Richard Barnes Michael Kantar Clarence Lehman Lee ...Evolutionary Simulation of Plant Strategies Richard Barnes Michael Kantar Clarence Lehman Lee DeHaan Donald Wyse University of

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.


Why?


Why?


Food Systems

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


Benefits

Nutrient sequestration

Soil formation

Soil retention

Pollination

Weed suppression

Aesthetic

CO2 sequestration


Is it possible?


Is it possible?

Apr 20 – May 3

May 4 – May 17


Is it possible?

May 18 – May 31

Jun 15 – Jun 28


Is it possible?

Jul 13 – Jul 26

Oct 5 – Oct 18


Is it possible?


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


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


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


1

2

�

Harvest


1

2

3

Gleaves


1

2

3

Groots


1

2

3

Wroots


1

2

3

Wleaves


1

2

Autumn


1

2

3

Gseeds

1


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)



Energy is derived from two sources, consider one

d


d


d


d


(ηlεl l1



· Erain(t)

)+ l1 ·Wl(t) · Ql + r1 ·Wr (t) · Qr


− s1 · Rs(t)− l1 · Rl(t)− r1 · Rr (t)

− w1 ·Mw

(1)



Energy/Inputs are combined to a useable form

d


d


d


d


(ηlεl l1



· Erain(t)

)+ l1 ·Wl(t) · Ql + r1 ·Wr (t) · Qr


− s1 · Rs(t)− l1 · Rl(t)− r1 · Rr (t)

− w1 ·Mw

(1)



This can be viewed in terms of biomass

d


d


d


d


(ηlεl l1



· Erain(t)

)+ l1 ·Wl(t) · Ql + r1 ·Wr (t) · Qr


− s1 · Rs(t)− l1 · Rl(t)− r1 · Rr (t)

− w1 ·Mw

(1)



Parts of the plant Grow

d


d


d


d


(ηlεl l1



· Erain(t)

)+ l1 ·Wl(t) · Ql + r1 ·Wr (t) · Qr


− s1 · Rs(t)− l1 · Rl(t)− r1 · Rr (t)

− w1 ·Mw

(1)



Growth comes at the expense of the reserve

d


d


d


d


(ηlεl l1



· Erain(t)

)+ l1 ·Wl(t) · Ql + r1 ·Wr (t) · Qr


− s1 · Rs(t)− l1 · Rl(t)− r1 · Rr (t)

− w1 ·Mw

(1)



Biomass Respires

d


d


d


d


(ηlεl l1



· Erain(t)

)+ l1 ·Wl(t) · Ql + r1 ·Wr (t) · Qr


− s1 · Rs(t)− l1 · Rl(t)− r1 · Rr (t)

− w1 ·Mw

(1)



Biomass has Mortality

d


d


d


d


(ηlεl l1



· Erain(t)

)+ l1 ·Wl(t) · Ql + r1 ·Wr (t) · Qr


− s1 · Rs(t)− l1 · Rl(t)− r1 · Rr (t)

− w1 ·Mw

(1)



Biomass can be Withdrawn

d


d


d


d


(ηlεl l1



· Erain(t)

)+ l1 ·Wl(t) · Ql + r1 ·Wr (t) · Qr


− s1 · Rs(t)− l1 · Rl(t)− r1 · Rr (t)

− w1 ·Mw

(1)



Some Withdrawn biomass can be regained

d


d


d


d


(ηlεl l1



· Erain(t)

)+ l1 ·Wl(t) · Ql + r1 ·Wr (t) · Qr


− s1 · Rs(t)− l1 · Rl(t)− r1 · Rr (t)

− w1 ·Mw

(1)


Growth & Withdrawal Functions

Piecewise linear interpolations One point per monthLast year repeats


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


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


MenagerieCompetition


MenagerieRoot Perennial


MenagerieRoot Perennial


MenagerieReservoir Perennial


MenagerieReservoir Perennial


MenagerieAnnual


MenagerieBiennial


Questions?

Richard Barnes ([email protected])

Michael Kantar Clarence Lehman Lee DeHaan Donald Wyse

University of Minnesota The Land Institute


Documents

Richard Barnes Michael Kantar Clarence Lehman Lee ...Evolutionary Simulation of Plant Strategies Richard Barnes Michael Kantar Clarence Lehman Lee DeHaan Donald Wyse University of