Richard Barnes Michael Kantar Clarence Lehman Lee ...Evolutionary Simulation of Plant Strategies...

Evolutionary Simulation of Plant Strategies

Richard Barnes Michael KantarClarence Lehman Lee DeHaan Donald Wyse

University of Minnesota

The Land Institute

Barnes et. al Perennial Grains

An Important Factoid Regarding Grains

You eat the seeds.

Barnes et. al Perennial Grains

Why?

Barnes et. al Perennial Grains

Why?

Barnes et. al Perennial Grains

Food Systems

Foley et al., Science 309, 570 – 574 (2005)

Barnes et. al Perennial Grains

Benefits

Nutrient sequestration

Soil formation

Soil retention

Pollination

Weed suppression

Aesthetic

CO2 sequestration

Barnes et. al Perennial Grains

Is it possible?

Barnes et. al Perennial Grains

Is it possible?

Apr 20 – May 3

May 4 – May 17

Barnes et. al Perennial Grains

Is it possible?

May 18 – May 31

Jun 15 – Jun 28

Barnes et. al Perennial Grains

Is it possible?

Jul 13 – Jul 26

Oct 5 – Oct 18

Barnes et. al Perennial Grains

Is it possible?

Barnes et. al Perennial Grains

Breeding Efforts

Perennial flax Intermediate Wheatgrass Perennial Rice

Perennial wheat Perennial maize Perennial sorghumBarnes et. al Perennial Grains

The Game Plan

Using a model of natural selection. . .

Reproduce what we see in nature

Using the same model under artificial selection. . .

Show something new

Barnes et. al Perennial Grains

Physiologic System

Reservoir(w)

Roots (r) Leaves (l)

Seeds (s)

Min

+

α α

Min

·αr r

1r1+r

2

·αr

r2

r1+r2

·α l

l1

l1+l2

·αl l2l1+l2

J F M A M J J A S O N D0

0.1

0.2

0.3

0.4

�

Erain

J F M A M J J A S O N D0

0.1

0.2

0.3

0.4

�

Esun

Erain(t) Esun(t)

w·G

seeds(t)

w ·Gleaves(t)w ·Groots(t)

l ·Wleaves(t) ·Qlr ·Wroots(t) ·Qr

s=

0

l = 0

l ·Mleavesr ·

Mroots

s ·Mseeds

Cseeds ·Gseeds(t)Croots ·Groots(t)Cleaves ·Gleaves(t)s ·Rseeds

r ·Rroots

l ·Rleaves

J F M A M J J A S O N D0

1

2

�

Harvest

J F M A M J J A S O N D0

1

2

3

Gleaves

J F M A M J J A S O N D0

1

2

3

Groots

J F M A M J J A S O N D0

1

2

3

Wroots

J F M A M J J A S O N D0

1

2

3

Wleaves

J F M A M J J A S O N D0

1

2

Autumn

J F M A M J J A S O N D0

1

2

3

Gseeds

1

Barnes et. al Perennial Grains

Physiologic Equations

Energy comes in

d

dtseeds = Gs(t) · w1 − s1 ·Ms

d

dtleaves = Gl(t) · w1 − l1 ·Wl(t)− l1 ·Ml

d

dtroots = Gr (t) · w1 − r1 ·Wr (t)− r1 ·Mr

d

dtreserve = ηw · min

(ηlεl l1

max(Kl , l1 + l2)· Esun(t),

ηr εr r1max(Kr , r1 + r2)

· Erain(t)

)+ l1 ·Wl(t) · Ql + r1 ·Wr (t) · Qr

− w1 · (Gs(t) · Cs + Gl(t) · Cl + Gr (t) · Cr )

− s1 · Rs(t)− l1 · Rl(t)− r1 · Rr (t)

− w1 ·Mw

(1)

Barnes et. al Perennial Grains

Physiologic Equations

Energy is derived from two sources, consider one

d

dtseeds = Gs(t) · w1 − s1 ·Ms

d

dtleaves = Gl(t) · w1 − l1 ·Wl(t)− l1 ·Ml

d

dtroots = Gr (t) · w1 − r1 ·Wr (t)− r1 ·Mr

d

dtreserve = ηw · min

(ηlεl l1

max(Kl , l1 + l2)· Esun(t),

ηr εr r1max(Kr , r1 + r2)

