Lecture 7 Population Properties and Dynamics BW
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Transcript of Lecture 7 Population Properties and Dynamics BW
ECOLOGY OF
POPULATIONS
ARNOLD V. HALLARE, Dr.rer nat
Professor
DB, CAS, UP Manila
NATURAL SCIENCE 5
Importance of this topic
1. To have a basic understanding of the fundamental
principles in population ecology and how these can
be applied to human populations.
2. To ensure prudent management of commercially and
recreationally important wild populations
3. To effectively control unwanted species of pests,
weeds, parasites, and disease agents.
Basic Questions at
Population Level What are the characteristics of populations? What population
parameters can we quantitatively measure? How do populations differ in such aspects as density, dispersion, age distribution, carrying capacity, and so on?
How do populations grow? What are the patterns of population increase (and decrease)? Are there consistent patterns in changes of abundance among species? What parameters can we use to describe quantitatively the changes in the populations?
How are the number of individuals in populations controlled? What factors determine the limits of population size? Are there processes that stabilize populations?
DEFINITION & STRUCTURE
Population – a collection of organisms of the same
species occupying a particular space at a particular time.
The ultimate constituents of the population are individual
organisms that can potentially __________ and produce
fertile offspring.
e.g. tilapia population in a lake
mahogany population in a forest
elephant population in savanna
human population
What is a Population?
Components?
Definition :
◦ One species
◦ One area
◦ Isolated from other
areas
◦ Able to interbreed
What is a Metapopulation?
Components?
Definition :
◦ One species
◦ Multiple areas
◦ Isolated from other
areas, further away
◦ Able to interbreed
Example: Only minimal genetic flow, at most
POPULATION PROPERTIES
Statistical measures that cannot be applied
to individuals such as density, dispersion,
natality, mortality, dispersal, age structure and
sex ratio.
Interpreted to be the summation of individual
properties or characteristics
Characteristics of a Population
What features can we measure of a population?
Features:
◦ Size (Density)
◦ Dispersion
◦ Age structure
◦ Sex ratios
◦ Birth rate
◦ Death rate
◦ Immigration
◦ Emigration
POPULATION DENSITY
Abundance (Size) – number of individuals in a given
area
Density – number of individuals expressed per
unit area or volume.
e.g. There are 100 birds in a 2.5 ha of land
Abundance = 100 birds
Density = 100/2.5 = 40 birds/hectare
- number of trees per acre of land
- number of humans per square km
- number of diatoms per cu m of water
Random Dispersion
(a) the environment is uniform
(b) resources equally available through the years
(c) no patterns of attraction or avoidance
Uniform Dispersion
(a) more even spacing than would
occur by chance
(b) Autotoxicity
Clumped Dispersion
(a) due to habitat differences
(b) reproductive patterns and social
behaviors
DISPERSION- how individuals are distributed in space
NATALITY- production of new individuals in a population through birth, germination, hatching, budding or fission.
e.g. bacteria by cell division
plants by production of seeds
animals by production of offspring
Birth rate – number of individuals born per 1000 individuals per year.
e.g. a population of 2000 individuals produce 20 offspring per year
BR = 10 per thousand per year
Most organisms produce many offspring than are needed to replace
themselves.
Related Terms:
FERTILITY – a physiological term which
refers to the ability of the organism to
breed and to produce offspring.
FECUNDITY – an ecological term
which grades an organism based on the
number of offspring it can produce in a
given period of time.
MORTALITY
- loss of individuals in a population as a result of death.
e.g. seed mortality is very high
immature animals die before they have the chance to reproduce
Death Rate – number of people who died
per 1000 individuals per year
“For population to grow, BR>DR”
WHAT IS SURVIVORSHIP CURVE?
- graphical representation of death schedules
I – heavy mortality at the ___ of
the species life span.
e.g. humans, sheep, mammals,
and some plants
II – constant age-specific mortality
rate; constant exponential
decrease in the population
with time
e.g. hydras, rodents, birds
perennial plants
III – high mortality rates in early life
e.g. oysters, fishes, invertebrates
AGE STRUCTURE
- refers to the relative proportion of individuals belonging to different age classes in a population.
Ecological Ages (Bodenheimer, 1939)
1. Prereproductive Age (1-14)
2. Reproductive Age (15-54)
3. Postreproductive Age (55- )
e.g. insects (long pre, short rep and no post)
Significance of Age Distribution
(1) influences both natality and mortality
(2) determines the current reproductive
status of the population and indicates
what may be expected in the ______.
(GROWING, DECLINING?)
(3) helps global agencies and local
government to plan for future
population trends and needs
Age Pyramid
Is constructed by getting the % of
population at different age classes. The %
is reflected on the lengths of horizontal
bars.
Types of Age Pyramid
Type A (Expanding) – shows broad base and sides bow
in. Large proportion of young and the population is said
to be ________.
Type B (Stable) – no increase nor decrease relative to
numbers in each age class and proportion maintained
through time.
Type C (Declining) – shows an increasing proportion in
the ______ age classes and decrease in membership in
the younger.
