Description
Apply one explicit Euler step of a supplied colonization-extinction occupancy model without clipping its result.
Ecological growth and scaling models express a chosen relationship between population, area, body mass or occupied patches. Supplied rates and exponents are model assumptions; a finite step can leave the intended physical domain.
Apply one explicit Euler step of a supplied colonization-extinction occupancy model without clipping its result.
When to use this tool
Use Patch Colonization Extinction One Step Term when checking one declared ecological growth or scaling term.
How to use the tool and how it works
- Enter occupiedFraction, colonizationRate, extinctionRate, step. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read colonizationFlux, extinctionFlux, nextFraction. Use the output convention below.
Require occupiedFraction in [0,1] and nonnegative colonizationRate, extinctionRate and step. colonizationFlux = c*p*(1-p); extinctionFlux = e*p; nextFraction = p+step*(colonizationFlux-extinctionFlux).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| occupiedFraction | Occupied Fraction | Required. Finite number; minimum 0; maximum 1. |
| colonizationRate | Colonization Rate | Required. Finite number; minimum 0. |
| extinctionRate | Extinction Rate | Required. Finite number; minimum 0. |
| step | Step | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| colonizationFlux | Colonization Flux | Required. Finite number. |
| extinctionFlux | Extinction Flux | Required. Finite number. |
| nextFraction | Unclamped explicit Euler occupancy step; can leave [0,1]. | Required. Finite number. |
{
"input": {
"occupiedFraction": 0.5,
"colonizationRate": 0.4,
"extinctionRate": 0.1,
"step": 1
},
"output": {
"colonizationFlux": 0.1,
"extinctionFlux": 0.05,
"nextFraction": 0.55
}
}Limitations and assumptions
- Rates and step must share a time basis. This explicit Euler step is not clamped to [0,1] and may leave the physical domain; it is not a fitted metapopulation model.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Use validated parameters, appropriate time steps and suitable data to assess a real population or extrapolation.
References
Similar or alternative tools
- Population Doubling Discrete Growth Factor
factor = (1+annualFraction)^years; population = initialPopulation*factor; doublingYears = ln(2)/log1p(annualFraction).
- Lotka Volterra Competition One Term
effectiveLoad = population+competitionCoefficient*competitor; growth = growthRate*population*(1-effectiveLoad/capacity).