lactationcurve (Python)

A toolkit for fitting dairy cow lactation curves, evaluating lactation curve characteristics (LCCs) (time to peak, peak yield, cumulative yield, persistency), and computing 305‑day milk yield using the ICAR guideline.

Contact: Meike van Leerdam, mbv32@cornell.edu

Authors: Judith Osei-Tete, Douwe de Kok, Lucia Trapanese & Meike van Leerdam

Initial authored: 2025‑08‑12

Updated: 2026‑02‑12

Main Lactation curve models implemented:

MilkBot – Flexible four-parameter model describing rise, peak, and decline. (Both frequentist and Bayesian fitting available)

Wood – Classic three-parameter gamma function model.

Wilmink – Linear–exponential hybrid model, with fixed or estimated decay rate.

Ali & Schaeffer – Polynomial–logarithmic model for complex curve shapes.

Fischer – Simplified exponential decay model.

Additional models available for a.o. symbolic LCC derivations: Brody , Sikka , Nelder , Dhanoa , Emmans , Hayashi , Rook , Dijkstra , Prasad .

Model Formulas

• Wood : y(t) = a * t^b * exp(-c * t)

• Wilmink : y(t) = a + b * t + c * exp(k * t) with default k = -0.05

• Ali & Schaeffer : t_scaled = t / 340, L = ln(340 / t)

  y(t) = a + b*t_scaled + c*t_scaled^2 + d*L + k*L^2

• Fischer : y(t) = a - b*t - a*exp(-c*t)

• MilkBot : y(t) = a * (1 - exp((c - t)/b) / 2) * exp(-d*t)

Features

• Frequentist fitting (numeric optimization & least squares):
  • Wood, Wilmink, Ali & Schaeffer, Fischer, MilkBot
• Bayesian fitting via MilkBot API:
  • MilkBot
• Lactation Curve Characteristics — symbolic + numeric:
  • time_to_peak, peak_yield, cumulative_milk_yield, persistency
• ICAR procedures cumulative milk yield:
  • Test Interval Method
  • Interpolation Standard Lactation Curve (ISLC) Method
  • Best Predict Method
• Input validation/normalization via validate_and_prepare_inputs
• Caching of symbolic expressions for performance

API Overview

The package is organized into three main modules:

1. lactationcurve.fitting
2. lactationcurve.characteristics
3. lactationcurve.preprocessing

Generated API documentation is available at bovi-analytics.github.io/bovi/lactationcurve.html.

Output Types Summary

| Function | Output |

|---------|--------|

| fit_lactation_curve | Predicted yields (np.ndarray) |

| get_lc_parameters | Tuple of numerical parameters |

| bayesian_fit_milkbot_single_lactation | Dict of MilkBot parameters |

| lactation_curve_characteristic_function | (expr, params, func) |

| calculate_characteristic | float (LCC value) |

| test_interval_method | DataFrame with lactation milk yield totals |

| ISLC | DataFrame with lactation milk yield totals |

| ISLC_original | DataFrame with original grid-based ISLC totals |

| best_predict_method | DataFrame with best-prediction lactation milk yield totals |

The meaning of a TestId

The TestId is an identifier for a lactation. It is not necessarily the same as a cow ID, because a cow can have multiple lactations across calvings. If a TestId column is not provided, the package treats all records as one lactation and creates a default TestId.

Bayesian (MilkBot API)

• Set fitting="bayesian" and model="milkbot" in fit_lactation_curve or calculate_characteristic.
• Provide an API key via .env
• Choose priors via continent="USA" | "EU" | "CHEN" (CHEN supplies published priors from literature).
• The helper bayesian_fit_milkbot_single_lactation(...) normalizes differing API responses.
• The key can be requested by sending an email to Jim Ehrlich jehrlich@MilkBot.com.
• More information about the API can be found here.

Citation

Citing the lactationcurve package

If you use the lactationcurve package in your research, please consider citing it as follows:

van Leerdam, M. B., de Kok, D., Osei-Tete, J. A., & Hostens, M. (2026). Bovi-analytics/bovi: (Insert your used version number here).

Zenodo. https://doi.org/10.5281/zenodo.18715144

A machine-readable citation is included in CITATION.cff.

If you also use the Bayesian fitting functionality that relies on the MilkBot API, please also cite the following paper:

Ehrlich, J.L., 2013. Quantifying inter-group variability in lactation curve shape and magnitude with the MilkBot® lactation model. PeerJ 1, e54.

https://doi.org/10.7717/peerj.54

License

GNU AGPLv3 License