Types of Age Pyramid
Expanding
Population
(Kenya, Nigeria,
Mexico, Philippines)
Stable Population
(USA, UK)
Declining
Population
(Sweden, Norway,
Germany, Italy)
Population
97,976,603 (July 2010 est.) (July 2010 est )
Country comparison to the world: 11
Age structure
0-14 years: 35.2% (male 17,606,352/female 16,911,376)
15-64 years: 60.6% (male 29,679,327/female 29,737,919)
65 years and over: 4.1% (male 1,744,248/female 2,297,381) (2010
est.)
Population growth rate
1.957% (2010 est.)
PHILIPPINES
SEX RATIO
Compares the number of male members
to the number of female members in the
population.
S.R. = number of males x 100
number of females
e.g. July 2010 (est.) SR for Philippines
SR = 49,029,927 x 100 = 100.17
48,946,676
Some general statements (for human
population only)
◦ There are more males than females in the
younger age groups.
◦ Mortality rates usually higher among males
than females, sex ratio tends to decrease with
age.
◦ Sex ratio is higher in rural than urban areas.
DEPENDENCY RATIO
Relates the size of the dependent segment of
the population to the economically productive
segment of the population (applicable for
human population)
Dependency Ratio – 0-14 yrs old + 60 yrs and over x 100
15-60 yrs old
dependents
productive
DISPERSAL (MIGRATION)
The mass directional movement of large numbers of individuals of a population from one location to another
Immigration – migration into a population
Emigration – movement out of a population
Net Migration Rate = I – E x 100
Total population
Why migrate?
1. Food
2. Space
3. Competition
4. Seasonal changes
Effects of migration
1. Population Size
2. Age Distribution
3. Genetic Pool
POPULATION GROWTH
PARAMETERS
Immigration (I) PopulationBoundary
Emigration (E)
Population Growth = (B+I) – (D+E)
Births (B)
Deaths (D)
Population Dynamics – pertains to the change in population
size due to changes in one or all of the four primary
population parameters
Population Growth
& Dynamics
TWO TERMS Population Growth – refers to the increase or
decrease in size, density,or number of individuals in
a population through time.
Growth = (B-D)+(I-E)
Biotic Potential – maximum reproductive power
of a population or the ability of the population to
reproduce under optimum environmental
conditions.
Space, food, and other organisms DO NOT
exert limiting effect
Biotic Potential
POPULATION GROWTH
PATTERNS
Exponential Growth Pattern
Logistic Growth Pattern
Expressions of the Biotic
PotentialA. Intrinsic rate of increase, r
dN/dt = rN
where r = intrinsic rate of increase
= innate capacity of increase
= Malthusian parameter
= mathematical expression of the biotic potential
N = existing population size
t = unit of time
The index “r” is basically the difference between birth
and death rates
r = b-d
dN/dt = (b-d)N = rN
dN/dt = rNGrowth rate is higher when?
1. __growth rate is higher__
e.g. Popn A Popn BNo = 100 No = 100
rA = 0.5 rB = 0.1dN/dt = (0.5)(100) dN/dt = (0.1)(100)
= 50 = 10N1 = 150 N1 = 110
2. _initial population size is higher_
e.g. Popn A Popn BNo = 10 No = 1000rA = 0.5 rB = 0.5dN/dt = (10)(0.5) dN/dt = (1000)(0.5)
N1 = 5 N1 = 50
Exponential Growth Pattern
dN/dt = rN Nt = Noert
where Nt = population size at time t
No = initial population size
e = base of natural log (2.71828)
r = rate of increase
t = unit of time
“ the population size at time t (Nt) is equal to the product of the initial
population size (No) and the natural log of the product of the intrinsic
rate of increase (r) and the time (t)
Differential Integral Eqn
Example: A growing insect population with an initial population size of 100 shows
an instantaneous birth rate of 0.65 and death rate of 0.10. Compute for the population size after 10 years.
Solution: r = b-d = 0.65 – 0.10 = 0.55
e = 2.71828
N10 = Noert = (100) (2.71828) (0.55) (10)
= 24,469
Doubling time = how long it takes for the population to double?
Nt/No = 2 = ert
ln2 = rt
t = ln2/r = 0.693/r = 0.693/0.55 = 1.26 years
Concept of doubling time
How long will it take for the population to double in
size?
Nt/No = e rt
ln (2) = rt
ln (2) = t
r
t = 0.693/r (doubling time) Rule of 70!
For the human population r = 0.02 = 2%
t = 0.693/0.02 = 35 years
t = 70/2 = 35
B. Finite Rate of Increase, λ
λ= N t+1/Nt 100/50 = 2
N t+1 = λNt
Nt = No λt
Factor by which a population increases during a single unit interval (hours, days, months, years)
Useful measure of population changes when the growth is seasonal
Biotic Potential in terms of Finite Rate of
increase,
• First, estimate :
• If Nt+1 = Nt , then = Nt+1/Nt, or 600/500 = 1.2
• If in 2001, there were 500 black bears in the Pasayten Wilderness, and
there were 600 in 2002, how many would there be in 2010?
