Mortality over Time Population Density Declines through Mortality.

Mortality over Time

Population Density Declines through Mortality

Experimental Evidence: Self Thinning

Lo

g m

ean

pla

nt

wei

gh

t (w

)

Log density (N)Low High

Low

HighChange during

one time interval

Experimental Evidence: Self Thinning

Lo

g m

ea

n p

lan

t w

eig

ht

(w )

Log density (N)

General pattern

1. Unimpeded growth

2. Mortality begins

3. Similar trajectories exhibited

once thinning starts

4. At some point thinning slows

1

1

1

1

2

2

2

34

Self Thinning in Thirty Species

Similar slope to thinning line across a range

of species

Attempts to Explain the

Thinning Line

An Intuitive Argument

Two stands of trees starting at different densities



Thinning occurs as trees increase in size.



Thinning occurs as trees increase in size.

Trees cannot grow larger unless enough space is made available through mortality.

Yoda et al. (1963)

propose the

“-3/2 Thinning Law” k ≈ -3/2

“-3/2 Thinning”

k ≈ -3/2Allometric relationships: those that scale with

body mass

They posit an underlying allometric relationship

“-3/2 Thinning”

k ≈ -3/2


kCNw

• w = average individual biomass

• C = constant

• N = population density

• -k = slope of thinning line

)log()log()log( NkCw

“-3/2 Thinning”

k ≈ -3/2


kCNw )log()log()log( NkCw

Why 3/2?


Biomass

Density

Volume –> m3

Area m2


Biomass

Density

Volume –> m3

Area m2

kCNw


Biomass

Density

Volume –> m3

Area m2

23CNw

k ≈ -3/2k ≈ -4/3

Revisiting the

“-3/2 Thinning Law”

X

k ≈ -3/2k ≈ -4/3

A Revised View of the

Allometric Relationship

34

Nw

Same as the scaling relationship of body mass to maximum density in animals!

A General Interpretation of the Thinning Relationship

Lemna

Sequoia



Permitted combinations

Prohibited combinations

Self Thinning RevisitedL

og

me

an

pla

nt

we

igh

t (w

)

Log density (N)

General pattern

1. Unimpeded growth

2. Mortality begins

3. Similar trajectories exhibited

once thinning starts

4. At some point thinning slows

4

?


og

me

an

pla

nt

we

igh

t (w

)

Log density (N)

Growth limited by space

Growth limited by resources


og

me

an

pla

nt

we

igh

t (w

)

Log density (N)

Growth limited by resources

Resource limitation regulating growth leads to the “Law of Constant Yield”

Proof of Constant Yield with a slope = -1

Lo

g m

ea

n p

lan

t w

eig

ht

Log density

Slope ≈ -1

log(N)log(N-z)

log YN

Ylog

(N-z)


Lo

g m

ea

n p

lan

t w

eig

ht

Log density

Slope ≈ -1

log(N)log(N-z)

log YN

Ylog

(N-z)

Calculation of slope

x

yslope


Lo

g m

ea

n p

lan

t w

eig

ht

Log density

log(N)log(N-z)

log YN

Ylog

(N-z)


)log()log(

loglog

zNN

zNY

NY

slope

x

yslope

X X


Lo

g m

ea

n p

lan

t w

eig

ht

Log density

log(N)log(N-z)

log YN

Ylog

(N-z)


)log()log(

loglog

zNN

NzNslope

x

yslope

= -1

Putting it all together

• Development of size hierarchies

• Thinning

• Law of Constant Yield

Mortality over Time Population Density Declines through Mortality.

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Transcript of Mortality over Time Population Density Declines through Mortality.