Species interactions and coevolution

Scott L. Nuismersnuismer@uidaho.edu

What is coevolution?

"Thus I can understand how a flower and a bee mightslowly become, either simultaneously or one after theother, modified and adapted to each other in the mostperfect manner, by the continued preservation of all theindividuals which presented slight deviations ofstructuremutually favourable to each other."— Charles Darwin, The Origin of Species

Coevolution: Reciprocal evolutionary change in interacting species (Janzen, 1980)

Species 1

Species 2

My lab uses mathematical models to study coevolution

Spatially structured

species interactions

Structure of biological

communities

Genomestructure

Species 1

Species 2

Coevolution

Focus on this project today

An example of spatially structured coevolution: toxic newts and resistant

snakes

Thamnophis sirtalis Taricha

+ =

• Predator-prey interaction

Butch Brodie

Toxic newts

Taricha granulosa

• Newts contain Tetrodotoxin, a potent neurotoxin

• Some newts contain enough toxin to easily kill a human

• Toxin causes snakes to only “taste” the newts

Resistant snakes

Thamnophis sirtalis

• Some snakes have evolved modified sodium channels

• These snakes are more resistant to tetrodotoxin

• Consequently, resistant snakes can eat toxic newts

Toxic newts and resistant garter snakes(Hanifin et al. 2008, PLoS Biology)

Observation #1:

Newt toxicity and snake resistance Are spatially variable

Toxic newts and resistant garter snakes(Hanifin et al. 2008, PLoS Biology)

Observation #2:

Newt toxicity and snake resistance are positively correlated

Predator resistance

Pre

y t

oxic

ity

Summarizing the Data(Hanifin et al. 2008, PLoS Biology)

• Newt toxicity varies across space

• Snake resistance varies across space

• Toxicity and resistance are positively correlated

These observations have led to the development of a coevolutionary hypothesis

Predator resistance

Prey

tox

icit

y

A coevolutionary hypothesis

Location 1: Strong coevolution

Time

*** We can test this coevolutionary hypothesis using mathematical models ***

Location 2: Weak coevolution

Resistance

&

Toxicity

Resistance

&

Toxicity

Developing an appropriate model

• The data consists of toxicity and resistance measured in many populations

mmz

mmz

6.1

2.1

2

1

mmz

mmz

6.1

3.1

2

1

mmz

mmz

3.1

1.1

2

1

mmz

mmz

7.1

4.1

2

1

mmz

mmz

9.1

8.1

2

1

Our model must predict mean trait

values in replicate populations

2z

1z

1.0 1.2 1.4 1.6 1.8 2.01.0

1.2

1.4

1.6

1.8

2.0

Let’s start by modeling one of these populations

If we assume that additive genetic variance is constant:

mmz

mmz

6.1

2.1

2

1

mmz

mmz

6.1

3.1

2

1

mmz

mmz

3.1

1.1

2

1

mmz

mmz

7.1

4.1

2

1

mmz

mmz

9.1

8.1

2

1

1

1

1

11

1

z

W

WGz

2

2

2

22

1

z

W

WGz

To predict (co)evolution we need to

calculate mean fitness

Defining individual fitness

),()()( jiBiAiT zzWzWzW

Abiotic environment:

WA

Species interactions:

Phenotype, z

Optimal phenotype,

Probabilityof

consumption

1.0 0.5 0.0 0.5 1.0

0.2

0.4

0.6

0.8

1.0

Snake resistance - Newt toxicity

Developing recursions for trait means

21212111 )}()(),()( dzdzzzzzWzWW BA

i

i

i

iiz

W

WGz

1

21211222 )}()(),()( dzdzzzzzWzWW BA

Assume weak selection

2

D2 OszGz iiiiiii

Incorporate genetic drift

Abiotic selection DriftBiotic selection

Model predictictions for local coevolution

Weak selection on newtsStrong selection on snakes

Toxicity and Resistance

Equilibrium trait values depend on the strength of biotic selection

Strong selection on newtsWeak selection on snakes

Strong selection on newtsStrong selection on snakes

But we need a model of MANY populations!

mmz

mmz

6.1

2.1

2

1

mmz

mmz

6.1

3.1

2

1

mmz

mmz

3.1

1.1

2

1

mmz

mmz

7.1

4.1

2

1

mmz

mmz

9.1

8.1

2

1

• Multiple populations

• Gene flow (island model)

Requires more equations

Empirical Data Minimal model

Adding multiple populations and gene flow

2

1,D1,1,M1,1,1, )1(22 OZmzmszzszGz iiiiiiijiiiiii

2

2,D2,2,M2,2,2, )1(22 OZmzmszzszGz iiiiiiijiiiiii

•

•

•

2

,D,,M,,, )1(22 OZmzmszzszGz iiiniiininjininiiini

• In principle, we could then just solve this system of 2n equations

• In practice, this is impossible

This difficulty can be overcome by making a change of variables that reveals a tractable approximation

What does our final approximation predict?

At equilibrium and assuming weak selection:

The spatial variability in toxicity or resistance is:

The correlation between toxicity and resistance is:

iiii

iz

GmN

Gi

22

ˆ 2

)(0ˆ 2 O

What is missing from these equations?

What does this tell us?

Does this provide support for the coevolutionary hypothesis?