Larval Headcapsule Log Growth Ratio Tool

Description

widthRatio = secondWidth/firstWidth; logIncrementPerInstar = ln(widthRatio)/instarSteps; dyarRatio = widthRatio^(1/instarSteps).

Development and size-growth summaries depend on temperature thresholds, elapsed exposure and the number of developmental steps. A degree-hour or geometric width ratio is a model term, not an independently established developmental stage.

widthRatio = secondWidth/firstWidth; logIncrementPerInstar = ln(widthRatio)/instarSteps; dyarRatio = widthRatio^(1/instarSteps).

When to use this tool

Use Larval Headcapsule Log Growth Ratio when checking a supplied thermal-exposure or per-instar growth term.

How to use the tool and how it works

Enter firstWidth, secondWidth, instarSteps. Use the units and conventions below.
Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
Read widthRatio, logIncrementPerInstar, dyarRatio. Use the output convention below.

Require positive firstWidth and secondWidth and positive whole instarSteps. widthRatio = secondWidth/firstWidth; logIncrementPerInstar = ln(widthRatio)/instarSteps; dyarRatio = widthRatio^(1/instarSteps).^[1]

Input field	Meaning and units	Accepted input
firstWidth	First Width	Required. Finite number; strictly above 0.
secondWidth	Second Width	Required. Finite number; strictly above 0.
instarSteps	Positive whole number of developmental steps separating the measured widths.	Required. Safe integer; minimum 1.

Output field	Interpretation	Returned shape
widthRatio	Width Ratio	Required. Finite number.
logIncrementPerInstar	Log Increment Per Instar	Required. Finite number.
dyarRatio	Dyar Ratio	Required. Finite number.

json

{
  "input": {
    "firstWidth": 1,
    "secondWidth": 4,
    "instarSteps": 2
  },
  "output": {
    "widthRatio": 4,
    "logIncrementPerInstar": 0.6931471805599453,
    "dyarRatio": 2
  }
}

Limitations and assumptions

Use one width unit. This geometric-growth summary assumes the supplied instar separation; it does not assign instars or prove that growth follows Dyar's rule.
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 a species-appropriate validated development model when predicting stages, emergence or seasonal timing.

References

Calculation and input contract: entomology/larval-headcapsule-log-growth-ratio — tool.io

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