Population EcologyPopulation Ecology

IntroductionIntroduction

All populations of organisms are dynamic.

Many factors, such as predation, available resources, or environmental changes, influence the changes in a species’ population.

Population dynamicsPopulation dynamics is the study of the long term changes in population sizes and the factors that cause a change.

History of Population History of Population DynamicsDynamics

Thomas Malthus proposed the first mathematical equation to characterize human population growth over 200 years ago.

This lead to the development of many equations for the various kinds of population growth, some of which we will cover in this unit.

There are four factors that affect a population’s growth:

1) Births (natality) (B)2) Deaths (mortality) (D)3) Immigration (I)4) Emigration (E)

These factors can be put into a simple equation to summarize the changes in a population from one moment in time

(N0) to another (N1):

N1 = N0 + (B – D) + (I – E)

Population DensityPopulation DensityPopulation DensityPopulation Density is a measure of how many individuals

of a given species are found in a given area.There are two types of density:

1) Crude densityCrude density is the total number of individuals divided by the total area of the entire habitat.2) Ecological densityEcological density is the total number of individuals divided by the total useable area in the habitat.

The equation for population density (D) is: D = N (population size)/S (area)

Population DispersionPopulation Dispersion

Population dispersion is how individuals of a species are arranged in their environment. There are three kinds.

Clumped dispersionClumped dispersion is usually due to a species being concentrated in areas most favourable for survival (ex. Cattails in wet soils lining ponds or lakes) or social behaviour (ex. fish in schools) for protection from predators

Uniform dispersionUniform dispersion is when the individuals of a species are spaced equally throughout a habitat. This usually occurs with territorial organisms (ex. penguins).

Random dispersionRandom dispersion is when organisms are spread throughout a habitat in an unpredictable and patternless way

Measuring PopulationsMeasuring Populations

Population density is found differently depending on whether the species being studied is mobile or stationary.

QuadratQuadrat studies are used for non-mobile populations such as plants.

Mark-RecaptureMark-Recapture studies are used for mobile populations such as animals.

Quadrat StudiesQuadrat StudiesA quadratquadrat is a small sample frame (usually a square) that is

placed randomly throughout a larger ecosystem in order to estimate the population density (D).

All the individuals counted in the quadrats are added together in the following equation:

Estimated density = total number of sampled individuals / total sample area

The population size (N) can then be estimated:

N = (estimated density)(total area of studied habitat)

Example CalculationsExample CalculationsA student wants to estimate the population of ragweed plants in a

large field which measures 100 m x 100 m. She randomly places three 2.0 m x 2.0 m quadrats in the field. Estimate the population density and size if she finds 18, 11, and 24 plants in her three quadrats.

average sample density = total number of individuals

total sample area

= 18 + 11 + 24

(4.0m)² + (4.0m)² + (4.0m)²

= 4.4 ragweed plants/m²

estimated population size = (estimated population density) (total size of study area)

= (4.4 plants/m²) x (10 000m²)

= 44 000 plants

Mark-Recapture MethodMark-Recapture MethodTo start, traps are laid out in the

study area and any subjects that are captured are marked and returned to the environment.

A short time later the traps are set again and individuals are captured.

This time it is noted how many individuals were recaptures and how many were new captures.

All this data can be plugged into an equation to estimate population density.

The equation is:M (total # marked on 1st day) = m (# of recaptures)

N (total estimated population) n (total # captured on 2nd day)

Example CalculationExample Calculation

Consider a fish population of unknown size where 26 individuals are randomly captured, marked, and released. Some time later, 21 individuals are captured and three of those appear to already have been marked. What is the estimated population size?

total # marked individuals in population 26 = 3 # marked in 2nd sample

estimated population size N 21 size of 2nd sample

N = 26 x 21 N = 182

3

Therefore, the estimated population size is 182.

