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Resilience and Innovation Resilience and Innovation
in Complex Systemsin Complex Systems
ResilienceResilience
Resilience is the ability of an system to remain within a state.
Resilience is a measure of the amount of perturbation required to cause a system to change states
Resilience is a cross-scale measure. Ecological resilience depends upon:
– Control of disturbance
– Regulation of renewal
Overlapping Function Within a ScaleOverlapping Function Within a Scale
At the same scale species from different functional groups specialize in the use of different resources, but each guild can use other resources at lower efficiencies.
Use of different resources at same scale
Guild C
Guild B
Guild A
Guild D
Functional Reinforcement Across ScalesFunctional Reinforcement Across Scales
Scale (species body mass)
Guild A
Species from the same guild can utilize the same resource at different scales. Resources that are more dispersed can be utilized be a large animal, but with a decrease in efficiency. Species are performing similar functions at different scales.
Birds and BudwormBirds and Budworm
Use of different resources at same scale
Scale (species body mass)
NectivoreCarnivoreGranivoreInsectivores
As budworm populations increase and occur larger aggregation both larger birds and birds that would not normally consume budworm switch to the use of budworm.This process provides robust control of budworm populations over a wide range of budworm densities.
predation of budworm at different aggregations
small birds large birds
Cross-Scale ResilienceCross-Scale Resilience
Use of different resources at same scale
Scale (species body mass)
Guild DGuild CGuild BGuild A
Overlapping function within scales and functional reinforcement across scales.
At the same scale species from different guilds specialize in the use of different resources, but each guild can use other resources at lower efficiencies. Species in a guild utilize the same resource, but at different scales.
Ecological ScalingEcological Scaling
Scale is the spatial and temporal frequency of a process or structure.
A scale domain is bounded by the grain size of processes detected and the extent or span of processes attended.
-1
0
1
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century
year
month
decade
420- 2- 4- 6
-3
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-4
1 000 yrs
day
hour
1cm
1000km
1km
10m
1m
Log Space (km)
10 000 yrs
Log Time
(years)
Vegetative ScalesVegetative Scales
LOG SPACE- km
-1
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1
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century
year
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decade
420- 2- 4- 6
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1 000 yrs
10 000 yrs
day
hour
1cm
1000km
1km
10km
100m
1m
standpatch
crown
needle
forest
regionBoreal forest, forExample, is patterned across a range of scales.
Larger slower structures usually constrain the behavior of faster smaller scales.
LOG TIME - years
LOG SPACE- km 420- 2- 4- 6
-1
0
1
2
3
4
minute
century
year
month
decade
kmcm m m km1 1001 100
-3
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-4
1 000 yrs
10 000 yrs
day
hour
DisturbanceProcesses
Vegetation
LOG TIME-years
-6
-5
-7
food choice
home range
dispersal & migration
moosebeaver
deer mouse
Herbivorous Mammals
Different species interact with the landscape at different scales.
An animal makes different decisions at different scales.
LOG SPACE - km
-6 -4 -2 0 2 4
LOG
TIM
E -
yea
rs
-2
-1
0
1
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Animal body mass patterns reflect the scale-specific domains of key structuring process.
Textural Discontinuity Hypothesis
Vertebrate body masses are discontinuous
Increasing body mass
A.
B.
C.
Cross-Scale ResilienceCross-Scale Resilience
Use of different resources at same scale
Scale (species body mass)
Guild DGuild CGuild BGuild A
Overlapping function within scales and functional reinforcement across scales.
At the same scale species from different guilds specialize in the use of different resources, but each guild can use other resources at lower efficiencies. Species in a guild utilize the same resource, but at different scales.
© Photohome.com
MethodsMethods
U.S. Census data set incorporating the U.S. Census data set incorporating the Urbanized Area definitionUrbanized Area definition
Bureau of Economic Analysis (BEA) Bureau of Economic Analysis (BEA) regionsregions
Data from the southwestern region of the Data from the southwestern region of the United StatesUnited States
MethodsMethods
Gap Rarity Index (GRI)Gap Rarity Index (GRI) Split moving-window (SMW) Split moving-window (SMW)
boundary analysis boundary analysis Hierarchical cluster analysis Hierarchical cluster analysis Aggregation = 3 or more cities Aggregation = 3 or more cities 48 cities in 1890 to 161 cities in 199048 cities in 1890 to 161 cities in 1990
Ga
p R
arity
In
de
x
0.0
0.2
0.4
0.6
0.8
1.0
Rank
0 10 20 30 40 50
Lo
g C
ity
Siz
e
3.5
4.0
4.5
5.0
5.5
6.0
6.5
1890
1990
1880
1890
1900
1910
1920
1930
1940
1950
1960
1970
1980
1990
2000
3.40 3.90 4.40 4.90 5.40 5.90 6.40
Yea
r
Log10 (City Size)1 2 3 4 5 6 7
Year Largest City1890 Dallas
1900 San Antonio
1910 San Antonio
1920 San Antonio
1930 Houston
1940 Houston
1950 Houston
1960 Houston
1970 Houston
1980 Dallas-Fort Worth
1990 Dallas-Fort Worth
City size distributions for the southwestern region of the United States were discontinuous
Distinct aggregations of cities were identified in each decade, by all methods of analysis.
