growthcurves 0.6.2
A package for fitting and analyzing microbial growth curves.
Requires Python: >=3.9

# 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

```bash
pip install growthcurves
```

For development:

```bash
pip install -e ".[dev]"
```

## Quick start

```python
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
spline_fit = gc.non_parametric.fit_non_parametric(t, N, umax_method="spline")
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` | spline_s (smoothing) |
| 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. This provides a flexible, model-free approach that adapts to the data shape. The smoothing parameter `spline_s` controls the balance between fit quality and smoothness (default: `0.01` for tight fit to data).

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:

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

| Parameter  | Meaning                           |
| ---------- | --------------------------------- |
| `spline_s` | Smoothing factor (default: 0.01)  |
| `k`        | Spline degree (default: 3, cubic) |

The smoothing parameter `spline_s` controls the tradeoff between fit quality and smoothness. Lower values produce tighter fits to data; higher values produce smoother curves. The default of 0.01 produces a tight fit that closely follows the data, which can be increased for noisier datasets.

### 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](docs/tutorial/analysis.ipynb). It covers model
fitting, derivative analysis, parameter extraction, and cross-model comparison
using a realistic microbial growth dataset.

## Citation

If you use this package, please cite it as described in [CITATION.cff](CITATION.cff).

## License

GPL-3.0-or-later. See [LICENSE](LICENSE).