Scaling Revealed by Spatial CrossCorrelation Analysis of Aquatic
Communities and Environmental
Drivers Using R-EMAP Data
Joel Trexler and Evelyn Gaiser
South East Research Center and Department of
Biological Sciences, Florida International
University, Miami, FL USA
CERP Trophic Hypothesis
• Aquatic fauna are monitored
because of their role linking
environmental drivers
controlled by management and
wading birds
• Annual or semi-annual life
cycles yield real-time responses
to management
• Linkage of periphyton mats to
prey populations is a key CERP
hypothesis in the causal model
Regional-scale
environment
Vegetation structure
Landscape configuration
Local-scale
environment
Frequency of drought
Time since end of last drought
Duration and severity of last
drought event
Periphyton standing
stock and composition
Dry season
Prey
concentration
Prey population
size
High-quality food patches
Food intake, foraging aggregation size,
spatial and temporal nesting patterns
Wading Bird
breeding
population size
Large fish
population size
Wading bird
characteristics
Morphology
Foraging Behavior
Directional relationships
Top avian carnivore
Top reptilian carnivore
Top fish carnivore
Reciprocal relationships
Nutrient regeneration
Interm Omniv/Carniv
Infauna Omniv/Carniv
Herb/Detrit
Infauna Herb/Detrit
Refuge
Disturbance/ Hydrology
Basal Food
(Qual + Quant)
Nutrients
CERP-MAP and REMAP
Aquatic Fauna
• CERP-MAP aquatic animals/periphyton for
wet season 2005
– 149 sites with three throw-trap/periphyton
samples each
• REMAP for wet season 2005
– 54 sites with three throw-trap samples each
• See Sargeant poster: #26 for path analysis
CERP-MAP
R-EMAP
A Little Statistics Jargon
with apologies to normal people
• Spatial cross-correlation may be used to
evaluate compromises in inter-dataset
combinations:
– Semivariograms illustrate the correlation of a single
PM between sites at incrementally increasing
distances (scaling)
– Cross-correlations illustrate the correlation between
two different PMs (or a PM and a ‘driver’ variable) at
sites with incrementally increasing distance
Hypothetical Result of Spatial Cross correlation between a
Performance Measure and Environmental Driver
Killifish density and
Periphyton tissue
TP
Sill: Relationship
weakens between
these distances
0.4
No Sill: Relationship
weakens between
these distances
R2
0.3
Algal species composition
and Periphyton tissue TP
0.2
0.1
0
5
10 20 40 80 160
0
5
Distance (km)
10 20 40 80 160
Hypothetical Result of Spatial Cross correlation #2
Anisotropy (directional bias) is possible in flow-linked parameters
Periphyton TP with Water TP
measured perpendicular to flow
Periphyton TP with Water
TP measured upstream
0.4
Predicted if
periphyton is
scouring TP
from water as
it flows
downstream
Typical
relationship
that weakens
with distance
R2
0.3
0.2
0.1
0
5
10 20 40 80 160
0
5
Distance (km)
10 20 40 80 160
Edible Algae (%)
• Measured as the relative abundance of
green algae and diatoms from mat samples
• Though some bluegreens are palatable, this
split is consistent with many literature
sources
• Experimental studies from the Everglades
support this designation (Geddes and
Trexler 2004, Chick et al. 2008, and others)
Edible Algae (%) = Periphyton Tissue TP (ug/g)
90
Edible Algae (%)
80
70
60
50
40
30
20
10
3
4
5
6
Log (Periphyton Tissue Phosphorus)
ENP
LOX
WCA2A
WCA3A
7
Edible Algae (%) = Conductivity (umhos/cm)
90
Edible Algae (%)
80
70
60
50
40
30
20
10
0
200
400
600
800
1000
Conductivity
ENP
LOX
WCA2A
WCA3A
1200
1400
1600
• Initial model = TP +
hydroperiod + DSD +
stem density
50
Edible Algae (%)
Edible Algae (%)
60
40
30
20
10
0
-10
-20
-30
-40
-2
-1
0
1
2
3
Log (Periphyton Tissue Phosphorus)
• Final model:
3
- Tissue TP + Hydroperiod
-
R2
= 0.327
• Partial Regression plots
Edible Algae (%)
2
1
0
-1
-2
-3
-300
-200
-100
0
Log (Hydroperiod)
100
200
Model Fit (R2)
Edible Algae (%) = Tissue TP + Hydroperiod (days)
0.36
0.34
0.32
0.30
0.28
0.26
0.24
0.22
0.20
0.18
0.16
0.14
0
10
20
30
40
50
60
70
80
90
Distance Class (kms)
* Isotropic tests, only
REMAP only
Edible Algae
Model Fit (R2)
• Final model TP +
hydroperiod
• R2 = 0.4899
• Low sample sizes
at shorter distance
classes
• Results suspect
N = 15
0.44
0.42
0.40
0.38
0.36
0.34
0.32
0.30
0.28
0.26
0.24
0.22
0.20
0.18
0.16
0.14
0.12
N = 27
N=6
0
10
20
30
40
50
60
Distance Class
70
80
90
Herbivores (#/m2)
• Measured as the sum of all snails, grass
shrimp, herbivorous fish (sailfin mollies and
flagfish) and tadpoles
• Isotope values grass shrimp suggest animal
prey is consumed, but algae is seen in gut
• Isotope values for other consumers in list
support herbivory or detritivory (Williams
and Trexler, Loftus et al.)
