growthcurves#

A Python package for fitting and analyzing microbial growth curves.

Supports logistic, Gompertz, and Richards parametric models with automatic growth statistics extraction (specific growth rate, doubling time, phase boundaries) and non-parametric methods (spline fitting and sliding window).

Installation#

pip install growthcurves

For development:

pip install -e ".[dev]"

Quick start#

import growthcurves as gc
import numpy as np

# Example time series (hours) and OD measurements
t = np.linspace(0, 24, 100)
N = 0.01 + 1.5 / (1 + np.exp(-0.5 * (t - 10)))  # synthetic logistic data

# Fit a parametric model and extract growth statistics
fit_result = gc.parametric.fit_parametric(t, N, method="mech_logistic")
stats = gc.inference.extract_stats(fit_result, t, N)

print(f"Max OD:               {stats['max_od']:.3f}")
print(f"Specific growth rate: {stats['mu_max']:.4f} h⁻¹")
print(f"Doubling time:        {stats['doubling_time']:.2f} h")

# Or use a non-parametric spline fit
# smooth: "fast" (auto-default), "slow" (GCV), or a float (manual lambda)
spline_fit = gc.non_parametric.fit_non_parametric(
    t, N, method="spline", smooth="fast"
)
spline_stats = gc.inference.extract_stats(spline_fit, t, N)

print(f"\nSpline fit results:")
print(f"Specific growth rate: {spline_stats['mu_max']:.4f} h⁻¹")
print(f"Doubling time:        {spline_stats['doubling_time']:.2f} h")

Available models#

Parametric models#

Mechanistic models (ODE-based)#

Model	Function	Parameters
Mech. Logistic	`models.mech_logistic_model`	mu, K, N0, y0
Mech. Gompertz	`models.mech_gompertz_model`	mu, K, N0, y0
Mech. Richards	`models.mech_richards_model`	mu, K, N0, beta, y0
Mech. Baranyi	`models.mech_baranyi_model`	mu, K, N0, h0, y0

Mechanistic models are defined as ordinary differential equations (ODEs) and fitted using numerical integration.

Phenomenological models (ln-space)#

Model	Function	Parameters
Phenom. Logistic	`models.phenom_logistic_model`	A, mu_max, lam, N0
Phenom. Gompertz	`models.phenom_gompertz_model`	A, mu_max, lam, N0
Phenom. Gompertz*	`models.phenom_gompertz_modified_model`	A, mu_max, lam, alpha, t_shift, N0
Phenom. Richards	`models.phenom_richards_model`	A, mu_max, lam, nu, N0

Phenomenological models are fitted directly to ln(OD/OD0) data.

Non-parametric methods#

Method	Function	Key parameters
Spline	`non_parametric.fit_non_parametric`	`smooth`, `use_weights`
Sliding window	`non_parametric.fit_non_parametric`	`window_points`

The spline method fits a smoothing spline to log-transformed OD data and calculates growth rate from the spline’s derivative. Smoothing is controlled by smooth:

"fast": automatic default lambda rule (fast)
"slow": weighted GCV selection (slower)
float: manual lambda value

The sliding window method estimates growth rate by fitting a linear regression to log-transformed data within a moving window, identifying the window with maximum slope.

Spline fitting (non-parametric)#

The spline method provides a model-free approach to growth curve analysis by fitting a smoothing spline to log-transformed OD data:

Transform OD data: \(y_{\text{log}} = \ln(N)\)
Fit a cubic smoothing spline \(s(t)\) to \((t, y_{\text{log}})\) using scipy.interpolate.make_smoothing_spline
Calculate specific growth rate: \(\mu(t) = \frac{d\,s(t)}{dt}\)
Find maximum growth rate: \(\mu_{\max} = \max_{t} \mu(t)\)

Parameter	Meaning
`smooth`	`"fast"`, `"slow"`, or manual float lambda value
`use_weights`	Apply OD-dependent weighting (default: `True`)

When smooth is a float, higher values produce smoother curves and lower values follow the data more tightly.

Derived growth statistics#

Statistic	Formula
Specific growth rate	\(\mu = \dfrac{1}{N}\dfrac{dN}{dt}\)
Doubling time	\(t_d = \dfrac{\ln 2}{\mu_{\max}}\)

Key features#

Parametric fitting — fit logistic, Gompertz, or Richards models with automatic parameter estimation
Non-parametric methods — model-free growth rate estimation using:
- Spline fitting — smoothing splines on log-transformed data with derivative-based growth rate calculation
- Sliding window — moving window linear fits to log-transformed data
Growth statistics — automatic extraction of max OD, specific growth rate (µ_max), doubling time, and exponential-phase boundaries
Derivative analysis — first and second derivatives with Savitzky-Golay smoothing
No-growth detection — automatic identification of non-growing samples
Model comparison — RMSE fit-quality metric for comparing fits

Documentation and tutorial#

An interactive tutorial notebook is available at docs/tutorial/analysis.ipynb. It covers model fitting, derivative analysis, parameter extraction, and cross-model comparison using a realistic microbial growth dataset.

growthcurves

Contents