HomeworkHomework

Page 659, # 3, 4, 5, 6

Measuring and Modelling Measuring and Modelling Population ChangePopulation Change

FecundityFecundity is the potential for a species to produce offspring in one lifetime. This relates to the species’ ability to increase population rapidly or over a long period of time.

High fecundityHigh fecundity is when a female of a species can produce large numbers of offspring (ex. star fish lay over 1 million eggs per year).

Low fecundityLow fecundity is when a female can produce a much more limited number of offspring in their lifetime (ex. a hippopotamus could produce maybe 20 young over an average life of 45 years).

Carrying capacityCarrying capacity is the maximum number of organisms that can be sustained by the available resources of a habitat over a given period of time. It is always changing as the resource levels are never constant and depend on the changing abiotic elements of habitat (ex. climate).

Biotic potentialBiotic potential is the maximum rate a population could increase under ideal conditions. It is represented mathematically by r.

Survivorship PatternsSurvivorship Patterns

Biologists recognize three general patterns of survivorship among species.

Type I Curve

- Low mortality rate until they are past their reproductive age

- Long life expectancy

- Slow to reach sexual maturity and produce low numbers of offspring

- Ex. Humans and most large mammals

Type II Curve

-Intermediate between types I and III

-Have a uniform risk of mortality over their lifetime (i.e. coral, squirrels, most reptiles, honeybees…)

Type III Curve

-Very high mortality rate when young

-Those that reach sexual maturity have a greatly reduced mortality rate

-Very low average life expectancy

-Ex. Green Sea Turtle, plants, oysters…

Population ChangePopulation Change

Population change (%) = [(birth+immigration)–(deaths+emigration)] x 100initial population size (n)

A negative result means population is declining.A positive result means population is growing.

In an open populationopen population all four factors come into play. In a closed closed populationpopulation, normally an island, only births and deaths are a factor.

Types of Population GrowthTypes of Population Growth

Geometric growthGeometric growth is a pattern where organisms reproduce at fixed intervals at a constant rate.

Exponential growthExponential growth is a pattern where organisms reproduce continuously at a constant rate.

Logistic growthLogistic growth is a pattern where growth levels off as the size of the population reaches the carrying capacity of their environment.

Geometric GrowthGeometric GrowthDeaths occur at a relatively constant rate over

time but births are restricted to a specific breeding period. These populations increase rapidly during breeding season and decline slowly the rest of the year.

Appears continuous

In reality…

Their growth rate is a constant (λ) and can be determined using the following equation:

λ = N (t + 1) N(t)

– λ is the fixed growth rate (from one year to the next)– N is the population size at year (t+1) or (t)

To find the population size at any given year, the formula is: N(t) = N(0)λt

– N(0) is the initial population size

Sample ProblemSample ProblemThe initial Puffin population on Gull Island, Newfoundland is 88 000. Over the

course of the year they have 33 000 births and 20 000 deaths. a) What is their growth rate?

ANSWERa) N (0) = 88 000 λ = N(t + 1) = 101 000 = 1.15 N (1) =101 000 N(t) 88 000 Therefore the growth rate is 1.15.

b) What will the population size be in 10 years at this current growth rate?

ANSWER: From a) growth rate, or λ = 1.15N(10) = N(0)λ10

* Remember BEDMAS! = 88 000 (1.15)10 = 356 009

Therefore the population size will be 356 009 in 10 years.

Exponential GrowthExponential GrowthMany species, such as bacteria, are not limited to a breeding season. These species can

reproduce at a continuous rate throughout the year. Since they grow continuously, biologists are able to determine the instantaneous growth

rate, or intrinsic (per capita) growth rate, r. (r = b (births per capita) – d (deaths per capita))

Population growth rate is given by:

dN = rN dt

To find the time it takes a population that is reproducing exponentially to double, we use the equation:

td = 0.69

r

Instantaneous growth rate

r is growth rate per capita and N is population size

Example CalculationsExample CalculationsA population of 2500 yeast cells in a culture tube is growing exponentially. If the intrinsic

growth rate is 0.030 per hour, calculate:

a) the initial instantaneous growth rate of the yeast population.

b) the time it will take for the population to double in size.

c) the population size after four doubling periods.

a) r = 0.030 per hour and N = 2500

dN = rN = 0.030 x 2500 = 75 per hour

dtWhen the population size is 2500 the instantaneous growth rate is 75 per hour.

b) r = 0.030 td = 0.69 = 0.69 = 23 hours

r 0.030

The yeast population will double in size every 23 hours.

