User:
Calculation of model coefficients
Storyboard
One way to calculate the coefficients of the ecosystem model is by surveying
- populations,
- its temporal variation and
- environmental parameters
of different situations (locations, times) and apply the technique of least squares.
ID:(1900, 0)
Calculation of model coefficients
Description
One way to calculate the coefficients of the ecosystem model is by surveying\n\n- populations,\n- its temporal variation and\n- environmental parameters\n\nof different situations (locations, times) and apply the technique of least squares.\n
Variables
Calculations
to 
,
then, select the variable: 
to 
Calculations
Variable
Given
Calculate
Target :
Equation
To be used
Equations
Examples
(ID 14290)
For the calculation of the coefficients, a least squares adjustment can be performed. In that case the equation
| $\displaystyle\frac{d n_i }{dt}=( \beta_i + \displaystyle\sum_k( \gamma_{ki} e_k + \delta_{ki} e_k ^2)) n_i + \displaystyle\sum_j \alpha_{ji} n_i n_j $ |
with which you have to adjust the equation
| $\displaystyle\sum_i (\displaystyle\frac{dn_i}{n_i dt}-\beta_i -\displaystyle\sum_k \gamma_{ki} e_k - \displaystyle\sum_k \delta_{ki} e_k ^2 - \displaystyle\sum_j \alpha_{ji} n_j )^2 = min$ |
\n\nwhere you have to add over the values of\n\n
$(n_i, dn_i, dt, e_k )$
(ID 14286)
If we derive the equation
| $\displaystyle\sum_i (\displaystyle\frac{dn_i}{n_i dt}-\beta_i -\displaystyle\sum_k \gamma_{ki} e_k - \displaystyle\sum_k \delta_{ki} e_k ^2 - \displaystyle\sum_j \alpha_{ji} n_j )^2 = min$ |
in
| $\displaystyle\sum_{n,e} (\displaystyle\frac{dn_i}{n_i dt}-\beta_i -\displaystyle\sum_k \gamma_{ki} e_k - \displaystyle\sum_k \delta_{ki} e_k ^2 - \displaystyle\sum_j \alpha_{ji} n_j )= 0$ |
(ID 14285)
If we derive the equation
| $\displaystyle\sum_i (\displaystyle\frac{dn_i}{n_i dt}-\beta_i -\displaystyle\sum_k \gamma_{ki} e_k - \displaystyle\sum_k \delta_{ki} e_k ^2 - \displaystyle\sum_j \alpha_{ji} n_j )^2 = min$ |
in
| $\displaystyle\sum_{n,e} (\displaystyle\frac{dn_i}{n_i dt} e_l -\beta_i e_l -\displaystyle\sum_k \gamma_{ki} e_k e_l - \displaystyle\sum_k \delta_{ki} e_k ^2 e_l - \displaystyle\sum_j \alpha_{ji} n_j e_l )= 0$ |
(ID 14287)
If we derive the equation
| $\displaystyle\sum_i (\displaystyle\frac{dn_i}{n_i dt}-\beta_i -\displaystyle\sum_k \gamma_{ki} e_k - \displaystyle\sum_k \delta_{ki} e_k ^2 - \displaystyle\sum_j \alpha_{ji} n_j )^2 = min$ |
in
| $\displaystyle\sum_{n,e} (\displaystyle\frac{dn_i}{n_i dt} e_l ^2 -\beta_i e_l -\displaystyle\sum_k \gamma_{ki} e_k e_l ^2 - \displaystyle\sum_k \delta_{ki} e_k ^2 e_l ^2 - \displaystyle\sum_j \alpha_{ji} n_j e_l ^2)= 0$ |
(ID 14288)
If we derive the equation
| $\displaystyle\sum_i (\displaystyle\frac{dn_i}{n_i dt}-\beta_i -\displaystyle\sum_k \gamma_{ki} e_k - \displaystyle\sum_k \delta_{ki} e_k ^2 - \displaystyle\sum_j \alpha_{ji} n_j )^2 = min$ |
in
| $\displaystyle\sum_{n,e} (\displaystyle\frac{dn_i}{n_i dt} n_l -\beta_i n_l-\displaystyle\sum_k \gamma_{ki} e_k n_l - \displaystyle\sum_k \delta_{ki} e_k ^2 n_l - \displaystyle\sum_j \alpha_{ji} n_j n_l )= 0$ |
(ID 14289)
ID:(1900, 0)