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Updated: Feb 7, 2026

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A flexible model for thermal performance curves.

Mauricio Cruz-Loya1, Erin A Mordecai1, Van M Savage2,3,4

  • 1Department of Biology, Stanford University, Stanford, California, USA.

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|February 6, 2026
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Summary
This summary is machine-generated.

We developed flexTPC, a new model for biological temperature responses. It uses interpretable biological parameters and accurately describes thermal performance curves (TPCs) across diverse organisms.

Keywords:
Briereclimate changeectotherminfectious disease ecologylife‐history traitmathematical modeltemperaturethermal performance curvethermal response

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Area of Science:

  • Ecology
  • Evolutionary Biology
  • Physiology

Background:

  • Biological traits often exhibit thermal performance curves (TPCs) modeled phenomenologically or mechanistically.
  • Existing TPC models lack flexibility or biological interpretability.

Purpose of the Study:

  • Introduce flexTPC, a novel model for TPCs.
  • Parameterize TPCs using biologically meaningful quantities.
  • Enable flexible and interpretable modeling of temperature-dependent biological responses.

Main Methods:

  • Developed flexTPC, a model using thermal minimum, optimum, maximum, peak value, and breadth.
  • Applied flexTPC to microbial and entomological datasets.
  • Compared flexTPC performance against the Briere model.

Main Results:

  • flexTPC accurately describes TPCs of varying skewness and breadth.
  • flexTPC demonstrated superior predictive performance compared to the Briere model in tested datasets.
  • The model's parameters are directly interpretable in biological terms.

Conclusions:

  • flexTPC offers a flexible, interpretable, and predictive approach to modeling TPCs.
  • Ideal for studying how thermal responses change with environmental factors or evolve.
  • Facilitates cross-species and cross-trait comparisons of thermal performance.