THE IMPLICATIONS OF SCALING
APPROACHES FOR UNDERSTANDING
RESILIENCE AND REORGANIZATION
IN ECOSYSTEMS
Date: 29th September
Erica Xie
Email: xiehaojing@hotmail.com
OUTLINE OF PAPER
1. Variability of biological and
ecological at multiple scales
2. Scaling Law in Regularities  E.g.
Scaling of human settlement size,
human fertility, distribution of forest
3. Ecological scaling indicates particular
structuring processes or perturbation of
ecosystem
4. Scaling provide a powerful tool for
understanding resilience in Ecology
BACKGROUND: STATE OF TODAY


Increasing ecological impacts brings by human
beings compel people to manage the dynamic of
ecosystem
Resilience of ecosystem maintains a sustainable
human population and human well beings.
BACKGROUND: STATE OF TODAY


Understanding resilience means identifying
relevant driving variables that reinforce
alternative states of the system of interest, and
the spatial and temporal scales over which those
variables operate
Primary impediments to developing a generalized
ecological theory, is the range of scales
encompassed by ecological phenomena
Driving
State of system
Spatial and
Temporal Scale
BACKGROUND: STATE OF TODAY


Understanding resilience means identifying
relevant driving variables that reinforce
alternative states of the system of interest, and
the spatial and temporal scales over which those
variables operate
Primary impediments to developing a generalized
ecological theory, is the range of scales
encompassed by ecological phenomena
AMAZING SCALE

Mass of a redwood / a bacterium is approximately
1021
CHANGES IN VIEWING OF SCALES
cells
biosphere,
organisms
landscapes,
populations
ecosystems,
communities
ecosystems
communities,
landscapes
populations,
biosphere
organisms,
Cell
WHAT IS ALLOMETRIC SCALING LAW?


Scaling laws are simply empirical generalizations
describing how some property of a system changes
along one of the fundamental dimensions of the
system.
Allometric scaling is common in nature, both when
comparing two animals of different sizes and when
comparing the same animal at two different sizes
(i.e., growth).
WHAT IS ALLOMETRIC SCALING LAW?
Allo = different;
Metric = measure
 When an animal
(or organ or tissue)
changes shape in
response to size changes
does not maintain
geometric similarity,
we say that it scales
allometrically.

WHAT IS ALLOMETRIC SCALING LAW?
Property of interest
e.g., metabolic rate,
species richness
Y=Y0
b
M
Size of the observed entity
(e.g., organism body mass, island
or patch area
Scaling exponent and
coefficient
Normally
used between
species
SCALING OF SINGLE LEVEL V.S. DIFFERENT
DIMENSION


Ecological scaling relationships relate to entities
at a single level of organization, the measured
variables are static, steady-state, or time
averaged, rather than dynamical.
However, the dimensions of the variables are
context independent, continuous, and
quantitative.
HOW SCALING AND RESILIENCE RELATED
Similar: Both highlight the importance of scale in
the development of generalized, predictive
ecological theory
 Difference:

Resilience
Scaling
Dynamic
Steady State
Unpredictability
Predictability
Treat scale in a discrete,
hierarchical fashion
Treat scale more
continuously
HOW SCALING AND RESILIENCE RELATED
HOW SCALING AND RESILIENCE RELATED
Common interest:
They share a common interest in ecological theory
and a common recognition that scale is a critical
consideration for understanding ecological systems.

POWER LAW1: ECOLOGICAL
SCALING IN HUMAN SYSTEMS
 The
number of firms of size S falling off as a
negative power of their size  NS = n0S–α
 Between firm size and environmental impact,
where IS is the impact of a firm of size S 
IS =i0Sβ
these two  NS IS = n0i0Sβ–α
If β>α, the environmental impact increases
more steeply with firm size
 Multiples
POWER LAW2: HUMAN FERTILITY AND
ENERGY USE
 Fertility
of human societies is plotted as a
function of per capita power consumption 
F = a*B –1/3
 (F,
births per female per year)
(B, watts [W])
UTILITY IN ADAPTIVE MANAGEMENT
Calder (2000) illustrates the use of scaling laws
to derive surrogate values in the face of
uncertainty as a powerful tool for adaptive
management in species conservation.
 Involving three-step process:
(1) derivation of the broadest possible scaling
relationships from empirical data,
(2) prediction from the empirical relationships
(3) fine-tuning predictions on the basis of
departures from scaling

ADJUST OF POWER LAW IN HUMAN
FERTILITY AND ENERGY USE


Scaling of fertility with energy use provides a
baseline for understanding variation in human
demography
Incorporating analyses of residual (energyadjusted) fertility and other economic or social
indicators (e.g., literacy, immigration, emigration
rates and other indicators of human well-being)
could enable better understanding of changing
human life histories in a rapidly industrializing
and urbanizing world.
POWER LAW3:PLANT POPULATION AND
COMMUNITIES
Self thinning explanation:
 All individuals share a common allometry of
resource use, which is proportional to metabolic
rate (B), where B is proportional to (∝) mass
raised to the 3/4 power (M3/4);
 All individuals in the population compete for
limiting resources, in steady state, the rate of
resource use approximates resource supply (R).
It follows that the maximum number of
individuals, Nmax , that can be supported per unit
area is related to the average whole plant size as

