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