ch. 5: population structure and changes. population models 4) transition matrix models life history...
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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%)