Population structure and plant demography - Alaska Geobotany ...

Lesson 5: Population structure and plant
demography
• Density and pattern
– Random, clumped, regular distribution patterns
• Plant demography
– Modular growth
– Plant age vs. stages
– Population growth models
– Transition Matrix Models
– Density dependence
• The law of constant yield
• Self-thinning rule
– Life tables and survivorship curves
• Fecundity
• Net reproductive rate
• Reproductive value
• Metapopulation studies

Billings focus on the individual plant
Billings focus was the
individual plant
within a complex of
environmental
factors, which he
called a
holocoenosis.
This diagram
summarizes an
autecological
approach to plant
ecology, with focus
being individual
species and their
adaptations to the
environment.
W.D. Billings, 1952. The environmental complex in relation to plant growth and
distribution. Quaterly Review of Biology 27: 251-265.

Plant population
“A group of plants of the same species occupying a particular space
at the same time.”
Based on Krebs 1972
The components from which plant communities are constructed.

Factors influencing plant populations:
• The same factors influencing the presence of a plant in our
original question “Why are organisms absent some places and
abundant in others?”
– Environmental conditions
– Resource availability
– Competition
– Disturbance
– Availability of propagules (biogeography)

Measurement and description of plant population
structure and dynamics
• Distribution of plants on the landscape (density and pattern)
• Measurement of plant demography (changes in plant population
size and structure through time)
• Distribution of suites of populations within landscapes
(metapopulation dynamics)

Density
• “Number of individuals per unit area (e.g., trees per ha, or plants per m 2 ).”
• Most easily used for populations of discreet individuals such as trees.
• Less useful for species that reproduce vegetatively, such as grasses.

Patterns of Distribution
• Can give more information on a population s habitat preference, competitive
dynamics, microhabitat distribution than density alone.
• In random distribution patterns, the location of one individual has no bearing on
another s.
• In clumped and regular patterns, the presence of one plant may be affecting another,
possibly through competition or allelopathy or clumped distribution of propagules
from a parent plant.
• A chi-square test can be used to test for random distribution.

Clumped patterns may also be due to the presence of special
microhabitats.
• Non-sorted circles,
Howe Island, AK.
• Example of regular
distribution of
habitats that causes
clumped distribution
of certain species.
• Centers of circles
have high
evapotranspiration
and salts
accumulate.
• Halophytic species,
such as Braya
purpurascens, are
distributed mainly
on the barren
circles.
Braya purpurascens.
www.mun.ca/biology/ delta/arcticf/images/l314.jpg

Plant demography
• “The study of changes in population structure through time.”
• Plant populations increase or decrease through birth and death
processes as well as immigration and emigration, and by and
vegetative sprouting.
• It includes counting:
– Number of genetically distinct individuals,
– Number of vegetatively reproduced individuals,
– Number of leaves, branches, tillers, stems, flowers, etc.,
– Movement of seeds into and out of the population and storage in the
soil.

The influence of John Harper on
plant population ecology
• The study of population biology
was almost solely a topic of
zoologists until John Harper
really created the field in the late
1940 s and 1950 s after he met
Charles Elton, a famous animal
ecologist who was noted
primarily for his studies of small
mammal populations.
• Harper made the field of plant
population biology quite
accessible through Population
Biology of Plants, which was first
published in 1977.

Major chapters in Harper s book
Dispersal, dormancy and recruitment
seed rain, dormancy, seed bank, recruitment of seedlings
Effects of neighbors
effects of density on yield and mortality, form and reproduction
Mixtures of species: space, proportions, changes with time
Effects of predators
Defoliation
Seasonality, search and choice
Grazing animal effects
Predation of seeds and fruits
Pathogens
Natural dynamics of populations
Annual and biennials
Herbaceous perennials
Woody plants
Plants, vegetation, and evolution
Reproduction and growth
Life cycles and fertility schedules
Community structure and diversity
Natural selection and population biology