· Erain(t)

)+ l1 ·Wl(t) · Ql + r1 ·Wr (t) · Qr

− w1 · (Gs(t) · Cs + Gl(t) · Cl + Gr (t) · Cr )

− s1 · Rs(t)− l1 · Rl(t)− r1 · Rr (t)

− w1 ·Mw

(1)

Barnes et. al Perennial Grains

Physiologic Equations

Energy/Inputs are combined to a useable form

d

dtseeds = Gs(t) · w1 − s1 ·Ms

d

dtleaves = Gl(t) · w1 − l1 ·Wl(t)− l1 ·Ml

d

dtroots = Gr (t) · w1 − r1 ·Wr (t)− r1 ·Mr

d

dtreserve = ηw · min

(ηlεl l1

max(Kl , l1 + l2)· Esun(t),

ηr εr r1max(Kr , r1 + r2)

· Erain(t)

)+ l1 ·Wl(t) · Ql + r1 ·Wr (t) · Qr

− w1 · (Gs(t) · Cs + Gl(t) · Cl + Gr (t) · Cr )

− s1 · Rs(t)− l1 · Rl(t)− r1 · Rr (t)

− w1 ·Mw

(1)

Barnes et. al Perennial Grains

Physiologic Equations

This can be viewed in terms of biomass

d

dtseeds = Gs(t) · w1 − s1 ·Ms

d

dtleaves = Gl(t) · w1 − l1 ·Wl(t)− l1 ·Ml

d

dtroots = Gr (t) · w1 − r1 ·Wr (t)− r1 ·Mr

d

dtreserve = ηw · min

(ηlεl l1

max(Kl , l1 + l2)· Esun(t),

ηr εr r1max(Kr , r1 + r2)

· Erain(t)

)+ l1 ·Wl(t) · Ql + r1 ·Wr (t) · Qr

− w1 · (Gs(t) · Cs + Gl(t) · Cl + Gr (t) · Cr )

− s1 · Rs(t)− l1 · Rl(t)− r1 · Rr (t)

− w1 ·Mw

(1)

Barnes et. al Perennial Grains

Physiologic Equations

Parts of the plant Grow

d

dtseeds = Gs(t) · w1 − s1 ·Ms

d

dtleaves = Gl(t) · w1 − l1 ·Wl(t)− l1 ·Ml

d

dtroots = Gr (t) · w1 − r1 ·Wr (t)− r1 ·Mr

d

dtreserve = ηw · min

(ηlεl l1

max(Kl , l1 + l2)· Esun(t),

ηr εr r1max(Kr , r1 + r2)

· Erain(t)

)+ l1 ·Wl(t) · Ql + r1 ·Wr (t) · Qr

− w1 · (Gs(t) · Cs + Gl(t) · Cl + Gr (t) · Cr )

− s1 · Rs(t)− l1 · Rl(t)− r1 · Rr (t)

− w1 ·Mw

(1)

Barnes et. al Perennial Grains

Physiologic Equations

Growth comes at the expense of the reserve

d

dtseeds = Gs(t) · w1 − s1 ·Ms

d

dtleaves = Gl(t) · w1 − l1 ·Wl(t)− l1 ·Ml

d

dtroots = Gr (t) · w1 − r1 ·Wr (t)− r1 ·Mr

d

dtreserve = ηw · min

(ηlεl l1

max(Kl , l1 + l2)· Esun(t),

ηr εr r1max(Kr , r1 + r2)

· Erain(t)

)+ l1 ·Wl(t) · Ql + r1 ·Wr (t) · Qr

− w1 · (Gs(t) · Cs + Gl(t) · Cl + Gr (t) · Cr )

− s1 · Rs(t)− l1 · Rl(t)− r1 · Rr (t)

− w1 ·Mw

(1)

Barnes et. al Perennial Grains

Physiologic Equations

Biomass Respires

d

dtseeds = Gs(t) · w1 − s1 ·Ms

d

dtleaves = Gl(t) · w1 − l1 ·Wl(t)− l1 ·Ml

d

dtroots = Gr (t) · w1 − r1 ·Wr (t)− r1 ·Mr

d

dtreserve = ηw · min

(ηlεl l1

max(Kl , l1 + l2)· Esun(t),

ηr εr r1max(Kr , r1 + r2)