Nmax ∝R(M-3/4)
POWER LAW3:PLANT POPULATION AND
COMMUNITIES
Multiple the above two Laws:
 Total energy consumed by a species per unit area
is invariant with body size

NB ∝ M-3/4*M3/4 ∝ M,
consistent with the EER
WHAT IS EER

In short, the EER is a type of size-density
relationship that states that total population
energy-fluxes by different species should be
equivalent, regardless of their respective body
masses
EER IN FOREST COMMINITIES

Tree size generally refers to stem diameter (D).
The plant allometric theory predicts, and
empirical data broadly document, that plant
mass is proportional to the 8/3 power of diameter.
Thus, the EER size distribution becomes N ∝ D–2
Explanation:
Multiple the law of number before with biomass
law above:

N ∝(M-3/4), M∝D 3/8
Thus, N ∝ D–2
Size distribution exponents for 226 0.1-hectare
forest plots
Examined data for the mean tree size (D) and total stem
density for disturbed and undisturbed plots of lowland
forests in Nicaragua
EER IN FOREST COMMINITIES
EER distribution appears to provide a reasonable
upper boundary for the data
 Forests from both locales support the hypothesis
that disturbance is manifested in the scaling
properties of forest size structure.

VIDEO TIME!

Geoffrey West: The surprising math of cities and
corporations
DISAGREEMENT IN RESEARCH OF MUNN,
A.,ET.AL RESEARCH OF AUSTRALIAN MARSUPIALS
Firstly, EER may not be a general ecological
‘rule’, and as such it is not universal or
predictive.
 Alternatively, the EER may indeed be causal, but
for reasons that are not yet clear it is not
operating at the continental scale for Australian
marsupials.

IMPLICATION FOR RESILIENCE OF
ECOSYSTEM
The author generated three open questions for us
to think for future work:
 1. If community-level scaling relationships do
represent structural attractors to the system,
what determines the speed and direction of
approach?
 2. How can studies of scaling and resilience
address variability, which is of critical concern
for understanding ecological change? Many
scaling studies deal only with the equilibrium,
average state of the system of interest; what can
they say about variance and covariance?

IMPLICATION FOR RESILIENCE OF
ECOSYSTEM

3. If all of these different communities converge
toward a similar structural state, what is the
implication for biodiversity? Does scaling offer
any insights on the role that species’ ecologies
play in the resilience of ecosystems?
IMPLICATION FOR RESILIENCE OF
ECOSYSTEM
Because resilience is related to the degree of
perturbation that is in some sense tolerable to a
system, modeling the expected levels of ecological
variance is critical.
 Taylor’s power law, which describes the scaling
relationship between mean abundance (m) and
its temporal (or spatial) variance (v) across
populations: v = amb.

IMPLICATION FOR RESILIENCE OF
ECOSYSTEM
The value of the exponent is of particular
interest, because when b < 2, relative variability
(as indexed by the coefficient of variation)
decreases with increasing mean; conversely,
when b > 2, it increases.
 Across a wide variety of animal and plant taxa,
mean-variance scaling exponents generally range
between approximately 1 and 2

DISCUSSION AND SUM UP
Many of the ecological scaling relationships we
have discussed, from community size
distributions to the scaling of population seed
output, appear relatively insensitive to the
diversity and taxonomic composition of the
systems described.
 On the surface, it appears that ecological scaling
may have little to say about the role of individual
species in ecosystems.
 On the contrary, we argue that the generality of
many scaling relationships provides an
indispensable baseline for determining what is
possible and predictable in ecological systems.

WORK CITED
Kurt Andrew Grimm drkurtgrimm.com
 Munn, A. J., Dunne, C., Müller, D. W., & Clauss,
M. (2013). Energy In-Equivalence in Australian
Marsupials: Evidence for Disruption of the
Continent’s Mammal Assemblage, or Are Rules
Meant to Be Broken?. PloS one, 8(2), e57449.
 Kerkhoff, A. J., & Enquist, B. J. (2007). The
implications of scaling approaches for
understanding resilience and reorganization in
ecosystems.Bioscience, 57(6), 489-499.
 Pictures are located in the remarks parts of this
slices

Video:
https://www.youtube.com/watch?v=BAwEQf_VR6
4
 https://www.youtube.com/watch?v=XyCY6mjWO
Pc

ADDITIONAL RESOURCES



Allometry is the study of the relationship of body size
to shape, anatomy, physiology and finally behaviour,
first outlined by Otto Snell in 1892
Allometry is a well-known study, particularly
in statistical shape analysis for its theoretical
developments, as well as in biology for practical
applications to the differential growth rates of the
parts of a living organism's body.
Arguing that there are a number of analogous
concepts and mechanisms between cities and
biological entities, Bettencourt et al. showed a
number of scaling relationships between observable
properties of a city and the city size. GDP,
"supercreative" employment, number of inventors,
crime, spread of disease,[19] and even pedestrian
walking speeds[32] scale with city population.