

Generalized linear models (GLM) are flexible generalizations of ordinary linear regression with non-normal error distributions Outcome

Regression

Family in R

Default Link Function

Binary (1/0)

Logistic

binomial

(link = "logit")

Binary (1/0)

Probit

binomial

(link = "probit")

Normal

Linear

gaussian

(link = "identity")

Continuous

Exponential, chi-square, lognormal, etc…

gamma

(link = "inverse")

Normal but μ and σ unknow

Inverse gamma

inverse.gauss ian

(link = "1/mu^2")

Frequencies (0, 1, 2.. n)

Poisson

poisson

(link = "log")

Unknown

Quasi (approximations to unknow functions)

quasi

(link = "identity", variance = "constant")

Excess of variance: Dispersion parameter is not one

Approximation to binomial

quasibinomial

(link = "logit")

Excess of variance: Dispersion parameter is not one

Approximation to poisson

quasipoisson

(link = "log")

Stepwise Logistic Regression

GLM Generalized Linear Models

Chlorophyll Content CL

Surface Sea Temperature SST Bathymetry BT

FWP = Probability of Fin Whales FWP