# Insects

## Simple degree-days model of temperature influence on development of plants and invertebrates

ModelId:
DegreeDays1
SimileVersion:
4.0

The development rate of plants and invertebrate animals often depends on amount of heat received while the ambient temperature is between minimum and maximum thresholds.

The number of degree-days is a commonly used statistic related to the development of plants and invertebrates. Degree-days, DD, is given by:

DD = ∫ Tt.dt

• T is temperature in degrees Celsius (could be Fahrenheit)
• t is time in days.

degree-days is then oC days or oF days.

Equations:

Compartment DegreeDays : Degree days

Initial value = 0
Rate of change = + dDt on dt
Also called temperature sum or less accurately "heat sum".

Flow dDt on dt : Rate of accumation of degree-days (degC)
dDt on dt = max(T_m-T_thresh,0)
Where:
T_m=../Environment/T_m

Variable Sdevelopment : State of development
Sdevelopment = min(DegreeDays/DDreq,1)
Value = 0 to 1

Equations in Environment

Variable T_m : Mean daily temperature

Results:

## Budworm population dynamics

ModelId:
budworm1
SimileVersion:
5.x

This is a simple, two-compartment model of the interaction between a spruce budworm population and the forest resource (foliage biomass) that it depends upon. As the budworm population expands, it tends to eat out the foliage, leading to a population crash and the eventual recovery of the forest.

Equations:

Compartments:

forest: initial value = 1
budworm: initial value = 10

Flows:
ageing = (if forest<4 then 0.02 else 0)
regression = (if budworm>300 then forest-1 else 0)
recruitment = forest*graph(0,400,400,5,0,400,1,21,points(292,315,346,346,328,311,302,301,301,308,318,327,332,339,345,346,348,352,352,352,353),budworm)*budworm where[budworm=budworm,forest=forest]

Model tags: