sars

Species-area relationship curve fitting in Python.

A conceptual mirror of the R sars package (Matthews et al. 2019), native to the Python scientific stack.

Installation

pip install sars

Features

• 20 SAR models — power, logarithmic, asymptotic, sigmoid, and more
• Multi-model inference — fit all models at once, ranked by AICc with Akaike weights
• Model averaging — weighted-average predictions across candidate models
• Bootstrap confidence intervals — percentile-based CIs for averaged predictions
• R-validated — all models tested against R sars package reference values

Quick start

import sars

# Load the built-in Galapagos dataset (Preston 1962)
galap = sars.load_galap()

# Fit a single model
fit = sars.sar_power(galap)
print(fit)
# SARFit(model='power', c=33.1792  z=0.2832, R²=0.4912, AICc=189.03)

# Fit all 20 models and compare
multi = sars.sar_multi(galap)
print(multi.summary[["model", "AICc", "delta_AICc", "weight"]].head())

# Model-averaged predictions
avg = sars.sar_average(galap)
predictions = avg.predict([1.0, 10.0, 100.0])

# Bootstrap confidence intervals
ci = sars.bootstrap_ci(galap, n_boot=100)

Available models

Type	Models
Non-asymptotic	power, powerR, loga, linear, epm1, epm2, p1, p2
Asymptotic convex	koba, monod, negexpo, asymp, ratio
Asymptotic sigmoid	mmf, gompertz, weibull3, weibull4, chapman, betap, heleg

Each model has a dedicated function (e.g. sars.sar_power(), sars.sar_negexpo()) and returns a SARFit object with parameters, R², AIC, AICc, and BIC.

Citation

If you use this software, please cite it:

McMeen, J. (2026). sars: Species-area relationship curve fitting in Python.

References

This package is a Python implementation inspired by the R sars package. The 20 SAR models and multi-model inference framework draw on the following works:

R sars package

• Matthews TJ, Triantis KA, Whittaker RJ, Guilhaumon F (2019). sars: an R package for fitting, evaluating and comparing species-area relationship models. Ecography, 42, 1446-1455.
• Matthews TJ, Guilhaumon F, Triantis KA, Borregaard MK, Whittaker RJ (2016). On the form of species-area relationships in habitat islands and true islands. Global Ecology and Biogeography, 25, 847-858.

SAR model reviews and synthesis

• Triantis KA, Guilhaumon F, Whittaker RJ (2012). The island species-area relationship: biology and statistics. Journal of Biogeography, 39, 215-231.
• Guilhaumon F, Mouillot D, Gimenez O (2010). mmSAR: an R-package for multimodel species-area relationship inference. Ecography, 33, 420-424.
• Tjorve E (2003). Shapes and functions of species-area curves: a review of possible models. Journal of Biogeography, 30, 827-835.
• Tjorve E (2009). Shapes and functions of species-area curves (II): a review of new models and parameterizations. Journal of Biogeography, 36, 1435-1445.

Original model formulations

• Arrhenius O (1921). Species and area. Journal of Ecology, 9, 95-99. (power)
• Gleason HA (1922). On the relation between species and area. Ecology, 3, 158-162. (loga)
• Gompertz B (1825). On the nature of the function expressive of the law of human mortality. Philosophical Transactions of the Royal Society of London, 115, 513-583. (gompertz)
• Kobayashi S (1975). The species-area relation. I. A model for discrete sampling. Researches on Population Ecology, 17, 87-96. (koba)
• Monod J (1950). La technique de culture continue: theorie et applications. Annales de l'Institut Pasteur, 79, 390-410. (monod)
• Morgan PH, Mercer LP, Flodin NW (1975). General model for nutritional responses of higher organisms. Proceedings of the National Academy of Sciences, 72, 4327-4331. (mmf)
• Ratkowsky DA (1990). Handbook of Nonlinear Regression Models. Marcel Dekker, New York. (asymp, ratio)
• Richards FJ (1959). A flexible growth function for empirical use. Journal of Experimental Botany, 10, 290-301. (chapman)
• Rosenzweig ML (1995). Species Diversity in Space and Time. Cambridge University Press. (powerR)
• Ulrich W, Buszko J (2003). Self-similarity and the species-area relation of Polish butterflies. Basic and Applied Ecology, 4, 263-270. (p1, p2)
• Weibull W (1951). A statistical distribution function of wide applicability. Journal of Applied Mechanics, 18, 293-297. (weibull3, weibull4)
• Minami M, Lennert-Cody CE, Gao W, Roman-Verdesoto M (2007). Modeling shark bycatch: the zero-inflated negative binomial regression model with smoothing. Fisheries Research, 84, 210-221. (betap)

Threshold models

• Matthews TJ, Rigal F (2021). Thresholds and the species-area relationship. Frontiers of Biogeography, 13, e49404.