QUANTITATIVE LAWS June 13 -June 24

1. Covariations in ecological scaling
laws
fostered by eco-evolutionary
dynamics
Silvia Zaoli
Andrea Giometto
Amos Maritan
Andrea Rinaldo

2. Silvia Zaoli - EPFL 2
Prob to find a species
of mass m
Community size-spec
Kleiber’s law
“Damuth’s law”
Species-Area
Ecological scaling laws
A= area of the
ecosystem
S= # species in the
ecosystem
m = body mass
n = abundance
Recurrent power-law patterns in ecosystems:
0 1z  0 
0 
[0,1] 
( )p m m

 0 
Relationships between two quantities Probability distributions of a quantity
|n m A m
 
  
b m


LINKED by
consistency and by
constraint on total
metabolism
   
m

m

m

(( |) )p ms m n m  

3. Silvia Zaoli - EPFL 3
Unified theoretical framework for ecological laws
( , | )P n m A
How does this probability distribution look like?
CONSISTENCY
ENSURED
Stochastic model of eco-evolutionary dynamics
| ,n m A 
( | )s m A
( | )P m A
Dynamics: birth, death, speciation
Zaoli et al., Covariations in ecological scaling laws fostered by eco-evolutionary dynamics, Submitted
Analytical characterization of the stationary state:
1
( , | ) ( | , ) ( | )
| ,
P n m A P n m A P m A n
n
m G
n m A
   
 
 




4. Silvia Zaoli - EPFL 4
Linking of ecological scaling laws
( , | )P n m A Scaling laws
Linking relationships among scaling exponents
Constraint on total metabolism TOT
B A 
Zaoli et al., Covariations in ecological scaling laws fostered by eco-evolutionary dynamics, Submitted
• Ecological patterns are linked and they influence each other
• Different values are possible for exponents, as long as the set (for a given ecosystem)
satisfies the relationships
Conclusions

5. THANK YOU FOR
YOUR ATTENTION
Collaborators Andrea Rinaldo, Amos Maritan, Andrea Giometto
Funding
EPFL
Suisse National Science
Foundation (SNF)