Idealized plant history (Harper 1977)
• Starting with seed pool (the
dormant phase), some of the
seeds will not sprout and
become seedlings due to
various factors, such as
unfavorable site, seed
herbivory, or climate (the
environmental sieve).
• Of the seedlings that sprout
(the seedling cohort), only a
few will reach maturity and
set seed.
• The diagram also allows for
vegetative reproduction,
shown as the vegetative
daughter connected to the
parent plant, (these
vegetative shoots are called
ramets). Each genetically
distinct parent plant is a
genet.
• The mature plants will
produce seeds, which in turn
must pass through the
environmental filter.
J.L. Harper 1977

Genets, clones and ramets
• Genet: a single genetic individual.
• Clone: a group of distinct individuals that are part of a single
genet (e.g., aspen trees)
• Ramet: a single member of a clone (a branch of genet).

Plants have very different growth from animals
• Animals have determinant growth (e.g. only one heart, two lungs, a liver,
two arms, etc.) and usually determinant size.
• Plants have indeterminant growth, (i.e., their size and abundance of parts
can vary a lot because of the different environmental conditions. Different
number of shoots, leaves, roots, flowers, fruits or seeds in response to
favorable conditions. Similarly, their size can vary markedly, depending on
the location.) They may react to stress by varying the number of parts.

For example, Chenopodium album (lambs quarter)
under nutrient deficiency or if grown at high
density, flowers and sets seed when only 50 cm
high, but, given ideal growth conditions it may
produce 50,000 times as many seeds and grow to
1 m height.
Thus, plant demographers are often more interested
counting leaves or flowers, or individual stems,
than they are in trying to count individual plants.
Modular growth (White 1979)
• Concept of a plant being a population of parts (roots, leaves, stems,
flowers, fruits) or modules.
• Plants may independently allocate growth to different modules, depending
on availability of resources and environmental conditions.

Fitness
• Fitness = the lifetime reproductive success of an organism.
• This concept is much easier to apply to animals than to plants.
• The ability of plants to reallocate reproductive effort to vegetative modules
during times of stress makes analysis of fitness difficult without following
the reproduction among all its vegetative shoots.

Another important difference between plants and
animals for population studies: Size distribution
• Unlike animals, mature plant sizes are rarely
distributed as a normal curve, in which most individual
are of moderate size.
• Plant sizes normally have an L-shaped frequency
distribution of sizes .
• Furthermore, the size of plants is rarely a direct
function of age.
• Age is also often not a good predictor of reproductive
status in plants.
Barbour et al. Fig. 4.4

Population dynamics of plant modules
Harper 1977, p. 22
• To get around
some of these
unique properties
of plants,
population
ecologists often
examine modules
of the plants.
• For example, in
this study Harper
examined the
survivorship of
cohorts of leaves
of three species
of grass during
one growing
season.
• Cohorts of
leaves were
marked at
different times
during the
summer and the
percent surviving
from previous
markings noted.

Number of leaves of each cohort (Linum usitatissimum)
(Bazzaz and Harper, 1976)
• Here Bazzaz
and Harper
counted the
number of
leaves in each
cohort and
followed their
history.
• Early leaves
were longest
lived, but more
leaves were
produced in
later cohorts.
Bazzaz and Harper, 1976

Morphological and physiological changes during
the life cycle of a plant module
Area, photosynthesis and
respiration
Sucrose and phosphorus
concentration
• Just like with whole
organisms or
complete
ecosystems, it is
possible to study
the ecophysiological
processes of plant
modules.
• These diagrams
show the changes in
size, respiration
rate, photosynthesis
rate, and
concentrations of
phosphorus and
sucrose, through
the life history of
cucumber leaves.
Milthorpe and Moorby 1974, cited in Harper 1977

Tree growth as the development of a population of
modules
Terminal shoots of Rhus typhina with age
• Each point on the graph
represents the number
of terminal growing
points on a tree of a
particular age.
• The borken line indicates
the number of shoots
expected if each growing
shoot give rise to two
new shoots in the next
growth period. (The
terminal meristem in this
species aborts.)
• The dark line shows the
actual number of shoots,
which is less than
expected because some
of the shoots die.
• Solid dots are trees in
unshaded habitats.
From J. White, unpublished, reproduced in Harper, 1977
Photo: http://ispb.univ-lyon1.fr/cours/botanique/photos_dicoty/dico%20Q%20a%20Z/Rhus%20typhina.jpg

