Population Ecology

Population – a group of organisms of the same species occupying a particular space at a particular time.

Populations are units of study.

Population Attributes

• Density – size of a population in relation to a definite unit of space

• Affected by:– Natality – the reproductive output (birth rate) of

a population– Mortality – the death rate of organisms in a

population– Immigration – number of organisms moving

into the area occupied by the population– Emigration – number of organisms moving out

of the area occupied by the population

Population Density

Four primary population parameters:

Density Examples

Two fundamental attributes that affect our choice of techniques for population estimation are the size and mobility of the organism with respect to humans.

Range of Population Density

Two Types of Density Estimates

• Absolute Density – a known density such as #/m2

• Relative Density – we know when one area has more individuals than another

Measuring Absolute Density

• Total Count – count the number of organisms living in an area– Human census, number of oak trees in a

wooded lot, number of singing birds in an area– Total counts generally are not used very often

• Sampling Methods – use a sample to estimate population size– Either use the quadrat or capture-recapture

method

Quadrat Method• A Quadrat is a sampling area of any shape

randomly deployed. Each individual within the quadrat is counted and those numbers are used to extrapolate population size.– Example: a 100 square centimeter metal

rectangle is randomly thrown four times and all of the beetles of a particular species within the square are counted each time: 19, 21, 17, and 19. This translates to 19 beetles per 100 cm2 or 1900 per m2.

Transects as Quadrats

• Each transect was 110 meters long and 2m wide (220 m2 or 0.022/ha). All trees taller than 25 cm counted.

Capture-recapture Method

• Important tool for estimating density, birth rate, and death rate for mobile animals.

• Method:– Collect a sample of individuals, mark them,

and then release them– After a period, collect more individuals from

the wild and count the number that have marks– We assume that a sample, if random, will

contain the same proportion of marked individuals as the population does

– Estimate population density

Assumptions For All Capture-Recapture Studies

• Marking technique does not increase mortality of marked animals

• Marked individuals are allowed to mix with population

• Marking technique does not affect catch probability

• Marks are not lost or overlooked• No significant immigration or emigration• No significant mortality or natality

Marked animals in second sample

Total caught in second sample

Marked animals in first sample

Total population size

=

520 N

16=

Peterson Method or Lincoln Index

N = 64N = (20)(16)5

Indices of Relative Density

• Assume that samples represent some relatively constant but unknown relationship to total population size.– # cars in the Piggly Wiggly parking lot

• Provides an index of abundance– Is population increasing, decreasing, or

staying the same– Are there more animals in one location than

another?– Can not quantify differences between sites

Twice the number of tracks does not = twice as many animals

Some Indices Used

• Traps• Number of Fecal

Pellets• Vocalization

Frequency• Pelt Records• Catch per Unit Fishing

Effort

• Number of Artifacts• Questionnaires• Cover• Feeding Capacity• Roadside Counts

Natality (birth rate)• Fecundity – physiological notion that

refers to an organism’s potential reproductive potential – Usually inversely proportional to the amount of

parental care given to young

• Fertility – Ecological concept that is based on the number of viable offspring produced during a specific period– Realized fertility – actual fertility rate

One birth per 15 years per human female in the child-bearing ages

– Potential fertility – potential fertility rate One birth per 10 to 11 months per human

female in the child-bearing ages

Natality Continued• Absolute or crude natality – number of

new individuals per unit time– 50 protozoa increase to 150 by division in one

hour, then crude natality = 100

• Specific natality – number of new members divided by the population size– 100 new protozoa in one hour from original 50 – 100/50 = 2 protozoa per original per hour

• 400 births in one year in a town of 10,000– Absolute natality = 400– Specific natality = 400/10,000 = 0.04 = 4%

Mortality

• Opposite of mortality is survival• Longevity focuses on the age of death of

individuals in a population– Potential longevity – maximum lifespan by an

individual of a particular species Set by the organisms physiology (dies of old age) Sometimes described as the average longevity of

individuals living in optimal conditions– Realized longevity – actual life span of an organism

Measured as an average for all animals living under real environmental conditions

Determining Mortality• Mark several individuals and measure how many survive

from time t to t+1.• If abundance of successive age groups is known, then you

can estimate mortality between successive age groups.• Can use catch curves for fish:

147292

Survival between age 2 and 3=

147/292=0.50

Or develop regression equation

Immigration and Emigration

• Seldom measured

• Assumed to be equal or insignificant (island pop’s)

• However, dispersal may be a critical parameter in population changes

Life Tables - Mortality

• Mortality is one of the four key parameters that drive population changes.

• We can use a life table to answer particular questions about population mortality rates.– What life stage has the highest mortality?– Do older organisms die more frequently than

young organisms• A cohort life table is an age-specific summary of

the mortality rates operating on a cohort of individuals.

