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General Statistical Scaling Laws for Stability in Ecological Systems

Adam Thomas Clark

Asst. Prof., University of Graz

2 August 2022

adam.clark@uni-graz.at; adamclarktheecologist.com

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Measuring Ecological Stability

Question:

  • What is long-term outcomes in THIS ecological community?
    • Coexistence, composition, productivity, ecosystem feedbacks, etc.

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Example:

  • 24 “Old” Fields
    • Abandoned from agricultural use between 1927 and 2016.
  • Surveyed since 1983
    • >2300 plots measuring vegetative cover and species-level plant biomass

Introduction

Patterns

Scales

Statistics

Future

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Introduction

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Statistics

Future

(Isbell et al. 2019)

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Introduction

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Clark et al. AmNat 2019

Clark et al. J. Ecology 2019

temporal extent, years

Annuals

Ambrosia artemisiifolia

(ragweed)

Erigeron canadensis

(Canadian horseweed)

Schizachyrium scoparium

(little bluestem)

Andropogon gerardii

(big bluestem)

C4 Grasses:

stable

unstable

C3 Grasses

Elymus repens

(quackgrass)

Poa pratensis

(Kentucky bluegrass)

Introduction

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Age (years)

Abundance (% cover)

r0

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empirical

neutral-OF

Levins-OF

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Problems:

  • Predictions vary across:
    • metrics
    • models
    • Scales
  • There is no combination of scales and metrics that guarantees the “correct” answer!!

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?

?

x

✔

✔

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Broader Question:

  • How do I measure and predict long-term outcomes in ecological communities?
    • Empirically tractable
    • Theoretically justified
    • Suitable for a wide range of sites and systems
    • Applicable across scales

Introduction

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Statistical Scaling?:

  • Relationship between CV and spatial scale
  • Holds for any “interpolations” within a region
  • Appears to hold well for extrapolations in some cases too

Wang et al. N. Comm. 2017

Introduction

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Statistical Scaling?:

  • Relationship between CV and spatial scale
  • Holds for any “interpolations” within a region
  • Appears to hold well for extrapolations in some cases too

Wang et al. N. Comm. 2017

Introduction

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x = standardized abundance (N - K)

r = linearized growth rate

t = time

ζ = process noise function

disturbances ~ rNorm(0, σ)

waiting time ~ rExp(λ)

Introduction

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Temporal Scaling:

  • No change with scale for unbiased estimates
  • BUT both r and σ are generally biased for “slow” sampling
  • Can correct based on expected value of variance
    • τ it timespan between observations, Λ is average number of disturbances over time τ

temporal scale (time between measurements)

Introduction

Patterns

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Clark et al. E. Letters 2021

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Spatial and Ecological Scaling:

  • Varies depending on covariance in abundances among species or sites
  • Example above: positive site covariance, negative species covariance

ecological scale (e.g. species vs. functional groups)

spatial scale (plot size)

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(Spatial and Ecological) Scaling of Stability:

  • Simple function of observed values at scale b, extrapolated to scale B
  • Assumes “representative” sampling

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Clark et al. E. Letters 2021

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Caveats:

  • In the real world, many different covariances are possible
    • Positive between species might be most common?
  • In diverse communities, r can behave strangely

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Introduction

Patterns

Scales

Statistics

Future

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Measuring Ecological Stability

Question:

  • How do I measure and predict long-term outcomes in ecological communities?

Answers:

  • Choose stability metrics that can be related to scalable statistical attributes
  • Sample representatively across space or species
  • Apply post-hoc corrections for temporal sampling regime, or implement “fast” sampling relative to system dynamics
  • Methods available on CRAN in the ecostatscale R package

Introduction

Patterns

Scales

Statistics

Future