Habitat preference

Functions
double	edal::Individual::preference_overlap (const Individual &other) const
	Exponent of \(C_y(I, J)\): competition on habitat preference. More...
double	edal::Individual::morphology_overlap (const Individual &other) const
	Exponent of \(C_x(I, J)\): competition on morphology. More...
double	edal::Individual::resource_overlap (const Individual &other) const
	\(C(I, J) = C_x(I,J) C_y(I,J)\) for competition
double	edal::Individual::habitat_preference_exp (const double height, const double diameter) const
	Exponent of \(\Xi(I, u, v)\) in anolis_v2. More...
double	edal::Individual::habitat_preference_quadratic (const double height, const double diameter) const
	\(\Xi(I, u, v)\) quadratic approximation in anolis_v3 More...
double	edal::Individual::calc_DI_analytical () const
	\(D_I\) analytical computation by Mathematica (fast but limited) More...
double	edal::Individual::calc_DI_numerical () const
	\(D_I\) numerical computation (slow) More...
double	edal::Individual::calc_Dxi_analytical () const
	Calculate quadratic \(\Xi(I, u, v)\) normalizer with analytical solution. More...
double	edal::Individual::calc_Dxi_numerical () const
	Numerical integration of quadratic \(\xi(I, u, v)\). More...

Detailed Description

Function Documentation

calc_DI_analytical()

double edal::Individual::calc_DI_analytical ( ) const

private

\(D_I\) analytical computation by Mathematica (fast but limited)

Returns

\(D_I\)

Bug:

not applicable in the parameter range where \(\Xi\) goes negative with high \(h_0\) and \(h_1\).

\[ D_I = \frac {12 - 6 h_0 (1 + 2 (-1 + y_0) y_0) + h_1 (-1 + 4 (1 - 3 y_1) y_1) - \alpha (-24 + h_1 + 6 h_0 (1 - 2 y_0)^2 - 8 h_1 y_1 + 24 h_1 y_1^2) } {12 + 24 \alpha} \]

calc_DI_numerical()

double edal::Individual::calc_DI_numerical ( ) const

private

\(D_I\) numerical computation (slow)

Returns

\(D_I\)

\[ D_I = \int_0^1 \int_0^{1-u} \Xi(y_0,y_1 \mid u,v) F(u,v) dv du \]

calc_Dxi_analytical()

double edal::Individual::calc_Dxi_analytical ( ) const

private

Calculate quadratic \(\Xi(I, u, v)\) normalizer with analytical solution.

Bug:

not applicable in the parameter range where \(\xi\) goes negative with high \(h_0\) and \(h_1\).

\[ \frac{1} 2 -h_0 (\frac{y_0^2} 2 + \frac{y_0} 3 - \frac{1} {12}) -h_1 (\frac{y_1^2} 2 + \frac{y_1} 3 - \frac{1} {12}) \]

calc_Dxi_numerical()

double edal::Individual::calc_Dxi_numerical ( ) const

private

Numerical integration of quadratic \(\xi(I, u, v)\).

\[ \int_0^1 \int_0^{1-u} \xi(y_0,y_1 \mid u,v) dv du = \int_0^1 \int_0^{1-u} \{1 - h_0 (u - y_0)^2 - h_1 (v - y_1)^2\} dv du \]

habitat_preference_exp()

double edal::Individual::habitat_preference_exp ( const double  height, const double  diameter  ) const

private

Exponent of \(\Xi(I, u, v)\) in anolis_v2.

Parameters

height	habitat environment
diameter	habitat environment

Returns

\(\Xi(I, u, v)\) before normalization

\[ \Xi(I,u,v) \propto \exp(-\frac{(u - y_0)^2}{2h_0^2} -\frac{(v - y_1)^2}{2h_1^2}) \]

habitat_preference_quadratic()

double edal::Individual::habitat_preference_quadratic ( const double  height, const double  diameter  ) const

private

\(\Xi(I, u, v)\) quadratic approximation in anolis_v3

Parameters

height	habitat environment
diameter	habitat environment

Returns

\(\Xi(I, u, v)\) before normalization

\[ \Xi(I,u,v) \propto 1 - h_0 (u - y_0)^2 - h_1 (v - y_1)^2 \]

morphology_overlap()

double edal::Individual::morphology_overlap

(

const Individual &

other

)

const

Exponent of \(C_x(I, J)\): competition on morphology.

Parameters

other

individual to interact

Returns

\(C_x(I, J)\)

Return values

1	for individuals with identical preferences

\[ C_x(I,J) = \exp(-\frac{(x_{0,I} - x_{0,J})^2}{2c_x^2} -\frac{(x_{1,I} - x_{1,J})^2}{2c_x^2}) \]

preference_overlap()

double edal::Individual::preference_overlap

(

const Individual &

other

)

const

Exponent of \(C_y(I, J)\): competition on habitat preference.

Parameters

other

individual to interact

Returns

\(C_y(I, J)\)

Return values

1	for individuals with identical preferences

following Roughgarden and others

\[ C_y(I,J) = \exp(-\frac{(y_{0,I} - y_{0,J})^2}{2c_y^2} -\frac{(y_{1,I} - y_{1,J})^2}{2c_y^2}) \]