· Erain(t)

)+ l1 ·Wl(t) · Ql + r1 ·Wr (t) · Qr

− w1 · (Gs(t) · Cs + Gl(t) · Cl + Gr (t) · Cr )

− s1 · Rs(t)− l1 · Rl(t)− r1 · Rr (t)

− w1 ·Mw

(1)

Barnes et. al Perennial Grains

Physiologic Equations

Biomass has Mortality

d

dtseeds = Gs(t) · w1 − s1 ·Ms

d

dtleaves = Gl(t) · w1 − l1 ·Wl(t)− l1 ·Ml

d

dtroots = Gr (t) · w1 − r1 ·Wr (t)− r1 ·Mr

d

dtreserve = ηw · min

(ηlεl l1

max(Kl , l1 + l2)· Esun(t),

ηr εr r1max(Kr , r1 + r2)

· Erain(t)

)+ l1 ·Wl(t) · Ql + r1 ·Wr (t) · Qr

− w1 · (Gs(t) · Cs + Gl(t) · Cl + Gr (t) · Cr )

− s1 · Rs(t)− l1 · Rl(t)− r1 · Rr (t)

− w1 ·Mw

(1)

Barnes et. al Perennial Grains

Physiologic Equations

Biomass can be Withdrawn

d

dtseeds = Gs(t) · w1 − s1 ·Ms

d

dtleaves = Gl(t) · w1 − l1 ·Wl(t)− l1 ·Ml

d

dtroots = Gr (t) · w1 − r1 ·Wr (t)− r1 ·Mr

d

dtreserve = ηw · min

(ηlεl l1

max(Kl , l1 + l2)· Esun(t),

ηr εr r1max(Kr , r1 + r2)

· Erain(t)

)+ l1 ·Wl(t) · Ql + r1 ·Wr (t) · Qr

− w1 · (Gs(t) · Cs + Gl(t) · Cl + Gr (t) · Cr )

− s1 · Rs(t)− l1 · Rl(t)− r1 · Rr (t)

− w1 ·Mw

(1)

Barnes et. al Perennial Grains

Physiologic Equations

Some Withdrawn biomass can be regained

d

dtseeds = Gs(t) · w1 − s1 ·Ms

d

dtleaves = Gl(t) · w1 − l1 ·Wl(t)− l1 ·Ml

d

dtroots = Gr (t) · w1 − r1 ·Wr (t)− r1 ·Mr

d

dtreserve = ηw · min

(ηlεl l1

max(Kl , l1 + l2)· Esun(t),

ηr εr r1max(Kr , r1 + r2)

· Erain(t)

)+ l1 ·Wl(t) · Ql + r1 ·Wr (t) · Qr

− w1 · (Gs(t) · Cs + Gl(t) · Cl + Gr (t) · Cr )

− s1 · Rs(t)− l1 · Rl(t)− r1 · Rr (t)

− w1 ·Mw

(1)

Barnes et. al Perennial Grains

Growth & Withdrawal Functions

Piecewise linear interpolations One point per monthLast year repeats

Barnes et. al Perennial Grains

Breeding: Genetics

Crossover

Point Mutations

Crossover points drawn from uniform distribution

Mutation points drawn from uniform distribution

Mutation degree drawn from normal distribution

Gene values always ≥ 0

Barnes et. al Perennial Grains

Breeding: Population

50 variants placed in pairwise competition: 2500 plots

Competitions last 8 years

Death during a competition → Replanting

Representation in breeding pool proportional to harvest

50 new variants generated

Barnes et. al Perennial Grains

MenagerieCompetition

Barnes et. al Perennial Grains

MenagerieRoot Perennial

Barnes et. al Perennial Grains

MenagerieRoot Perennial

Barnes et. al Perennial Grains

MenagerieReservoir Perennial

Barnes et. al Perennial Grains

MenagerieReservoir Perennial

Barnes et. al Perennial Grains

MenagerieAnnual

Barnes et. al Perennial Grains

MenagerieBiennial

Barnes et. al Perennial Grains

Questions?

Richard Barnes (rbarnes@umn.edu)

Michael Kantar Clarence Lehman Lee DeHaan Donald Wyse

University of Minnesota The Land Institute

Barnes et. al Perennial Grains