SORTIE-ND
Software for spatially-explicit simulation of forest dynamics

# Exponential Growth and Resource-Based Mortality

This behavior calculates probability of mortality as a function of growth and some second resource. The identity of the second resource is unimportant and could be anything, from exchangeable calcium levels to soil moisture.

Trees killed by this behavior will have a mortality reason code of "natural".

### Parameters for this behavior

Parameter nameDescription
Exponential Growth-Resource - aThe mortality at zero growth scaled as a function of the resource.
Exponential Growth-Resource - bThe light-dependent mortality parameter.
Exponential Growth-Resource - cThe resource-dependent mortality parameter.
Exponential Growth-Resource - dFunction term d.

### How it works

The probability of mortality for a tree is calculated with the following equation:

Prob = (d + a * R) * exp( -( b + c * R) * G)
where:
• Prob is the annual probability of mortality, as a value between 0 and 1
• R is the amount of the second resource
• G is the amount of radial growth, in mm/yr
• a is the Exponential Growth-Resource - a parameter - the mortality at zero growth scaled as a function of the resource R
• b is the Exponential Growth-Resource - b parameter - the light dependent mortality
• c is the Exponential Growth-Resource - c parameter - the resource dependent mortality
• d is the Exponential Growth-Resource - d parameter

The amount of the second resource is captured in a grid object called Resource. Currently it is up to you to enter a map of the values for this resource grid; for instructions on how to do this, see the Grid Setup Window topic. This behavior does not in any way alter the values in this grid.

The mortality probability as calculated above is an annual probability. For multi-year timesteps, the timestep probability is 1 - (1 - AP)X, where AP is the annual probability and X is the number of years per timestep. Once a tree's timestep survival probability has been calculated, it is compared to a random number to determine whether the tree lives or dies.

### How to apply it

This behavior can be applied to seedlings, saplings, and adults of any species. Any tree species/type combination to which it is applied must also have a growth behavior applied. You must also enter a map of second resource values into the Resource grid.