Integrating coevolution into the tree of life
0
𝝉𝟏
𝝉𝟐
𝝉𝒑
Scott L. Nuismer
What is coevolution?
Species 1
Species 2
Coevolution: Reciprocal evolutionary
change in interacting species
(Janzen, 1980)
"Thus I can understand how a flower and a bee might
slowly become, either simultaneously or one after the
other, modified and adapted to each other in the most
perfect manner, by the continued preservation of all the
individuals which presented slight deviations of
structure mutually favourable to each other."
— Charles Darwin, The Origin of Species
The importance of coevolution
Much of what we know about coevolution comes from mathematical models
A key assumption of coevolutionary theory
A key assumption of comparative methods
The current state of affairs
Coevolutionary theory
ignores phylogeny
Phylogenetic comparative
methods ignore coevolution
This raises two important questions
Question 1:
Do coevolution and
phylogeny interact to shape
contemporary trait values?
Question 2:
Can we predict contemporary
rates of interaction?
Our goal is to use a mathematical model to answer these questions
Merging coevolution and evolutionary history
Species 1
Species 2
+
A general modeling approach
First time interval
Second time interval
Third time interval
(no coevolution)
(2-way coevolution)
(3-way coevolution)
Our approach will be agnostic with respect to the process of speciation
How do traits mediate interactions?
Model 1: Phenotype Differences
𝑃𝑖𝑗 =
1
1 + 𝐸𝑥𝑝[𝛼 𝑧𝑖 − 𝑧𝑗 ]
How do traits mediate
interactions
𝑃𝑖𝑗
𝑧𝑖
𝑧𝑗
Best suited for interactions that depend on interference competition
How do traits mediate interactions?
Model 2: Phenotype Matching
2
𝑃𝑖,𝑗 = 𝐸𝑥𝑝[−𝛼 𝑧𝑖 − 𝑧𝑗 ]
How do traits mediate
interactions
𝑃𝑖,𝑗
𝑧𝑗
𝑧𝑖
Best suited for interactions that depend on exploitation of shared resources
Predicting trait coevolution
Individual fitness
𝑛
𝑊𝑖 = 1 − 𝑠𝑖
𝑓𝑗 𝑃𝑖𝑗
𝑗=1
Random encounters
among individuals
Gaussian trait
distributions
Classical
quantitative genetics
∆𝒛 𝒊 = 𝑮 𝒊
𝟏 𝝏𝑾𝒊
+ 𝜺𝒊
𝑾𝒊 𝝏𝒛𝒊