We observed 4 to 7 aggregations in each decadal dataset
Maintenance of similar discontinuous structure over time suggests this structure is conserved and resilient.
How does the discontinuous distribution of body masses, or other complex system components (e.g., cities)relate to the emergence of innovation and novelty?
The South Florida The South Florida terrestrial terrestrial vertebrate vertebrate faunafauna
NATIVE DECLINE N.I.S.
MAMMALS 35 10(29%) 10(22%)
BIRDS 120 22(18%) 32(21%)
HERPS 49 7(14%) 21(30%)
Historic body mass Historic body mass structure,structure,South Florida vertebratesSouth Florida vertebrates
mam
mal
sm
amm
als
herp
sbi
rds
Increasing body mass
Tests of selected Tests of selected hypotheses in South hypotheses in South Florida:Florida: invasive species don't tend to be smaller than native speciesinvasive species don't tend to be smaller than native species endangered species don't tend to be larger than non-endangered species don't tend to be larger than non-
endangered native speciesendangered native species no gross differences in trophic level between endangered no gross differences in trophic level between endangered
and invasive speciesand invasive species no niche replacementno niche replacement no phylogenetic influence on endangermentno phylogenetic influence on endangerment
Taxonomic groups as replicates; Mann-Whitney Utests, Fisher's exact test, chi-square goodness-of-fit.
Random
In lumps
In gaps
Within asingle scale
At lump edges
Possible patterns of invasive or declining species in terms of lump structure
Null hypothesis.No relationship withbody mass structure.
Hypothesissupported
Gaps are repellant.
Morphologicaloverdispersion -competitivestructuring.
Scale-specific effect or
.Turbulencebetween rangesof scale.
phylogeny
Historic body mass Historic body mass structure,structure,South Florida vertebratesSouth Florida vertebrates
mam
mal
sm
amm
als
herp
sbi
rds
Increasing body mass
Species Rank
0 5 10 15 20 25 30 35
Log
Bod
y M
ass
0
1
2
3
4
5
0 5 10 15 20 25 30 35
Gap
Sta
tistic
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
*
*
Everglades Mammals
INVASIVE SPECIES AND ENDANGERED INVASIVE SPECIES AND ENDANGERED SPECIES ARE NON-RANDOMLY SPECIES ARE NON-RANDOMLY DISTRIBUTED IN RELATION TO THE DISTRIBUTED IN RELATION TO THE BODY MASS DISTRIBUTIONS OF BODY MASS DISTRIBUTIONS OF EVERGLADES ECOSYSTEM VERTEBRATESEVERGLADES ECOSYSTEM VERTEBRATES Invasive species are Invasive species are
successful at the edge of successful at the edge of aggregationsaggregations
Endangered species occur Endangered species occur at the edge of aggregationsat the edge of aggregations
Results are similar for all Results are similar for all taxonomic groups analyzedtaxonomic groups analyzed
RUSSIACANADA
UNITED STATES
MEXICO
CHINA
MONGOLIAKAZAKHSTAN
INDIA
UZBEKISTAN
PAKISTAN
AFGHANISTAN
TURKMENISTAN
KYRGYZSTAN
TAJIKISTAN
NEPALBHUTAN
BANGLADESH
BURMAVIETNAM
THAILAND
LAOS
CAMBODIA
MALAYSIA
INDONESIAPAPUA NEW GUINEA
AUSTRALIA
NEW ZEALAND
GUATEMALA
BELIZEHONDURAS
EL SALVADOR
COSTA RICA
PANAMA
DOMINICAN REPUBLIC
CUBAHAITI
VENEZUELA
COLOMBIA
ECUADOR
PERU
BOLIVIA
GUYANASURINAME
FRENCH GUIANA
BRAZIL
ARGENTINA
CHILE
PARAGUAY
URUGUAY
JAPAN
NORTH KOREA
SOUTH KOREA
PHILIPPINES
TAIWAN
WHY?WHY? NOT due to morphological overdispersion. NOT due to morphological overdispersion.
With the addition of exotics, the result is not a With the addition of exotics, the result is not a continuous distribution; exotics aren't "filling in the continuous distribution; exotics aren't "filling in the gaps".gaps".