• Cohort – a collective group of individuals– Fish year class, all mice born in March, tadpoles from a

single frog, freshman year class

X = age

nx = number alive at time t

lx = proportion of organisms surviving from the start of the life table to age x (ex: l1 = n1/n0, 0.217 = 25/115; l2=n2/n0, 0.165=19/115)

dx = number dying during the age interval x to x + 1 (ex:d0=n0-n1, 90 = 115-25; d1=n1-n2, 6=25-19)

qx = per capita rate of mortality during the age interval x to x + 1 (ex: q0=d0/n0, 0.78 =90/115; q1=d1/n1)

Cohort Life Table:

Per Capita Rates• Per capita is a presentation of data as a

proportion of the population.

• Suppose a disease kills 400 ducks:– If total duck population = 250,000 then the per

capita mortality = 400/250,000 = 0.16%.– If total duck population = 2,500 then the per

capita mortality = 400/2,500 = 16%.

• Per capita gives us an idea of how the entire population is affected.

• Allows us to standardize a population

Suvivorship Curve

Types of Survivorship Curves

• Type 1 – Mortality rates high late in life span

• Type 2 – Mortality rates fairly constant with age

• Type 3 – Mortality rates highest early in life span

Survivorship Curves

• Can be a reflection of the amount of parental care

• Can be affected by population density

Managed for hunting

Unmanaged area

bx = natality; (lx)(bx) = reproductive output for that age class

R0 = (lx)(bx) = net reproductive rate

Population net reproductive rate

Fertility Schedule

0.6% increase each generation

Adding Reproduction

Net Reproductive Rate

Under stable conditions R0 is usually around 1.

R0 < 1 population is declining, R0 = 1 population is stable, R0 > population is increasing.

Can greatly affect the population growth rate, and natural selection works towards an adaptive reproductive schedule

Population Age Structure

R0 > 1 R0 = 1 R0 < 1

Population Age Pyramids

Dominant Year Class

• Fish reproduction strongly affected by year-to-year fluctuations

• Population Age Pyramids will be different

Relationships

Environmental factors

Mortality Rates

Natality Rates

Age Composition

Rate of increase or decrease of the population

Growth With Discrete Generations• Species with a single annual breeding season

and a life span of one year (ex. annual plants).• Population growth can then be described by the

following equation:

• Where– Nt = population size of females at generation t

– Nt+1 = population size of females at generation t + 1

– R0 = net reproductive rate, or number of female offspring produced per female generation

• Population growth is very dependent on R0

Nt+1 = R0Nt

Multiplication Rate (R0) Constant

• If R0 > 1, the population increases geometrically without limit. If R0 < 1 then the population decreases to extinction.

• The greater R0 is the faster the population increases: Geometric Growth

Multiplication Rate (R0) Dependent on Population Size

• Carrying Capacity – the maximum population size that a particular environment is able to maintain for a given period.– At population sizes greater than the carrying capacity,

the population decreases– At population sizes less than the carrying capacity, the

population increases– At population sizes = the carrying capacity, the

population is stable

• Equilibrium Point – the population density that = the carrying capacity.

Y = mX + b

Y = b – m(X)

Intercept

Net Reproductive rate (R0) as a function of population density:

N = 100, then R0 = 1.0 population stable

N > 100, then R0 < 1.0 population decreases

N < 100, then R0 > 1.0 population increases

Remember, at R0 = 1.0 birth rates = death rates

Growth With Overlapping Generations

• Previous examples were for species that live for a year, reproduce then die.

• For populations that have a continuous breeding season, or prolonged reproductive period, we can describe population growth more easily with differential equations.

Multiplication Rate Constant

• In a given population, suppose the probability of reproducing (b) is equal to the probability of dying (d).– Instantaneous rate of

population growth = r = b – d

– Then dN/dt = (b – d)N = rN

– Population grows geometrically

Multiplication Rate Dependent on Population Size

dNdt = rN

K - N

K

Where:

N = population size

t = time

r = intrinsic capacity for increase

K = maximal value of N (‘carrying capacity’)

K

r Pop. Size (K-N)/K Growth Rate

1.0 1 99/100 0.99

1.0 50 50/100 25.00

1.0 75 25/100 18.75

1.0 95 5/100 4.75

1.0 99 1/100 0.99

1.0 100 0/100 0.00

dNdt = rN

K - N

K

Logistic Growth

Theoretical Growth Forms

Population Fluctuations

• Irruption – a boom in numbers followed by a bust

• Unpredictable, but usually happen when weather, food, and shelter are all ideal

Population Cycles

• Population increase and decrease follow a multiple year cycle

• Usually predator prey cycles, but not always

Modeling Population Cycles

Population Level Pulsing

Density Independent / Dependent Factors

• Physical factors such as unpredictable weather, water currents, chemical limiting conditions, or pollution can affect the population no matter the size

• Biotic factors such as competition, parasites, and predation often work as a density dependent factor (more important at higher densities)

Metapopulations

• Subpopulations occupying discrete patches of suitable habitat separated by unsuitable habitat (except dispersal corridors)

• Source vs. sink

r vs K selection

• r – intrinsic rate of increase– r-selected species have evolved to put a lot of

energy into reproduction and growth

• K – carrying capacity– K –selected species have evolved to put a lot

of energy into maintenance

r vs K selection