Herbivore Density (log #/m 2)
Herbivores = Edible Algae (%)
6
5
4
3
2
1
0
10
20
ENP
LOX
WCA2A
WCA3A
30
40
50
60
Edible Algae (%)
70
80
90
Herbivores = Conductivity (umhos/cm)
Herbivore Density (log #/m2)
6
5
4
3
2
1
0
0
200
400
600
800
1000
Conductivity
ENP
LOX
WCA2A
WCA3A
1200
1400
1600
• Initial model = Edible algae
+ hydroperiod + DSD +
stem density
• Final model:
- Edible algae + stem density
- R2 = 0.147
• Partial Regression plots
3
2
1
0
-1
-2
-40
-30
-20
-10
0
10
20
30
40
50
60
Edible Algae (%)
3
Log Herbivore Density (#/m^2)
Herbivore Density
(#/m2)
Log Herbivore Density (#/m^2)
4
2
1
0
-1
-2
-3
-4
-3
-2
-1
0
1
2
Log Emergent Stem Density (#/m2)
3
Model Fit (R2)
Herbivore Density (#/m2) = Edible algae (%) + Stem density (#/m2)
Distance Class (kms)
Omnivorous Fishes (#/m2)
• Measured as the sum of all fishes except
herbivores (sailfin mollies and flagfish)
• Isotope values support this designation
• Size limited by throw-trap efficiency to over
several mm and under 8 cm
• Crayfish are treated separately. Isotope values
for both species support detritivory/omnivory
(Loftus et al.)
Omnivore Density (log #/m^2)
Omnivorous Fish Density = Edible Algae (%)
5
4
3
2
1
0
10
20
30
40
50
60
Edible Algae (%)
ENP
LOX
WCA2A
WCA3A
70
80
90
Omnivore Density (log #/m^2)
Omnivorous Fish Density = Conductivity (umhos/cm)
5
4
3
2
1
0
0
200
ENP
LOX
WCA2A
WCA3A
400
600
800
1000
Conductivity
1200
1400
1600
• Initial model = Edible algae
+ hydroperiod + DSD +
stem density
• Final model:
- Edible algae + stem density
- R2 = 0.172
• Partial Regression plots
2
1
0
-1
-2
-3
-40
-30
-20
-10
0
10
20
30
40
50
60
Edible Algae (%)
3
Log Omnivore Density (#/m^2)
Omnivorous Fish
Density (#/m2)
Log Omnivore Density (#/m^2)
3
2
1
0
-1
-2
-3
-4
-3
-2
-1
0
1
2
Log Emergent Stem Density (#/m^2)
3
Omnivore Density (#/m2) = Edible algae
(%) + Stem density (#/m2)
0.32
Model Fit (R2)
0.28
0.24
0.20
0.16
0.12
0.08
0.04
0.00
0
10
20
30
40
50
60
Distance Class
70
80
90
Summary of Spatial Models
Parameter
Final Model
R
2
Max R
Distance
class (kms)
Edible algae
TP +
Hydroperiod
0.3
0.351
10 to 15
Herbivores
Edible algae +
stem density
0.1
0.320
1 to 10
Omnivorous
fish
Edible algae +
stem density
0.2
0.296
10 to 15
Everglades
crayfish
Edible algae
0.1
0.266
1 to 10
Slough
crayfish
Edible algae
0.1
0.476
10 to 15
2
Conclusions
• We noted a robust relationship between
periphyton mat algal composition relevant to
edibility and tissue phosphorus and
hydroperiod (more phosphorus and longer
hydroperiods yielded more edible algae)
• Density of aquatic herbivores and omnivorous
fishes in the size class sampled were positively
correlated with algal edibility and density of
emergent vascular plants
Conclusions
• Periphyton – TP/hydroperiod relationship was
best revealed from syntopic measurements
• Consumer density – periphyton/stem-density
relationships were strongest when measured at 1
to 10 km scale
• Periphyton and consumer difference may be tied
to effects of consumer movements on scaling
Acknowledgements
• South Florida Water Management
District, US Environmental Protection
Agency, and Everglades National Park
have funded CERP-MAP and REMAP
• Pete Kalla, Dan Scheidt, Jennifer
Richards, Brooke Sargeant, Charles
Goss