Measuring and Modelling Population Change

Fecundity

FecundityFecundity - the potential for a species to produce offspring in one lifetime

this relates to the species’ ability to increase population rapidly over a long period of time

Fecundity is……HIGH when a female can produce many offspring (eg. 1 million eggs/year for a starfish)…LOW when a female can produce a limited # of offspring in their lifetime (eg. 20 offspring in 45 years for a hippo)

Carry capacity

Carrying capacityCarrying capacity - the maximum number of organisms that can be sustained by the available resources of a habitat over a given period of time

The CC is always changing since resource levels are never constant and depend on the changing abiotic elements of habitat (eg. climate).

Biotic potentialBiotic potential - the maximum rate a population could increase under ideal conditions (represented mathematically by r)

Survivorship Patterns

Biologists recognize three general patterns of survivorship among species

Type I Curve

•low mortality rate until past reproductive age

•long life expectancy

•slow to reach sexual maturity

•produce low # of offspring (eg. humans)

Survivorship Patterns

Biologists recognize three general patterns of survivorship among species

Type II Curve

•Intermediate between types I and II

•Have uniform risk of mortality throughout lifetime(eg. songbirds)

Survivorship Patterns

Biologists recognize three general patterns of survivorship among species

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(eg. sea turtles)

Population Change

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

initial population size (n)

a - result means population is declining. a + result means population is growing.

In an open populationopen population all four factors come into play

In a closed populationclosed population (eg. an isolated island) only births and deaths are a factor

Types 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 Growth

Deaths 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…

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

λ = N(t + 1)

N(t)

λ = fixed growth rate (from 1 year to the next) N = population size (at year “t”)

To find the population size at any given year, the formula is:

N(t) = N(0)λt

N(0) = initial population size

Geometric Growth

Sample Problem1. The 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. What is their growth rate?

ANSWER

N(0) = 88,000

N(1) = 88,000 + (33,000 – 20,000)

= 101,000

Therefore λ = N(1) = 101,000 = 1.15

N(0) 88,000

The growth rate is 1.15

Sample Problem2. What will the population size be in 10 years at this current growth

rate?

ANSWER

From the first question: λ = 1.15

Therefore N(10) = N(0)λ10

= 88,000(1.15)10

= 356,009

The population will be 356,009 individuals in 10 years

Exponential Growth Many species (eg. humans) are not limited to a breeding

season and can reproduce at a continuous rate throughout the year

Since they grow continuously, we can determine their intrinsic growth rate (r)

r = b (births per capita) – d (deaths per capita)

Instantaneous growth rate = N = rN

t

r = intrinsic growth rate

N = population size

Exponential Growth Many species (eg. humans) are not limited to a breeding

season and can reproduce at a continuous rate throughout the year

Since they grow continuously, we can determine their intrinsic growth rate (per capita), r

r = b (births per capita) – d (deaths per capita)

Doubling time = td = 0.69

r

td = doubling time

r = intrinsic growth rate

Sample Problem

A 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

N = rN = 0.030 x 2500 = 75 per hour

t

When 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.

Logisitc Growth The previous two models assumed an unlimited resource

supply (NEVER the real case) When a population just starts out the population follows the

exponential model As the population gets larger it nears the ecosystem's carrying

capacity and the growth rate drops to a stable equilibrium of births and deaths

The population size is now the carrying capacity (K).

This is known as a sigmoidal curveA: Small population, increasing

slowlyB: Large population, increasing

fastestC: Approaching K, dynamic

equilibrium established (b = d, no net increase)

t

Logistic Growth, continued.

Logistic growth is the most common/realistic growth pattern in nature

rmax = maximum intrinsic rowth rate

K = population at carrying capacity

N = population size

If the population size is close to K there is virtually no growth (K - N = 0)

This equation takes into account declining resources as the population increases

N= rmaxN

K - NK

Sample 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.

Answer

a)

rmaxPopulation size, N (K - N)

K

New members of population

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 Change

There are many things that can alter a population size:

Density-independent factorsDensity-independent factors limit population growth no matter what the population size

(eg. natural disaster, human intervention, etc.)

Density-dependent factorsDensity-dependent factors limit population growth

and intensify as the population increases in size (eg. competition for resources, disease, etc.)

Density-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 (eg. 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

Density-dependent FactorsIntraspecific competitionIntraspecific competition - individuals of the same species

compete for resources

PredationPredation – (you know what this means) If more prey is available, predators will eat better

Illness/diseaseIllness/disease – spreads faster when a population has a high density