Coevolutionary dynamics on a star phylogeny
Phenotype differences
Phenotype matching
𝑛
∆𝑧𝑖 ≈ 𝐺𝑖
𝑛
𝑓𝑗 𝑆𝑗 + 𝜉𝑖
𝑗=1
How do traits mediate interactions
∆𝑧𝑖 ≈ 𝐺𝑖
𝑓𝑗 𝑆𝑗 𝑧𝑖 − 𝑧𝑗 + 𝜉𝑖
𝑗=1
How do traits evolve?
Integrating evolutionary history:
Phenotype differences
𝑃𝑖𝑗 =
1
1 + 𝐸𝑥𝑝[𝛼 𝑧𝑖 − 𝑧𝑗 ]
How do traits mediate
interactions
𝑃𝑖𝑗
𝑧𝑖
𝑧𝑗
Best suited for interactions that depend on interference competition
Integrating evolutionary history
First interval:
After speciation
Before speciation
𝜇1,𝜏1 = 𝜇1,0
2
𝜎1,𝜏
1
= 𝐺 𝑛 𝜏1
𝜇1,𝜏1 = 𝜇1,0
𝜇2,𝜏1 = 𝜇1,0
2
𝜎1,𝜏
= 𝐺 𝑛 𝜏1
1
2
𝜎2,𝜏
= 𝐺 𝑛 𝜏1
1
𝜎12,𝜏1 = 𝐺 𝑛 𝜏1
0
𝝉𝟏
Integrating evolutionary history
After speciation
Second interval:
𝜇1,𝜏2 = 𝜇1,0 + 𝐺𝑆 𝜏2 − 𝜏1
Before speciation
𝜇2,𝜏2 = 𝜇1,0 + 𝐺𝑆 𝜏2 − 𝜏1
𝜇1,𝜏2 = 𝜇1,0 + 𝐺𝑆 𝜏2 − 𝜏1
𝜇3,𝜏2 = 𝜇1,0 + 𝐺𝑆 𝜏2 − 𝜏1
𝜇2,𝜏2 = 𝜇1,0 + 𝐺𝑆 𝜏2 − 𝜏1
2
𝜎1,𝜏
= 𝐺 𝑛 𝜏2
2
2
𝜎1,𝜏
= 𝐺 𝑛 𝜏2
2
2
𝜎2,𝜏
= 𝐺 𝑛 𝜏2
2
2
𝜎2,𝜏
= 𝐺 𝑛 𝜏2
2
𝜎12,𝜏2 = 𝐺 𝑛 𝜏1
2
𝜎3,𝜏
= 𝐺 𝑛 𝜏2
2
𝜎12,𝜏2 = 𝐺 𝑛 𝜏1
𝜎13,𝜏2 = 𝐺 𝑛 𝜏2
𝜎23,𝜏2 = 𝐺 𝑛 𝜏1
0
𝝉𝟏
𝝉𝟐
Integrating evolutionary history
Third interval:
𝜇1,𝜏2 = 𝜇1,0 + 𝐺𝑆 𝜏3 − 𝜏1
𝜇2,𝜏2 = 𝜇1,0 + 𝐺𝑆 𝜏3 − 𝜏1
𝜇3,𝜏2 = 𝜇1,0 + 𝐺𝑆 𝜏3 − 𝜏1
2
𝜎1,𝜏
= 𝐺 𝑛 𝜏3
2
2
𝜎2,𝜏
= 𝐺 𝑛 𝜏3
2
2
𝜎3,𝜏
= 𝐺 𝑛 𝜏3
2
𝜎12,𝜏2 = 𝐺 𝑛 𝜏1
𝜎13,𝜏2 = 𝐺 𝑛 𝜏2
0
𝝉𝟏
𝝉𝟐
𝝉𝟑
𝜎23,𝜏2 = 𝐺 𝑛 𝜏1
This result can be easily generalized for any phylogeny
⋯
Coevolution and phylogeny do not interact
Phylogeny explains phenotypic similarity
Coevolution explains expected trait values
Contemporary interactions can be predicted
Expected outcome?
Expected asymmetry?
1
𝑃𝑖𝑗 ≈
2
𝛼2 𝐺
𝐴≈
𝜏 − 𝜏𝑖𝑗
2 𝑛 𝑝
How do traits mediate interactions
How do traits evolve?
Integrating evolutionary history:
Phenotype matching
2
𝑃𝑖,𝑗 = 𝐸𝑥𝑝[−𝛼 𝑧𝑖 − 𝑧𝑗 ]
How do traits mediate
interactions
𝑃𝑖,𝑗
𝑧𝑗
𝑧𝑖
Best suited for interactions that depend on exploitation of shared resources
Integrating evolutionary history
First interval:
After speciation
Before speciation
𝜇1,𝜏1 = 𝜇1,0
2
𝜎1,𝜏
1
= 𝐺 𝑛 𝜏1
𝜇1,𝜏1 = 𝜇1,0
𝜇2,𝜏1 = 𝜇1,0
2
𝜎1,𝜏
= 𝐺 𝑛 𝜏1
1
2
𝜎2,𝜏
= 𝐺 𝑛 𝜏1
1
𝜎12,𝜏1 = 𝐺 𝑛 𝜏1
0
𝝉𝟏
Integrating evolutionary history
After speciation
Second interval:
