lsw_sews: Indicators based on the LSW distribution

In spatialwarnings: Spatial Early Warning Signals of Ecosystem Degradation

Indicators based on the LSW distribution

Description

LSW indicators for systems with density-dependent aggregation

Usage

lsw_sews(mat, wrap = FALSE)

raw_patch_radii_skewness(mat, wrap = FALSE)

raw_lsw_aicw(mat, wrap = FALSE)

Arguments

mat	A logical matrix (TRUE/FALSE values) or a list of such matrices
wrap	Determines whether patches are considered to wrap around the matrix when reaching on of its edges

Details

In systems where a mobile resource or consumer can be fixed in space by a sessile species, specific patterns are expected to appear. Such systems can include situations where nutrients available in the environmeent are fixed by a sessile species (e.g. seagrasses or corals), or where the behavior of herbivores is altered to restrict them to certain areas (see full theoretical background in Siteur et al. 2023).

In those systems, as environmental conditions change and the global density of the sessile species decreases, its spatial structure is expected to change. The area of patches of the sessile species (as measured by their radii, which assumes circular patches), is expected to go from a log-normal to a Lifshitz–Slyozov–Wagner (LSW) distribution. Thus, measuring how close the observed distribution of radii are to those two candidate distributions can constitute an indicator of ecosystem degradation.

This function measures this through the relative support based on AIC for the two distributions (equal to 1 when the empirical distribution is best-approximated by an LSW, and 0 when it is a log-normal distribution (dlnorm), and the skewness of the observed patch radii, which should approach a value around -0.92 as conditions worsen.

Value

lsw_sews returns an object of class simple_sews_single (a list) if mat is a single matrix or an object of class simple_sews_list if mat is a list. You probably want to use some of the methods written for these complicated objects instead of extracting values directly (they are displayed using print(<object>)).

Author(s)

This code has received contributions from Koen Siteur

References

Siteur, Koen, Quan-Xing Liu, Vivi Rottschäfer, Tjisse van der Heide, Max Rietkerk, Arjen Doelman, Christoffer Boström, and Johan van de Koppel. 2023. "Phase-Separation Physics Underlies New Theory for the Resilience of Patchy Ecosystems." Proceedings of the National Academy of Sciences 120 (2): e2202683120. https://doi.org/10.1073/pnas.2202683120.

See Also

dLSW, dda, raw_patch_radii_skewness, raw_lsw_aicw

Examples

data(dda)
data(dda.pars)

# Compute all indicators at once (skewness and relative AIC support)
indics <- lsw_sews(dda)
plot(indics, along = dda.pars[ ,"tau"]) 

# Compute individual indicators 

# Skewness of the distribution of patch radii
radii_skewness <- compute_indicator(dda, raw_patch_radii_skewness)
plot(radii_skewness, along = dda.pars[ ,"tau"])

# Aic weight of LSW distribution relative to a lognormal distribution. tau here 
# represents the density at equilibrium in Siteur et al's model (2023)
lsw_aicw <- compute_indicator(dda, raw_lsw_aicw)
plot(lsw_aicw, along = 1 - dda.pars[ ,"tau"])

spatialwarnings documentation built on Sept. 11, 2024, 8:55 p.m.