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Chapter 9

BIOB50H3 Chapter Notes - Chapter 9: Density Dependence, Logistic Function, Song Sparrow

Biological Sciences
Course Code
Marc Cadotte

of 6
Human Population Growth: A Case Study
Human population was over 6.8 billion in 2010 and 3 billion in 1960
From 1860-1991, while the human population has quadrupled in size, our energy
consumption has increased 93-fold
Previously, our population increased relatively slow.
We reached 1 billion in 1825, after 200,000 years, for the first time as a result of
Industrial Revolution.
No one knows for sure when we switched from a relatively slow to explosive
increases in population size
According to best info, there were 500 million people in 1550 and population was
doubling every 275 years.
Population started growing at a very rapid rate once it hit 1 billion
First it doubled from 1 to 2 billion by 1930, in 105 years, and then to 4 billion by
1975, in 45 years.
By 1975, it was growing at an annual rate of 2% which means it doubled after
every 35 years
With that rate, our population would increase to more than 27 billion by 2080,
which is quite unlikely, however
Over the last 50 years, the annual rate has slowed considerably, from 2.2% in
early 1960s to a present rate of 1.18%
Currently, our population increases by about 80 million per year (more than 9100
per hour)
5 countries account for about half of the annual increase: India (21%), China
(11%), Pakistan (5%), Nigeria (4%), and United States (4%)
If this current rate sustains, there will be 15 billion people by 2080
Earth is finite and can't support ever-increasing population, thus restricting our
capacity for rapid population growth
Fungi, known as giant puffballs, can produce about 7 trillion offspring per
individual but not all of them reach adulthood.
In the case of loggerhead sea turtles, even if you protect these endangered
species by increasing their newborn survival to 100%, their population would
continue to decline.
An ecologist must understand what factors promote and limit population growth
Life Tables
To obtain life table data for a plant, you mark a large number of seeds as they
germinate and then follow their fate over growing seasons
Life table provides a summary of how survival and reproductive rate vary with
age for organisms. It can be based on age, size, or life cycle stage
In a life table,
x is a variable such as age
Nx is the number of individuals alive at age x
Sx = Nx+1 / Nx. It is the age-specific survival rate, which is the chance that
an individual of age x will survive to be x + 1.S2.
Ix = Nx / No. It represents survivorship, which is the proportion of
individuals that survive from birth to age x
Fx represents fecundity, which is the average number of offspring
produced by a female of age x
A cohort life table is where the fate of a group of individuals born during the
same time period (a cohort) is followed from birth to death. These are often for
plants or other sessile organisms because they can be marked and followed
A static life table is often used for highly mobile organisms or ones with long life
spans. It is a table where the survival and reproduction of individuals of different
ages during a single time period are recorded.
You construct a static life table by first estimating the organisms' ages,
determining age-specific birth rates by counting # of offspring by individuals
produced, and then determining age-specific survival rate (only if we assume the
survival rate has remained constant during organisms' lifetimes)
When birth and death rate are hard to find or correlate poorly with age, life tables
are based on sizes or life cycle stages
For some, reproduction rate is closely related to size than age
We can also predict change in size and composition over time by using birth and
death rates
Many economic, sociological, and medical applications rely on human life table
data such as life insurance companies
2009 report by U.S. Centres for Disease Control and Prevention provided
information on Ix , Fx , and life expectancy (expected # of years remaining) of
In U.S., Ix doesn't drop greatly until age 70, while in Gambia, many people die at
young age especially those born in the annual "hungry season" (July-Oct)
E.g., 47%-62% of Gambian reached age 45, compared to >96% of U.S. females
Ix can be graphed as a survivorship curve where the data is plotted from
hypothetical cohort (typically of 1000 individuals) that will reach different ages
Ix curves can be classifies into 3 types
Type I survivorship curve is where newborns, juveniles, and young
adults have high survival rates and most survive until old age. E.g. US females
and Dall mountain sheep
Type II survivorship curve is where individuals have a constant chance
of dying throughout their lives. E.g. mud turtles (after second year) and some
fish, plants, and birds
Type III survivorship is where most individuals die young. It's the most
common one in nature since many species produce a lot of offspring. E.g. giant
puffballs, oysters, marine corals, most known insects, and plants like desert
Age Structure
Age class - individuals whose ages fall within a specified range
Age structure - describes proportions of the population in each age class
Age structure influences how rapidly population grows or shrinks
In general, population with more individuals of reproductive age will grow more
Age structure and population size can be predicted from life table data
Life table data can be used to predict how many individuals our population will
have the following year by first multiplying # of individuals in each age class by
survival rate for that age class to find out the # of survivors of age x that will
survive in the next time period. E.g., N2 x S2
Then, determine the # of newborns those survivors will produce in the next time
period by multiplying fecundity of one age class with the # of survivors of that age
class in the next time period and adding it with a sum of fecundity and # of
survivors in the next time period of another age class. E.g. (F2 x (N2 x S2)) + (F3 x
(N3 x S3))
Check out Table 9.4 on p. 205
We can calculate ratio of population size to find year-to-year growth rate by using
λ = Nt+1/Nt
# of individuals in different age classes vary a lot in the first few years but
eventually different age classes and population as a whole increases at the same
Similarly, λ fluctuates a lot initially but eventually comes to a constant value
A population has a stable age distribution when its age structure doesn't
change from one year to next
A single change in Fx at any age class can change the stable age distribution
Birth, death, and growth rates can change gradually or dramatically when
environmental conditions change
Thus, we can change birth and death rates by manipulating the abiotic and biotic
An efficient way to do this is by identifying the age-specific birth and death rates
that strongly influence the population growth rate
E.g. most effective way to increase endangered turtle populations was to
increase survival rates of juvenile and mature turtles
Study by van Mantgem and colleagues showed gradual increase of coniferous
forest trees across western U.S. due to rapid temperature increase which
increased trees' climatic water deficit (amount by which plant's annual
evaporative demand for water exceeds available water)
Exponential Growth
In general, populations can grow rapidly when individuals leave an average of
more than one offspring over substantial periods of time
Populations grow geometrically when reproduction occurs in synchrony or
discrete time periods (regular time intervals). E.g. cicadas and annual plants
Geometric growth occurs when population changes in size by constant
proportion from one discrete time period to the next and forms a J-shaped set of
points when plotted on a graph
First geometric growth equation is Nt+1 = λNt where λ is a multiplier that allows
you to predict size of the population in the next time period and is any # greater
than 0