Population growth models
Used to predict populations of plants at some future time.
Discrete models: Based on Harper s diagram, we can derive the simple equation:
N t+1
= N t
+ B - D + I - E
N t+1 = Number of plants at some future time.
N t = Number of plants at present time.
B = Number of plants established from the seed bank.
D = Number of plants that die.
I = Number of seeds immigrating to the site.
E = Number of seeds emigrating (dispersing) from the site.
The rate of the population growth, , in this discrete model is equal to the population at
some future time divided by the present population.
= N t+1
/N t
However, it is not so simple to make these calculations because we rarely have all
the information needed, and in many cases the data are impossible to obtain.

Continuous-time growth models
• Useful for predicting population
at any time in the future.
• Need to know the rate of
population increase, r,
where r=b-d (number of births
minus the number of deaths).
• With r, we can calculate rate of
change in a population N:
dN/dt = rN.
What is r for the Curve A (0)?

Continuous-time growth models
Exponential growth:
Curve A: r>0.
• If r > 0, the population will grow
exponentially.
• If r = 0, the rate of change in the
population is zero (stable
population).
• If r

Continuous-time growth models
Logistic growth:
Curve B.
In this case the population is
constrained by some
environmental limitation to a
carrying capacity (K).
The population will slow as it
reaches K.
The equation for Curve B is:
dN/dt = rN(K - N)/K,
the Verhulst-Pearl equation.

Limitation of resources in the alga Chlorella
• Gause (1924) showed that the Verhulst-Pearl
equations fit population growth of
Paramecium reasonably well.
• An example from the plant world is the alga
Chlorella (regarded as a superfood):
– “Help your body remove the heavy metals and other pesticides in
your body, improve your digestive system, including decreasing
constipation, help you focus more clearly and for greater duration,
balance your body's pH, and help eliminate bad breath”. Joseph
Merkola http://www.mercola.com/forms/chlorella.htm
• This alga forms clumps and so experiences
the effects of density when there are still
available resources in the medium. The
initially exponential growth rate declines
after 8 days (dashed curve).
• If the lumping is prevented by shaking, the
exponential rate continues for four more
days before the nutrient limitation of the
solution is reached.
Pearsall and Bengry 1940, cited in Harper 1977,
http://www.bioschool.co.uk/bioschool.co.uk/images/images/chlorella%20culture%201_JPG.jpg

The exponential and logistic growth curves well express the
ideas of Malthus regarding the limitation of resources
Through the animal and vegetable kingdoms, nature has scattered the seeds of life
abroad with the most profuse and liberal hand. She has been comparatively sparing
in the room and nourishment necessary to rear them. Their germs of existence
contained in this spot of earth, with ample food, and ample room to expand in would
fill millions of worlds in the course of a few thousand years. Necessity, that imperious
all pervading law of nature, restrains them within the prescribed bounds. The race of
plants, and race of animals shrink under this great restrictive law.
Malthus, 1798, “An essay in the principal of population”
What are some reasons
Verhulst-Pearl might not
apply to real plant
populations?

Why Verhulst-Pearl equation does not usually apply
to the real world of plants
• Carrying capacities are rarely constant. They vary with
environmental conditions.
• Birth and death rates are not constant. Therefore, r is not
constant.
• Biomass of plants may have more impact on the carrying
capacity than the number of individuals.
• Population boundaries are usually poorly defined.