Gaps may be analogous to zones of phase transition, Gaps may be analogous to zones of phase transition, and represent zones of crisis and opportunity for and represent zones of crisis and opportunity for species exploiting them.species exploiting them.
Other ecosystems and faunas should reveal the same association between population status (invasive, declining)and body-mass lump edges.
PREDICTION:
TEST:Mexican cave bat community (declining/vulnerable species)Mediterranean-climate faunas (invasive)
Mexican cave bats: - relatively large proportion of vulnerable species- well studied: status not politically derived
Mediterranean -climate faunas:- well studied- relatively large number of invasions
0 5 10 15 20 25 30
Log
Bod
y M
ass
0.4
0.6
0.8
1.0
1.2
1.4
1.6
Species Rank
0 5 10 15 20 25 30
Gap
Sta
tistic
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8*
*
Mexican Cave Bats. Association with scale breaks
Dist. to Edge: Median, End. = 0.00, Median safe = 0.02, M-W P = 0.014
Location N Obs. Exp. PMAMMALS
California 2 2 0.38Chile 11 5 1.63Greece 4 2 0.58South Africa 8 1 1.11Southwestern Australia 8 2 1.14Southcentral Australia 10 5 1.61 0.0001
BIRDS California 18 3 1.59Chile 7 2 0.85South Africa 8 5 0.89Spain 4 1 0.47Turkey 3 0 0.23Southwestern Australia 9 4 1.02 <0.0001
Successful introductions should have body masses closer to body-mass lump edges than unsuccessful introductions.
PREDICTION:
TEST:
Avian introductions in the Everglades sub-ecoregion:
- Well documented- Large number in both categories- Sufficient information to differentiate between species withand without a sufficient propagule
Successful v. unsuccessful introductions in south FloridaLogistic regression
35 successful introductions45 unsuccessful introductions
Variables: body mass, distance to nearest neighbor (in terms of body mass), year of introduction, presence of congeners, distribution in a body mass aggregation or gap, and distance to body-mass aggregation edge (in terms of body mass).
* Successful introductions have body masses that place them closer to body-mass lump edges.
Other variable phenomena reflecting species turnover should be associated with the edge of body mass aggregations.
PREDICTION:
TESTS:
Nomadic birds in South Central Australia:
- Well documented- Large number in both categories
Migrant birds in South Florida, South Carolina and Costa Rica:- Well documented
Significant predictors ofnomadism:(model selection based on AIC)
Parameter WaldVariable estimate Chi-Square Probability
Mass 1.31 14.97 0.0001
Edge -1.21 6.42 0.0113
MedianClass edge distance N T P
Migratory 0.00133 10
Permanent residents 0.0108 96 374.0 0.042
Migratory birds in the south Florida everglades ecosystem:
Migratory birds body masses place them 10 times closer, onaverage, to body mass aggregation edges.
Log Body Mass
-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0
Mammals
Herpetofauna
Avifauna
Historic - Future comparisons of the South Florida fauna
Invasions and extinctions represent turnover in species composition(25% declining in SFL, a further 25% are non-native)
The generation of innovation in complex systems? Entrainment
Hierarchically Structured Landscape
Discontinuous Animal Size Distributions
Species Pool, Continuous Distribution ?
Self Organization
SCALE-SPECIFIC STRUCTURING PROCESSES
Stochastic Climatic and Edaphic Patterns
Vegetation Architecture
Forest Stands Patch
Structure
Forest Patch
Structure
Clump 1 Clump 2 Clump 3
Character Displacement and/or Species Assortment
Over-Dispersed Size Distribution Within Clump
Gap Gap
Competition?
Inter-specific Interactions
Increasing Size
The generation of innovation in complex systems?
Increasing Size
Aggregations Discontinuities
Increasing Size
Var
iatio
n in
res
ourc
esLo
w -
- -
- -
- -
- -
hig
h
Increasing Size
Sta
bilit
y in
com
pone
nts
Low
- -
- -
- -
- -
- h
igh
Increasing Size
Inno
vatio
nLo
w -
- -
- -
- -
- -
hig
h
Variability and innovation between ranges of scales?
The profile
-Nomadic birds in SC Australia.-Migrant birds, Everglades and South Carolina.-Invasive herpetofauna, birds, and mammals,Everglades.-Invasive species, global mediterranean-climate systems.-Declining herpetofauna, birds, and mammals, Everglades.-Declining cave bats, Mexico.
Variability between ranges of scales?The significance
-Understanding of the link between landscape change and the composition of species communities.
-Understanding complex phenomena such as invasions, migration and nomadism.
-Understanding how resilience is generated – turnover at scalebreaks does not alter gross system structure but propagatesinnovation.
- Insight into the evolution of complex behaviors and species.