Core Model Structure

First step


The first step is to enter a few of parameters for population structure - as well as number of populations (i.e. regions) - for the model.


Note: all fields left blank will either throw an error or default to a value of 0. If needed, you can switch to a tutorial / walk-through of the model by clicking the following button.



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Adjusted Leslie Matrix Equation

Leslie variables:
    age: i
    time: t
    male: m
    female: f
    Age-class weight: w
    survival: s

We use an adjusted Leslie Matrix model expressed in terms of parameters listed above. This equation corresponds to a two-sex model structure.

$$ \begin{eqnarray*} x_{1m}(t+1) & = & s_{0m} \sum_{i=1}^{n} b_{im}x_{if}(t) \nonumber \\ x_{i+1 \, m}(t+1) & = & s_{im} x_{im}(t) \ \ i=1,\dots, n-2 \\ x_{n \, m}(t+1) & = & s_{n-1 \, m} x_{n-1 \, m}(t) + s_{n m} x_{nm}(t) \nonumber \end{eqnarray*} $$



Adjusted Leslie Matrix:
Calculating Density Dependence

This Population Viability Analysis (PVA) application uses an adjusted Leslie Matrix structure with initial number of individuals, survival rates, and birth rates (for females if two-sex is used) in some set number of age-classes (n variable in figure). Population biomass is calculated as well as stocking and harvesting amounts and intervals (set later in this application).


Connectivity and proclivity:
Node to Node Connectance

This example figure shows a three population (i.e. three regions) with relative region-fitness from density dependence of young as well as region-to-region connectivity (arrows). In later pages we will set carrying capacity values and density dependence scalars for young, old, and mature-males (if two-sex).









Number of Regions

Enter the number of metapopuations (or regions):


The number of regions can be between 1 - 3. A three-region meta-population model will have connectance between nodes 1-2, nodes 1-3, and nodes 2-3 (and vice versa).



Number of Age Classes

Enter the number of age classes for this PVA:


The number of age classes can be between 1 - 10 per sex. Thus, a two-sex PVA structure could have up to 20 age classes (10 males and 10 females).



One or Two Sex

Enter whether or not this is a one or two sex model:


Note: if using the two-sex option, the number you entered for age-classes will be doubled so that there are that many age-classes for both males and females.



Create Framework

After entering all of the data:


Generate a responsive PVA framework based on the number of nodes and age classes. In the next page, you can add region and age class specific demographic and environmental rates.

Next: enter population parameters