Transition Matrix Models
Present Census
• Often the stage of life history of a plant is a
more useful representation of survivorship
and reproductive performance than age.
• Transition matrix models are used to
estimate the birth growth and death
probabilities for individuals within different
age classes or stages of a plant population.
• Using discrete time steps populations of
individuals within each age class may be
projected into the future.
• The matrix above shows is a general matrix
that presents the probability values that
represent the chance that a plant in a given
stage of development will arrive at a different
(or remain at the same) stage during the
census interval. The matrix is for a plant with
a 3-stage growth cycle (a biennial with seed,
rosette, and flower stages).
Leslie, P.H. (1945) The use of matrices in certain populations mathematics. Biometrika 33: 183-
212.
• For example: in the rosette column, if 60% of
the rosettes of a plant die, and of these 25%
remain as rosettes, and 75% become flowers.
Then probabilities in the Rosette column are
a rs =0, a rr = .4 x 0.25=0.1, and a rf = 0.4 x
0.75 = 0.3.

Calculating future population size
with transition matrices
Transition matrix for a biennial. Seeds cannot produce flowers
in the first year; and rosettes cannot produce seeds. Therefore,
a sf and a rs are 0.
1. To calculate the population
structure of a future population. A
census of the number of individuals
in each stage of the present
population is taken and portrayed
in a column matrix ( B 1 ).
2. This matrix is multiplied by the
transition matrix (A). This matrix
was obtained by monitoring the
probability of individuals in each
stage class (s = seed, i= immature, f
= flowering) making the transition
to another stage class or remaining
at the same stage class. The
resulting matrix ( B 2 ) shows the
number of individuals that make the
transition from one stage to the
next.
3. A new column matrix that portrays
the future population structure is
obtained by summing the values in
each row to arrive at the total
number of seeds, immature, and
flowering plants.
4. This new column matrix, which
shows the population structure of
the future population, can then be
multiplied by the transition matrix
to find the population structure at
the next time interval. This assumes
that the transition probabilities
remain constant for future
generations (which they don t).
5. This is repeated until the
population structure stabilizes
(stable stage distribution).

Transition matrix model application to study of
Dipsacus sylvestris (Teasel)
• Werner and Caswell studied
teasel populations in open
field and shrubland.
• Teasel is a weedy invasive
biennial species with a stem
up to 2 m tall, that is
increasingly prickly toward
the tip. It has a huge eggshaped
head that is armed
with numerous, sharppointed
bracts. The mature
plants are much sought after
for dry flower arrangements.
The plants occur mostly on
disturbed soil with high soil
moisture. Native to Europe
but is common throughout
most of the lower 48 states.
Wilde Karde 212.185.118.226/ bilddb/Bild.asp?I=119
www.chicagobotanic.org/.../ dipfu05.jp
http://bailey.aros.net/nature/images/
Teasel%20reduced.jpg

Example of the use of transition matrices in the
study of teasel populations (Dipsacus sylvestris)
r = 0.957
Upper: Transition matrix for
the open field.
Lower: Transition matrix for
the shrub-covered field.
Lowest row: Percent
occurrence of each stage in
the open field.
r = -0.465
Shrub covered field has lower seed
production and lower probabilities
of plants reaching the flowering
stage.
Result shows an increasing population
for the open field (r = 0.957), and
declining population in the shrub
covered field (r = -0.465).
Werner, P.A. & Caswell, H. 1977. Population growth rates and age versus state-distribution models for teasel…Ecol. 58: 11-3-1111.

Law of constant yield
• Biomass is a better
estimate of carrying
capacity for plants than
density of plants or seeds.
• When the number of plants
are high enough for
interspecific interference to
be important, the yield is
constant regardless of
planting density.
Trifolium subteraneum
Bromus uniloides
(3 levels of nitrogen in soil)
• McDonald (1951) showed
that the yield of Trifolium
subteraneum and Bromus
was constant regardless of
the number of seeds or
seedlings. (Seeds of Trisub
in upper diagram varied
across three orders of
magnitude.)
• The yield, however, is
dependent on the
availability of resources.
The lower figure shows the
response to three different
levels of nitrogen.
McDonald 1951, cited in Barbour et al. 1999.

