Ch. 5: Population Structure and Changes

Population Models• 4) Transition matrix models • Life history stages + matrix algebra

Fig. 5.6

Population Models• Matrix algebra• Matrix: numbers rows/columns

– Rules (adding, multiplying, etc.)

Population Models• Ex: Column matrix (vector) = pop’n status: population

vector• Life history stages: s=seeds, r=rosettes, f=flowering

140

16

10

# seeds

# rosettes

# flowering

Lab 2: who am I?Rosette forming perennial

Population Models• Transition matrix:

probability transition b/w 1 census & next

Population Models• Ex: teasel (Dipsacus sylvaticus)• Perennial pasture/roadside weed.

Population Models• Transition matrix: teasel (Dipsacus sylvaticus)

Note columns don’t always sum to 1.0: accounts for mortality

Population Models• Model: pop’n vector X transition matrix• New matrix: pop’n structure next time

Population Models• Ex: 3 stages. Seed, rosette, flowering• Pop’n vector

140

20

10

# seeds

# rosettes

# flowering

Population Models• Ex: 3 stages. Seed, rosette, flowering• Transition matrix

0.5

0.2

0

seed rosette flowering

seed

rosette

flowering

year 1

year 2

0

0.2

0.5

20

0.2

0.1

Note: columns not summing to 1.0 includes mortality

Population Models• Ex: 3 stages. Seed, rosette, flowering• Next year’s pop’n.? Multiply.

0.5

0.2

0

0

0.2

0.5

20

0.2

0.1

140

20

10

X

s r fl

=

s

r

fl

Population Models• Ex: 3 stages. Seed, rosette, flowering• Next year’s pop’n.? Multiply.

0.5

0.2

0

0

0.2

0.5

20

0.2

0.1

140

20

10

X

s r fl

=

s

r

fl

70 + 0 + 200

28 + 4 + 2

0 + 10 + 1

=

270

34

11

New Pop’n Vector

Model Summary• 1) Explore changes (seedling survival, etc.)• 2) Future managed pop’ns

PVA

Model Ex: Florida Torreya• Rare conifer (Torreya taxifolia)

• Steep ravines: Apalachicola River

Florida Torreya• Population viability analysis (PVA)

– Models predict

Ch. 6: Evolutionary Processes/Outcomes

Plants and Environment• Plant/environment interactions

• 1) Liebig (1840)– German agriculturist– Discovered mineral fertilizer

Plants and Environment• 1) Liebig (1840)

– Law of the Minimum: Growth/distribution depends on

A Festive MoB CuMnZn Clapping Nicely

Plants and Environment

• 1) Liebig (1840)– Australia legumes (soil

deficient Mo)– 13 oz/acre every 5-10

years increased yield 600-700%

Plants and Environment• 2) Shelford (American:

early 1900s)

Plants and Environment• 2) Shelford (American:

early 1900s)– Upper limits for factors– Proposed “Theory of

Tolerance”

Plants and Environment• 2) Shelford (American:

early 1900s)– Upper limits for factors– Proposed “Theory of

Tolerance”– Abiotic factors define

“potential range”

Plants and Environment• 2) Shelford (American: early 1900s)

– “Physiological” or “potential” optimum: best point

Plants and Environment• 2) Shelford (American: early 1900s)

– Biotic factors: give actual (ecological) range and optimum

– Ex, add sp. Y

Plants and Environment– Ex: Klamath weed (Hypericum perforatum) from

Europe– Cattle avoid (chemicals cause sunburn)

Plants and Environment– Chrysolina beetle (biocontrol)

Plants and Environment– Chrysolina beetle (biocontrol)– Grows only in

Plants and Environment• Phenotype:

• Genotype:

• Phenotype: determined by

Plants and Environment• Equation:

• Vp = Vg + Ve

• Vp = total phenotypic variation

• Vg = variation due to

• Ve = variation due to

Focus Vg

Plants and the Environment• Adaptation: What is an adaptation?

Plants and the Environment• Adaptation:

– 1) Genetically – 2) With

• How determine trait adaptation? Hard!

Genetic importance

Plants and the Environment• Genetic basis:• Heritability (h2): resemblance b/w relatives

• h2 = Vg / Vp

– Vg = variation due

– Vp = total phenotypic

Plants and the Environment• 1 approach: slope regression line (r2)

y = mx + b;

r2=0

r2=0.52

r2=1

Plants and the Environment• Plant height ex.

Fig. 6.3

(r2)=0.21 (21%)

(h2)=0.21 (21%)