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14.2-Measuring and Modelling Population Change
Carrying capacity: maximum number of organisms that can be sustained by available resources over a
given period of time
Population dynamics: changes in population characteristics determined by natality, mortality,
immigration and emigration
Fecundity: the potential for a species to produce offspring in one lifetime
Births, deaths, immigration and emigration can be used to calculate changes in population size
Population size= [(births + immigration)-(deaths + emigration)]/initial population size x100
Open population: a population in which change in number and density is determined by births, deaths,
immigration and emigration
Closed population: a population in which change in size and density is determined by natality and
mortality alone
Biotic potential: the maximum rate a population can increase under ideal conditions
Geometric growth: a pattern of population growth where organisms reproduce at fixed intervals at a
constant rate
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Can be determined by comparing the population size in one year to the population size at the
same time the previous year
λ= N(t+1)/N(t)
Exponential growth: a pattern of population growth where organisms reproduce continuously at a
constant rate
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dN/dt= rN
per capita growth rate (r)
o difference between the per capita birth rates and the per capita death rates
population size (N)
Logistic growth: a model of population growth describing growth that levels off as the size of the
population approaches its carrying capacity
dN/dt= rmaxN[(K-N)/K]
dN/dt population growth at a given time
rmax  maximum per capita growth rate
N  population at a given time
K  carrying capacity of the environment
The curve formed by the logistic growth pattern on a graph has three distinct phases:
Lag phase: the initial stage in which population growth rates are slow as a result of small population size
Log phase: the stage in which population growth rates are very rapid
Environmental resistance: any factor which limits a population’s ability to realize its biotic potential
when it nears or exceeds the environment’s carrying capacity
Stationary phase: the phase in which population growth rates decrease as the population size reaches
the carrying capacity and stabilizes
Dynamic equilibrium: the condition of a population in which the birth rate equals the death rate and
there is no net change in population size
Practice Problems:
1a) 32,000 – 29,000= 3,000
3,000 + 50,000= 53,000
53,000/50,000= 1.06
The geometric growth rate is 1.06.
1b) N(2)= 53,000 x 1.00
= 56,180
N(10)= 50,000 x (1.06)10
= 89,542
The population size after two years will be 56,180 and 89,542 after 10 years.
2a) 980 x 0.345= 338
The initial instantaneous growth rate of the population is 338 per day.
2b) 0.69/0.345= 2
The doubling time for the population is 2 days.
2c) 11 doubling times (22 days) will have to pass in order for the population to exceed 2,000,000.
3)
r
max
1.00
1.00
1.00
1.00
1.00
1.00
Population size N
20
200
500
900
990
1,000
((K-N)/K)
980/1,000
800/1,000
500/1,000
100/1,000
10/1,000
0
Population growth rate
19.6
160
250
90
9.9
0
4) The maximum growth rate influences the relationship between population size and the
environment’s carrying capacity because it leads to an increase in population growth rate.
Section Questions:
1) population: 34, births/migration: 57+20+4, deaths/emigration: 28+9+11+8
81-56=25
25+34=59
59/34= 1.74
The population growth rate is 1.74.
2) population: 90, births: 342, deaths: 43, emigration: 0, migration: ?
4.29x90=386
342-43=299
386-299=87
87 mice migrated into the field.
3) population: 42, births: 263, deaths: 26+8+12=46
42+263-46=259/42
= 6.2
The population growth rate of the frogs in the ravine from April to August is 6.2.
4a) Exponential growth is occurring.
4b) N(8)= 2x(4.5)8
= 336,302
The number of individuals in the population after eight years is about 336,302.
5a) Exponential growth is occurring.
5b) Factors that would have to be in place for the population to its biotic potential could include enough
food supply and a large area of living space.
5c) Types of environmental resistance that might restrict the cats from reaching their biotic potential
could include a decrease in food supply and an increase in predation.
7a) population: 198, births: 34, deaths: 86, migrated:12
34+12-86= -40/198
= -0.2
The growth rate of the population is -0.2.
7b) It may be a concern considering almost half of the population of frogs died in the first year.
7c) I do not think that tracking the population growth rate of one population of frogs over one year in
this marsh is an adequate to make a conclusion about the environment because of the short time span
that they were studied. Many factors could have contributed during the year that may have not been
applied in previous years. Other years need to be studied so that they can be compared.
8b) Exponential growth has occurred throughout the generations.
8c) The growth curve of the graph would differ if there were only three offspring instead of six because
the graph would be increasing at a lower rate, however it would still be an exponential graph.
14.3-Factors Affecting Population Change
Density-dependent factor: a factor that influences population regulation, having a greater impact as
population density increases or decreases
Intraspecific competition: an ecological interaction in which individuals of the same species of
population compete for resources
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As population density increases, there is more competition so the growth rate slows
Can have an effect on reproductive success
Predation: an ecological interaction in which a predator catches and consumes prey
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Can result in density-dependent regulation of the preferred species of prey (faster prey may
escape being killed by the predator)
→ Some density-dependent factors reduce population growth rates at low rather than high densities
Allee effect: density-dependent phenomenon that occurs when a population cannot survive or fails to
reproduce enough to offset mortality once the population density is too low
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If a population is too small, it may be difficult to find mates
Some species need a large population density to display social interaction
Threatened populations may have low reproductive success
If a species has low reproductive rates, they need increased numbers to maintain the population
Minimum viable population size: the smallest number of individuals needed for a population to
continue for a given period of time
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Consists of enough individuals to ensure the population can cope with variations in death as well
as environmental changes and disasters
Varies among species
Density-independent factors: factors that influence population regulation regardless of population
density
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Human intervention, extreme weather changes
Species may not breed in extreme temperatures
Limiting factor: any essential resource that is in short supply or unavailable
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Determines how much the individual or population can grow
→ More drastic population growth or decline can result in adverse changes to the habitat or even to the
population itself
→ When the population passes the carrying capacity, the number of deaths increase and the number of
births decrease
Section Questions:
1) Natality and immigration makes the population bigger because individuals are being added to
the total population and mortality and emigration makes the population smaller because
individuals are being removed from the population.
2) Density-dependent factors are factors that influence the population regulation which has an
impact as population density increases or decreases. Density-independent factors are factors
that influence the population regulation regardless of the population density.
3a) density-independent factor
3b) density-independent factor
3c) density-dependent factor
4) A density-independent factor is pollution and a density-dependent factor is disease. These
factors could limit the growth of the population.
5a) This is a case of density-dependent regulation
5b) I think that when food supply is on the y-axis and population density is on the x-axis, the slope of
the graph is negative because as there is more individuals of the population, there is less food per
individual.
7
Food Supply
6
5
4
3
2
1
0