Ch' 5: Population Structure and Changes

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Ch. 5 Population Structure and Changes
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Population Models

• Transition matrix models
• Use life history stages and matrix algebra

Fig. 5.6
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Population Models

• Transition matrix models
• Matrix algebra

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Population Models

• Matrix algebra special type of mathematics
• Matrix is numbers in rows/columns
• Special rules for manipulating matrices (adding,
  multiplying, etc.)

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Population Models

• Column matrix below shows population status
  population vector
• Life history stages sseeds, rrosettes,
  fflowering

140 16 10
number seeds
number rosettes
number flowering
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Population Models

• Transition matrix shows probability of
  transition between one census time and next

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Population Models

• Example for teasel (Dipsacus sylvaticus)
• Perennial herb. Pasture/roadside weed in many
  places.

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Population Models

• Example transition matrix for teasel (Dipsacus
  sylvaticus)
• Note columns dont always sum to 1.0 accounts
  for mortality

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Population Models

• Making a model multiply population vector by
  transition matrix
• To produce new matrix predicting population
  structure in next census period

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Population Models

• Example 3 stages. Seed, rosette, flowering
• Population vector

140 20 10
number seeds
number rosettes
number flowering
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Population Models

• Example 3 stages. Seed, rosette, flowering
• Transition matrix

year 1
seed
rosette
flowering
20 0.2 0.1
0.5 0.2 0
seed
0 0.2 0.5
rosette
year 2
flowering
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Population Models

• Example 3 stages. Seed, rosette, flowering
• Next years population? Multiply matrices.

s
r
fl
140 20 10
270 34 11
0.5 0.2 0
0 0.2 0.5
20 0.2 0.1
s
70 0 200 28 4 2 0 10 1


X
r
fl
New Population Vector
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Model Summary

• 1) Help us understand factors determining popn
  size and structure
• 2) Predict future for managed popns or those of
  conservation interest

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Use of models PVA

• Population viability analysis (PVA)
• Use models to predict time to extinction, or
  probability of extinction in 50 or 100 yrs

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Example Florida Torreya

• Rare conifer (Torreya taxifolia)
• Found only in steep ravines along Apalachicola
  River (S. GA and N. FL)

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Florida Torreya

• 98.5 of trees estimated to exist in 1900 are
  dead
• Since 1950s, disease has been killing trees
  (pathogen ID debated)
• About 5 mortality per year

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Florida Torreya

• Diseased trees resprout from base, but dont
  produce seeds
• PVA models predict extinction in wild over next
  century

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Model Summary

• 3) Help explore consequences of changing
  population features (seedling survival, seed
  production, etc.) to population future

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Age/stage distributions

• Can be used as predictive tool
• Example, succession in pine/hardwood stand

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Age/stage distributions

• Can be used as predictive tool
• Often, stable population will show L-shaped
  distribution curve
• Example, red spruce (Picea rubens) in White Mts.
  of New Hampshire

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Age/stage distributions

• L-shaped distribution curve
• Example, red spruce (Picea rubens) in White Mts.
  of New Hampshire

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Age/stage distributions

• But not always. Some species have episodic
  establishment
• Ex, Pinus banksiana (Jack pine)

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Age/stage distributions

• Has serotinous cones (is a closed-cone pine)
• Cones release seeds only after fire that kills
  mature trees

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Age/stage distributions

• Ex, Pinus banksiana (Jack pine)
• Stand then regenerates from that point, having
  single age distribution