• If N0 = 500, = 1.2, then in 2010 (9 breeding cycles later)
• N9 = N0 9 = (500)(1.2)9 = 2579
• In 2060 (59 breeding seasons), N = 23,478,130 bears!
• In general, with knowledge of the initial N and ,
one can estimate N at any time in the future by:
• Nt = N0 t
THE EXPONENTIAL
GROWTH PATTERN invading a new territory previously
unoccupied by the species.
exploiting a transient, unlimited favorable
conditions (presence of abundant
resources)
Bottom line: no limits!!!
A population growing at its maximum rate
grows slowly at first then faster and faster!
Exponential Population Growth
Examples of this?
◦ Think close to home
Often an unnatural occurrence
Conditions under which this
occurs naturally
◦ Introduced species (eg. janitor
fish)
◦ Nutritionally enriched
environments (algal blooms)
EQUATIONS
dN/dt = rN (differential equation)Expresses the rate of population change as the product of r and N.
Nt = Noert (integral equation)
Calculates the population size at specific time points during the
course of growth.
“As the population increases in size, N is getting bigger
and bigger, and the same “r” value continuously applied
would yield ever-greater increases”.
J-SHAPED CURVE
Exponential growth of a colonizing
population of Scots pine.
Hunting and habitat destruction reduced the
whooping crane. Protection and intensive
management of this population has led to
its dramatic recovery
What happens if there ARE limits?
(And eventually there ALWAYS are!)
LOGISTIC POPULATION GROWTH
Environmental limitations logistic growth
11.9
11.11
11.14
Higher N leads to lower realized r
<
Logistic Growth Pattern
As resources are depleted, population growth
slows and eventually stops
dN/dt = rN (K-N)
K
(Verhulst-Pearl Equation)
Logistic Growth Pattern
Same as differential growth equation
BUT, with a new term [1-(N/K)],
which is the same as [(K-N)/K].
Environmental Resistance Equation
without this term population grows very fast at the rate rN
with this term population slows down since (K-N/K) puts a break in the in the normal geometric growth pattern
dN/dt = rN (K-N)
K
Logistic Growth Pattern dN/dt = rN (K-N) (Verhulst Pearl Equation)
K
K – carrying capacity or the maximum population size allowed by the environment
(K-N)/K – “nearness to carrying capacity equation”
(1) If N is small in comparison to (K=100)
e.g. when N=5 K= 100
dN/dt = 1 x 5 (100 -5) = 5 x 0.95 = 4.75
100
(2) If N is close to (K=100)
e.g. when N= 98 K = 100
dN/dt = 1 x 5 (100-98) = 2.5
100
(3) At carrying capacity, when N=K
e.g. when N = 100 K= 100
dN/dt = 1 x 100 (100-100) = 0 (ZPG) – “zero population growth”
100
“A population following logistic growth grows at slower and slower
rate as it nears the carrying capacity” S-shaped curve!
Lo
gis
tic G
row
th
Logistic growth curve
Environmental limits
result in logistic
growth
Carrying capacity
New or changed
environment
No limits
S-shaped curve
Inflection Point
For most populations, four
factors interact to set the
carrying capacity, K.
(1) Availability of raw materials
(2) The availability of energy
(3) The accumulation of waste
products and their means of
disposal
(4) Interactions among
organisms
All factors above act together to limit
population size and they are
collectively called as
environmental resistance
factors
Carrying Capacity
Examples 1. Grass populations limited by
a. availability of nutrients (N2 and Mg) and water
b. number of insects feeding on them
c. competition with one another
2. Intraspecific competition within a population as manifested by crowding: causes breakdown in normal social behavior which leads to fewer birth rates and increased death rates
a. shrinkage of reproductive organs
b. abnormal mating behavior
c. decreased litter size
d. fewer litters per year
e. lack of maternal care
f. increased aggression in some rats
Density Dependent Factors
Factors whose effects intensify as the density of the population increases.
Tend to reduce population size by decreasing natality or increasing mortality as population size increases.◦ e.g. Food availability
breeding spaces
diseases
predation rate
competition
REGULATING POPULATION GROWTH
Density Dependent Forces
Types?
Examples
◦ Within species
Breeding spaces
Food
Mates
Foraging spots
◦ Between species
Predation
Parasitism
Pollinators
Competition
In Sum: Biotic factors
Density Independent Factors
Factors whose effects do not vary
regardless of population density.
Tend to be abiotic components.
Do not directly regulate population size.
e.g. weather and climate
volcanic eruptions
storms, fires, hurricanes
Density Independent Forces
Types?
Examples
◦ Climate
◦ Topography
◦ Latitude
◦ Altitude
◦ Rainfall
◦ Sunlight
In Sum: Abiotic factors
Life History Patterns
r and K selection
END OF LECTURE
NEXT MEETING:
August 16 Human Populations
August 19 Start of Reporting
Deadline for Project (poster)
for BIOWEEK 2011