Self-thinning rule
Biomass vs. number of individuals
B=CN -1/2 ,
where B = biomass, and N is the population density,
and C is a constant.
Yoda et al. 1963, Westoby 1981. Cited in Barbour et al. 1999.
• With plants large individuals
usurp greater amounts of
resources, which tends to
eliminate smaller individuals.
Thus large indviduals have a
greater competitive effect on
small individuals than small
individuals have on large. This
leads to size hierarchies.
• Plant populations are thus
dependent on a combination of
biomass and density (crowding
dependent).
• Yoda et al. (1963) presented a
self-thinning rule that describes
the interaction between
biomass and population
density. This diagram is from
another study by Westoby
(1981), whereby the original
equation of Yoda et al. takes
another form.
• Below the line, biomass will
tend to increase toward the
line(vertical, up pointing
arrows). Above the line, plant
mortality will reduce density
(horizontal left pointing arrow)
toward the line.
• Once at the self-thinning line,
individuals will die at a rate
related to biomass
accumulation rates.

Application of self-thinning rule to plants of various sizes
Plant mass vs. density
• The equation appears
to hold for plants of all
sizes.
• The slope of the line =
1/2 for trees, shrubs,
and herbs, across 12
orders of magnitude in
size!
J.White 1985, cited in Barbour et al. 1999.

Life tables: cohort table for
Phlox drummondii
www.eeob.iastate.edu/.../ Phlox_drummondii.jpg
• Used for short-lived
species, where the
investigator can follow
the survivorship of each
individual.
Leverich & Levin 1979 cited in Barbour et al. 1999.

Examples of survivorship curves
Eurterpe globosa
(= Prestoea acuminata)
Phlox drummondii
Van Valen 1975 for Eurterpe globosa and Leverich and Levin 1979 for P. drummondii. Cited in Barbour et al. 1999.

Survivorship curves (Deevey, 1947)
Type I: characteristic of organisms
with mortality concentrated in the
later stages of life (e.g., annuals
with seed dormancy).
Type II: characteristic of organisms
with constant mortality rates.
Type III: characteristic of organisms
with high juvenile mortality (e.g.,
most trees).
Note that large animals tend to have
Type I survivorship and small
animals tend to have Type III;
whereas the opposite is true of
large and small plants.
Deevey 1947. Cited in Barbour et al. 1999.

Fecundity and net reproductive rate
Fecundity (b x
) is the age-specific birthrate of individuals. It is a
measure of the average number of seeds produced by individuals
of a single size or age cohort during an interval (x).
Net reproductive rate (R o
) is a combination of the fecundity and the
probability of that an individual will survive to the necessary age
category. It is the product of the survivorship (l x
) times fecundity,
summed for the cohort over its life time:
R o = l x b x .

Reproductive value of an individual of age x
Reproductive value (V x
) is the relative contribution that individuals of
age x are likely to make to the seed pool before they die. It is
calculated as the sum of the average number of seeds it produces
in the current year (b x
) plus the the average number of seeds
produced by an individual in each age class older than b x
(e.g.,
b x+1
,b x+2
, etc.) times the probability that an individual will survive
to each older age category (l x+1
/l x
):
Vx = bx +
(l x+i /l x )b x+i

Example: reproductive value of Phlox drummondii through its lifetime
Leverich & Leven 1979

Size or age distribution of trees
• Size (dbh) or age
(no. of tree rings)
can be used.
• Used to examine the
population
dynamics of longer
lived species.
• Diagram shows the
number of plants in
each size category
for hardwoods and
pines in one stand
of trees.
• What does this
distribution
suggest?
Heyward 1939, cited in Barbour et al. 1999.

Metapopulations
“The suite of populations in a region that are
semi-isolated from each other because of
habitat heterogeneity, but which show
significant interchange of pollen and/or
propagules.” (paraphrased from Levin,
1970)
Species are patchily distributed because of
habitat heterogeneity.
Erickson s (1945) study showed that plant
showed patchy distribution at all scales
he mapped.
Patches that are interconnected and show
significant interchange are considered
metapopulations.
Ralph O. Erickson, 1945. The Clematis fremontii var. riehlii
population in the Ozarks,” Annals of the Missouri Botanical Garden,
vol. 32

Adding complexity to Harper s original
model
Regional seed pool
• Numerous studies have examined the
exchange of propagules between local
populations. Colonization at new sites
can be a function of a variety of factors.
For example:
– Availability of open sites. Good sites may be
going extinct through climate change,
succession, or anthropogenic disturbances.
– All good sites are currently occupied.
• These and other factors can influence
whether a species will expand into new
areas, maintain itself in the landscape, or
go extinct.
Local populations

Metapopulations
Pulliam (1989) recognized two distinct types of populations:
Source populations: Populations in favorable areas that
produce a lot of seed and potential emigrants.
Sink populations: Populations in unfavorable habitats that
must receive an constant influx in immigrants to maintain
themselves.

