Spatial early warning signs - R package

This package helps computing spatial early warning signals of critical
transitions, and metrics commonly-used in the related literature. This has been
initiated by a collaborative project between Sonia Kefi's group
(Institut de Sciences d'Evolution, CNRS, IRD, Université Montpellier, France) and
Vishwesha Guttal's (Center for Ecological Sciences,
Indian Institute of Science, Bangalore, India).

The R package provides several sets of functions related to the computation of
early warning signals of ecosystem tipping points and irreversible
transitions (also known as catastrophic shifts). In particular, it
facilitates computing those indicators, assess their significance and plot
their trends.

To understand the context behind those indicators, and see how they
can be computed, the best way is to have a look at our paper about the package:

Génin, A. , Majumder, S. , Sankaran, S. , Danet, A. , Guttal, V. , Schneider, F. D. and Kéfi, S. (2018), Monitoring ecosystem degradation using spatial data and the R package
'spatialwarnings'. Methods in Ecology and Evolution.

For more advanced users and/or technical questions that may arise,
a FAQ is also available there.

Contributors

Alain Danet, Alexandre Génin (Maintainer),
Vishwesha Guttal, Sonia Kefi, Sabiha Majumder, Sumithra Sankaran, Florian Schneider

spatialwarnings has also benefited from contributions from Angeles Garcia-Mayor, Vasilis Dakos and Koen Siteur

Installation

spatialwarnings is available on CRAN and can be installed through:

install.packages('spatialwarnings')

The development version of this package can be installed using the
devtools package in R:

if ( ! require(devtools) ) {
  install.packages("devtools")
}
devtools::install_github("spatial-ews/spatialwarnings")

The spatial indicators

Ecological systems can suffer drastic transitions such as desertification or
eutrophication, sometimes even after a slight change in one or more external
parameters, such as aridity or nutrient input. These qualitative changes in the
behavior of a system at a threshold represents a critical or bifurcation point,
and can give rise to catastrophic shifts when associated with irreversibility.
A growing body of litterature suggests that a dynamical system should exhibit
certain measurable properties around those critical points.

This package aims at providing a practical set of tools for the detection of
these upcoming critical points in spatial datasets, by using indicators based on
those properties. Some of those indicators fall within broad families around
which the package is centered, such as "generic" spatial indicators or
indicators based on patch-size distributions. Significance of patterns
can be assessed using permutation-based tests and results can be displayed
using familiar summary/plot methods.

In total, spatialwarnings provides the following spatial indicators published
in the literature:

• lag-1 autocorrelation (Moran's I, Dakos et al. 2010)
• Variance (Guttal et al. 2008)
• Skewness (Guttal et al. 2008)
• SDR Ratio (Kéfi et al. 2014)
• Patch-size distribution shape (Kéfi et al. 2011)
• Power-law range (Berdugo et al. 2017)
• Flowlength (Rodriguez et al. 2017)
• Kolmogorov complexity (Dakos et al. 2017)
• Variogram-based indicators (Nijp et al. 2019)
• Clustering of pairs (Schneider et al. 2016)

In addition, this package provides a straightforward way to implement and test
new indicators, so you can design your favorite spatial metric for your
ecosystem of interest.

Code sample

A simple analysis with spatialwarnings can fit in a few lines of code:

> library(ggplot2)
> library(spatialwarnings)
>
> # Compute indicators
> serengeti.ic <- generic_sews(serengeti,
>                              subsize = 5,
>                              moranI_coarse_grain = TRUE)
> serengeti.test <- indictest(serengeti.ic)

> # Textual summary of trends
> summary(serengeti.test)
Generic Spatial Early-Warnings

 Mat. # Mean Moran's I P<null     Skewness P<null     Variance P<null
      1 0.98      0.58 <1e-03 ***    -6.94  0.999        0.011 <1e-03 ***
      2 0.98      0.62 <1e-03 ***    -6.17  0.999        0.012 <1e-03 ***
      3 0.97      0.51 <1e-03 ***    -5.59  0.999        0.015 <1e-03 ***
      4 0.96      0.68 <1e-03 ***    -4.56  0.999        0.022 <1e-03 ***
      5 0.96      0.66 <1e-03 ***    -4.37  0.999        0.024 <1e-03 ***
      6 0.95      0.62 <1e-03 ***    -3.84  0.999        0.031 <1e-03 ***
      7 0.95      0.79 <1e-03 ***    -3.96  0.999        0.034 <1e-03 ***
      8 0.94      0.75 <1e-03 ***    -3.40  0.999        0.041 <1e-03 ***
      9 0.93      0.66 <1e-03 ***    -3.26  0.999        0.040 <1e-03 ***
     10 0.93      0.58 <1e-03 ***    -3.02  0.999        0.040 <1e-03 ***
     11 0.89      0.58 <1e-03 ***    -2.29  0.999        0.054 <1e-03 ***
     12 0.85      0.62 <1e-03 ***    -1.75  0.999        0.074 <1e-03 ***
     13 0.71      0.72 <1e-03 ***    -0.87  0.999        0.131 <1e-03 ***

 Significance tested against 999 randomly shuffled matrices
 Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

> # Plot trends
> plot(serengeti.test, along = serengeti.rain) +
>  geom_vline(xintercept = 593, color = "red", linetype = "dashed") +
>  labs(x = "Annual rainfall",
>       y = "Mean cover/indicator value",
>       title = "Early warning signals of a shift in tree cover in Serengeti, Tanzania (Eby et al. 2016)",
>       subtitle = "Grey ribbons indicate the 5-95% quantiles of the null distribution")

Getting help

There is also a quite thorough user guide with tutorials, answers to technical
problems and examples of analyses at this address:

https://alex.lecairn.org/spatialwarnings-faq.html

We also welcome any question or constructive criticism! Please feel free to
open an issue or send us an email if you have any question about the package, or
would like to see improvements.

Original authors and License

This package is derived from the Dakos et al.'s work on early warnings signals (see also the
reference website for the early-warnings signals toolbox).

This work is licensed under an MIT license. Some code included in unit tests has
been written by Cosma Rohilla Shalizi http://bactra.org/
and is redistributed in its entirety with the source of this R package as
per the recommandations in its README file.

The MIT License (MIT)

Copyright (c) 2015 the authors

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
THE SOFTWARE.

References

Génin, A., Majumder, S., Sankaran, S., Danet, A., Guttal, V.,
Schneider, F. D. and Kéfi, S. (2018),
Monitoring ecosystem degradation using spatial data and the R package
'spatialwarnings'. Methods in Ecology and Evolution.

Kéfi S., Guttal V., Brock W.A., Carpenter S.R., Ellison A.M., et al. (2014)
Early Warning Signals of Ecological Transitions: Methods for Spatial Patterns.
PLoS ONE 9(3): e92097.

Ecologists interested in this package will also probably like the
following review:

Nijp, J. J., Temme, A. J.A.M., van Voorn, George A.K., Kooistra, L.,
Hengeveld, G.M., Soons, M.B., Teuling, A.J. and Wallinga, J. (2019)
Spatial early warning signals for impending regime shifts: A
practical framework for application in real‐world landscapes