Population Biology

1
Population Biology

• As a field, dates to the 1960s, with John Harper
  (Harpers Population Biology of Plants, is on
  reserve)
• Population dynamics depend on both individual
  plant properties and their interactions

2
Population Biology

• Basic premise
• N t1 N t B D I E
• N now N then B D I E
• N population size
• B birth I immigration
• D death E emigration

3
Plant issues

• What is birth?
• Seed formation, not germination, usually
• Seeds can be dormant in seed bank for many years
• Birth may also be separation of a ramet from the
  rest of the genet (plants are modular) what is
  an individual?

4
Plant issues

• What are immigration/emigration?
• Seed dispersal I and E are coupled
• Pollen movement is NOT immigration, as pollen
  grains arent individuals but gametes
• Ramet movement more complicated. Can have
  immigration without emigration (same genetic
  individual still present in source population)

5
Population structure

• In animals, usually age structured repro rate,
  survival, even emigration related to age of
  individual
• In plants, usually stage-structured birth,
  death, etc. depend more on size or physiological
  status than age
• In plants, size is fluid (can increase or
  decrease) and plastic (depends on microsite
  conditions)

6
Life Tables

• Per generation growth rate (lambda), other
  parameters were traditionally derived using life
  tables for age-based populations
• A way to organize information on survival and
  fecundity for different ages or stages

7
Life Table for Phlox drummondii
8
Life tables

• Net reproductive rate R0 the average number
  of offspring produced by an individual
• From life table for annual sum of the products
  of relative survival (lx) and relative fecundity
  (mx)
• For an annual, the per generation rate of
  increase (lambda) R0

9
Growth rate of Phlox population(in an annual,
lambda R0)
10
Life cycle graphs

• A cartoon of the probability of shifting between
  stages ( transition probabilities)
• Stages will be defined specific to plant species
  of interest

11
Mauna Kea silversword

• Usually semelparous reproduce once and die
• F fecundity P34 and P44 are vanishingly small

Read probabilities P21 is probability of
transitioning to stage 2 from stage 1
12
Ladyslipper Orchid

• Iteroparous reproduces many times in life

13
Coryphantha robbinsorum
14
Cactus example

• Remember N t1 N t B D I E
• We will ignore I and E for now how to get B and
  D from life cycle graphs?
• Matrix algebra

15
Cactus example

• n1(t1) P11 0 F n1(t)
• n2(t1) P21 P22 0 n2(t)
• n3(t1) 0 P32 P33 n3(t)

16
WHAT IF THE LIFE CYCLE GRAPH DIFFERED?

• n1(t1) P11 P12 F n1(t)
• n2(t1) P21 P22 0 n2(t)
• n3(t1) 0 P32 P33 n3(t)

P12
17
Problem 4 Part 1

• The following two slides show transition matrices
  for teasel, Dipsacus sylvestris, growing in a) an
  open field and b) a shrub-covered field.  Data
  for stable size distribution are in percent. The
  number in the flowering column is the average
  number of seeds produced per flowering plant.
   Data from Werner and Caswell, 1977.  
• Using the transition matrix for the open field,
  construct a life cycle graph for teasel.
• Which conditions, a or b, appear more conducive
  to population growth for this species? Give a few
  examples from the tables to support your answer.

18
A. Open Field
   
19
B. Shrub-covered Field
20
Problem 4 Part 2

• Make a matrix from the ladyslipper life cycle
  graph (earlier in lecture).

21
What can we do with this info?

• If we multiply the population vector by the
  transition matrix many times, we can calculate
  the stable age distribution and the stable lambda
  for the population
• If ? gt 1, population is growing if ? lt 1,
  population is declining

22
What can we do with this info?

• Can calculate elasticity, and sensitivity
• Elasticity is the proportional change in lambda
  with a change in a matrix element helps us
  determine the important life stage for population
  growth and decline
• Sensitivity is similar, but not proportional
  elasticity is better for this reason

23
Elasticities for our cactus
TO
TO
FROM
FROM
Adult survival important for lambda (?)
Adult survival less imp. Juvenile production imp.
24
Survivorship curves

• Estimated from life table/transition matrix data
• Shape of survivorship curves varies between
  species with different life histories

25
Survivorship curves
26
Survivorship curves

• Type I convex. Mortality late in life.
  Annuals without seed dormancy, most individuals
  survive to reproduce.
• Type II linear. Mortality constant
• Type III concave. Mortality early in life,
  followed by low mortality later. Forest trees.

27
Survivorship curve

• Phlox drummondii, an annual herb

28
Survivorship curve

• A tropical palm

29
Survivorship curve

• Our endangered cactus

30
An example herbivory and pollen limitation in
Trillium grandiflorum

• Ecological Applications 14(3) 915-928
• Herbivory by deer
• Pollen limitation reduction in seed formation
  due to lack of pollinator visits

31
Change in transition probabilities and fecundity
with no herbivory or pollen limitation
32
Population growth rates under different treatments
33
Elasticity analysis
34
Summary of Knight 2004

• Deer herbivory leading to population extinction
  pollen limitation not very important for
  population growth
• Removing herbivory shifts elasticities,
  increasing the relative importance of larger or
  reproductive individuals to population growth

35
Application

• Demographic work is time intensive but is
  considered the single most important thing for
  conservation (Schemske et al. 1994. Evaluating
  approaches for the conservation of rare and
  endangered plants. Ecology 75584-606)
• Used to determine whether populations are growing
  or declining important for monitoring
• Elasticity analysis used in to determine which
  life stage to focus on