Models of
movement of
species between
populations
• Infinite island models: Sewall Wright's (1943) infinite island model is a "landscapeneutral"
model that assumes equal population size and equal exchange of migrants
across all populations.
• Metapopulation models: (Levins 1970), is a demographic model that describes a set
of populations with certain extinction probabilities that are connected by migration of
colonists.
• Landscape models: Use spatially explicit information about the mosaic of habitat
types to describe the landscape. This model can be combined with a metapopulation
model or any model that describes a set of connected populations that occur within a
landscape. For further discussion of metapopulation models and landscape
approaches see Harrison and Taylor 1997, Wiens 1997. (For all models, lines indicate
gene flow or migration, solid patches are populations; dotted patches indicate extinct
populations.)
From: Proceedings from a Workshop on Gene Flow in Fragmented, Managed, and Continuous PopulationsJanuary 5-9, 1998. National Center for
Ecological Analysis and SynthesisUniversity of California-Santa BarbaraProceedings written byV. L Sork, D. Campbell, R. Dyer, J. Fernandez, J. Nason,
R. Petit, P. Smouse, and E. Steinberg.

Two recent studies of metapopulation genetics
Giles, B.E. and J. Goudet. 1997. Genetic differentiation in
Silene dioica metapopulations: Estimation of
spatiotemporal effects in a successional plant species.
American Naturalist, 149: 507-526.
Olson M.S. and D.E. McCauley. 2002. Mitochondrial DNA
diversity, populaiton structure, and gender association in
the gynodioecious plant Silene vulgaris. Evolution, 56: 253-
262.

Summary
• Density and pattern
– Random, clumped, regular distribution patterns
• Plant demography (Harper 1977)
– Modular growth (White 1979)
– Plant age vs. stages
– Population growth models
• Discrete-time model: difficult to apply
• Continuous time model: exponential growth equation
• Limitation of resources: Verhulst-Pearl logistic equation
• Exponential vs. logistic population growth
– Transition Matrix Models (Leslie 1975)
– Density dependence
• The law of constant of yield (Kira et al. 1975)
• Self-thinning rule (Yoda et al. 1963)
– Life tables and survivorship curves (Deevey 1947, Phlox example from Leverich
and Levin 1975)
• Fecundity
• Net reproductive rate
• Reproductive value
– Forest population dynamics (Examples from Heyward 1939, Oosting and Billings
1952)
• Metapopulations
– Interchange of propagules between local populations (Levin 1970).
– Source and sink populations (Pulliam 1989).
– Different models of gene flow between populations.

Literature for Lesson 5
Werner, P.A. and J. Caswell. 1977. Population growth rates and age versus
stage-distribution models for teasel (Dipsacus sylvestris Huds.)
Ecology 58: 1103-1111.
Giles, B.E. and J. Goudet. 1997. Genetic differentiation in Silene dioica
metapopulations: Estimation of spatiotemporal effects in a
successional plant species. American Naturalist, 149: 507-526.
Leverich, W.J. and D.A. Levin,. Age-specific survivorship and reproduction in
Phlox drummondii. American Naturalist 113: 881-903.
Platt, W.J. and M. Weiss. 1985. An experimental study of competition among
fugitive prairie plants. Ecology 66: 708-720.
Olson M.S. and D.E. McCauley. 2002. Mitochondrial DNA diversity, populaiton
structure, and gender association in the gynodioecious plant Silene
vulgaris. Evolution, 56: 253-262.
Westoby, M. 1981. The place of the self-thinning rule in population dynamics.
American Naturalist 118: 581-587.