Doubling Time Time (hours) Population Size

0 0 2500

1 23 5000

2 46 10 000

3 69 20 000

4 92 40 000

c)

After 4 doubling periods, the population of the yeast culture is 40 000 cells.

Logistic GrowthLogistic GrowthThe previous two models assume an unlimited resource supply, which is never the

case in the real world.

However, when a population is just starting out, resources are plentiful and the population grows rapidly.

As the population grows, resources are being used up and the population nears the ecosystem's carrying capacity (K). The growth rate drops and a stable equilibrium exists between births and deaths. The population size is now at the carrying capacity (K).

This is known as a sigmoidal curve.A: Population small, increasing slowlyB: Population goes through largest increaseC: Dynamic equilibrium (at carrying capacity), b=d, no net population increase

Logistic Growth, continued.Logistic Growth, continued.Logistic growth represents the effect of carrying capacity on the growth of a population. It is

the most common growth pattern in nature.

dN = rmax

N (K – N)

dt K

Notice if the population size is close to the carrying capacity, there is virtually no growth (K-N = 0), thus the equation takes into account declining resources as the population increases.

Population growth at a given time

Max intrinsic growth rate

Population size at given time

Carrying capacity

Sample ProblemSample ProblemA population of humans on a deserted island is growing continuously. The carrying

capacity of that island is 1000 individuals and the maximum growth rate is 0.50.a) Determine the population growth rates over 5 years if the initial population size is 200.b) Describe the relationship between population size and growth rate.

Answera)

rmaxPopulation size, N (K-N)

K

Population growth rate

0.50 200 800/ 1000 80

0.50 500 500/1000 125

0.50 900 100/1000 45

0.50 990 10/1000 4.95

0.50 1000 0 0

b) When the population is small the rate of growth is slow. The rate of growth increases as the population gets larger and then, as it approaches carrying capacity, the growth rate declines and levels off.

Factors Affecting Population Factors Affecting Population ChangeChange

There are many things that can alter a population size.

Density-independent factorsDensity-independent factors limit population growth no matter what the population size (ex. natural disaster, human intervention, etc).

Density-dependent Density-dependent factorsfactors limit population growth and intensify as the population increases in size (ex. competition for resources, disease, etc).

Density-dependent FactorsDensity-dependent FactorsIntraspecific competitionIntraspecific competition is when individuals of the same

species compete for resources. If this is high then the population will have a low growth rate.

PredationPredation is a density-dependent factor. If there is more prey available they will be chosen more by predators.

Illness/disease spreads faster when a population has a higher density.

Allee EffectAllee Effect

Warder Allee found that some density-dependent factors reduce population growth when the population is at a low density rather than high density.

This is known as the Allee effectAllee effect.

For example, at times when a population has such a low density it is harder for individuals to find a mate and successfully reproduce thus lowering the growth rate of the species.

Small populations also may go through inbreeding depressioninbreeding depression which reduces the populations’ genetic variability and may prevent successful population growth.

The minimum viable population minimum viable population sizesize is the smallest number of individuals that ensures the population will persist for a certain period of time. It is different for different species. Allows biologists to determine whether a species is endangered.

Density-independent FactorsDensity-independent FactorsThe resource in the ecosystem

that is in the shortest supply is known as the limiting factorlimiting factor since it is preventing massive population growth.

Often times these are based on human influences on the ecosystem (ex. pollution, urban sprawl, etc.) but it could also be related to changes in climate (ex. a dry season that growth of plants for food) or natural disasters.