𝜇1,𝜏2 = 𝜇1,0
Before speciation
𝜇1,𝜏2 = 𝜇1,0
2
𝜎2,𝜏
=
2
𝐺 −1 + 𝑒 4𝑆
𝜏2 −𝜏1
+ 4𝑆 𝜏1 + 𝜏2
8𝑛𝑆
𝐺 −1 + 𝑒 4𝑆
𝜎12,𝜏2 =
𝜇3,𝜏2 = 𝜇1,0
2
𝜎1,𝜏
2
𝜇2,𝜏2 = 𝜇1,0
2
𝜎1,𝜏
=
2
𝜇2,𝜏2 = 𝜇1,0
𝜏2 −𝜏1
+ 4𝑆 𝜏1 + 𝜏2
=
2
𝜎2,𝜏
=
2
2
𝜎3,𝜏
=
2
𝐺 −1 + 𝑒 4𝑆
𝐺 1−𝑒
+ 4𝑆 𝜏1 + 𝜏2
8𝑛𝑆
𝐺 −1 + 𝑒
𝐺 −1 + 𝑒
4𝑆 𝜏2 −𝜏1
𝝉𝟏
𝝉𝟐
+ 4𝑆 𝜏1 + 𝜏2
8𝑛𝑆
𝜎12,𝜏2 =
𝜎13,𝜏2 =
𝜎23,𝜏2 =
0
+ 4𝑆 𝜏1 + 𝜏2
8𝑛𝑆
4𝑆 𝜏2 −𝜏1
8𝑛𝑆
4𝑆 𝜏2 −𝜏1
𝜏2 −𝜏1
𝐺 1−𝑒
+ 4𝑆 𝜏1 + 𝜏2
8𝑛𝑆
+ 4𝑆 𝜏1 + 𝜏2
4𝑆 𝜏2 −𝜏1
8𝑛𝑆
+ 4𝑆 𝜏1 + 𝜏2
𝐺 1−𝑒
4𝑆 𝜏2 −𝜏1
𝐺 1−𝑒
4𝑆 𝜏2 −𝜏1
8𝑛𝑆
+ 4𝑆 𝜏1 + 𝜏2
8𝑛𝑆
Integrating evolutionary history
Third interval:
𝜇1,𝜏3 = 𝜇1,0
𝜇2,𝜏3 = 𝜇1,0
𝜇3,𝜏3 = 𝜇1,0
3
2
𝜎1,𝜏
3
1
𝐺(−17 + 𝑒 4𝑆(𝜏2 −𝜏1 ) − 4𝑒 2𝑆(𝜏3 −𝜏2 ) + 12𝑒 3𝑆(𝜏3 −𝜏2 ) + 4𝑒 𝑆(𝜏2 +3𝜏3 −4𝜏1 ) + 4𝑒 2𝑆(5𝜏2 +3𝜏3 −8𝜏1 ) + 12𝑆(3𝜏1 + 𝜏2 + 2𝜏3 ))
=
72𝑛𝑆
2
𝜎2,𝜏
=
3
𝐺(−17 + 𝑒 4𝑆
𝜏2 −𝜏1
3
− 8𝑒 2𝑆
𝜏3 −𝜏2
1
+ 16𝑒 𝑆 𝜏2 +3𝜏3 −4𝜏1 − 8𝑒 2𝑆(5𝜏2 +3𝜏3 −8𝜏1 ) + 12𝑆(3𝜏1 + 𝜏2 + 2𝜏3 ))
72𝑛𝑆
3
2
𝜎3,𝜏
3
𝜎12,𝜏3 =
𝜎13,𝜏2 =
𝜎23,𝜏3 =
0
𝝉𝟏
𝝉𝟐
1
𝐺(−17 + 𝑒 4𝑆(𝜏2 −𝜏1 ) − 4𝑒 2𝑆(𝜏3 −𝜏2 ) + 12𝑒 3𝑆(𝜏3 −𝜏2 ) + 4𝑒 𝑆(𝜏2 +3𝜏3 −4𝜏1 ) + 4𝑒 2𝑆(5𝜏2 +3𝜏3 −8𝜏1 ) + 12𝑆(3𝜏1 + 𝜏2 + 2𝜏3))
=
72𝑛𝑆
3
𝐺(7 + 𝑒 4𝑆
𝜏2 −𝜏1
+ 2𝑒 2𝑆
𝐺(7 + 𝑒 4𝑆
𝜏2 −𝜏1
− 4𝑒 2𝑆
𝐺(7 + 𝑒 4𝑆
𝜏2 −𝜏1
+ 2𝑒 2𝑆
3
3
1
𝜏3 −𝜏2
− 8𝑒 𝑆
− 2𝑒 2𝑆(5𝜏2 +3𝜏3 −8𝜏1 ) + 12𝑆(3𝜏1 + 𝜏2 + 2𝜏3 ))
72𝑛𝑆
𝜏3 −𝜏2
− 12𝑒 3𝑆(𝜏3 −𝜏2 ) + 4𝑒 𝑆(𝜏2 +3𝜏3 −4𝜏1 ) + 4𝑒 2𝑆(5𝜏2 +3𝜏3 −8𝜏1 ) + 12𝑆(3𝜏1 + 𝜏2 + 2𝜏3 ))
72𝑛𝑆
𝜏3 −𝜏2
− 8𝑒 𝑆
𝜏2 +3𝜏3 −4𝜏1
1
1
− 2𝑒 2𝑆(5𝜏2 +3𝜏3 −8𝜏1 ) + 12𝑆(3𝜏1 + 𝜏2 + 2𝜏3 ))
72𝑛𝑆
𝜏2 +3𝜏3 −4𝜏1
𝝉𝟑
Unfortunately, this result cannot easily be generalized
Coevolution and phylogeny interact
Phylogeny creates a template of phenotypic
similarity
And coevolution modifies this template
Contemporary interactions can be predicted
Expected intensity of competition
(without coevolution)
Expected intensity of competition
(with coevolution)
If we also have information about the historical strength of coevolution
Conclusion 1: Coevolution leaves a signature
Conclusion 2: Interactions can be predicted
We can predict asymmetries
How do traits evolve?
We can predict intensity
Acknowledgements
Funding
National Science Foundation
Luke Harmon