chapter 9: population growth and regulation
CHAPTER 9: POPULATION GROWTH AND REGULATION 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 Introduction • 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
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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 easily 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 females 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 shrub Age Structure Age class - individuals whose ages fall within a specified range Age structure - describes proportions of the population in each age class
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Age structure influences how rapidly population grows or shrinks In general, population with more individuals of reproductive age will grow more rapidly 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 rate 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 environment 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
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λ is the geometric population growth rate or the per capita finite rate of increase When λ is between 0 and 1, the population decreases over time A second geometric equation is Nt = λt N0 where N0 is the initial population size (population size at t=0) Use 1st equation if population size in current and previous time periods is known Use the second equation to predict size of population after any # of discrete time periods Populations grow exponentially when reproduction occurs continuously and where generations can overlap Exponential growth - Change in population size by a constant proportion at each instant in time and forms J-shaped curve when plotted on a graph Exponential growth can be described in 2 equations: 1) dN/dt = rN 2) N(t)=N(0)ert - here e=2.718 and ert can be calculated using function ex dN/dt represents rate of change at each instant in time N(t) is the population size at each instant in time. r is called the exponential population growth rate or the per capita intrinsic rate of increase r is a multiplier that gives a measure of how rapidly a population can grow Exponential curve can be drawn through discrete points of geometrically grown population Since these 2 types of growth curves overlap, both are sometimes lumped together and referred to as "exponential growth" Geometric and exponential curves are similar except that λ is replaced by ert So we can calculate λ from r and vice versa using these equations: λ=er or r=ln(λ) Note that ln(λ) is loge(λ) and can be plotted on a graph versus time to show whether population is growing exponentially (or geometrically). Straight line means exponential (or geo) growth When λ0), population will decline to extinction When λ>1 (or r
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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 easily 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 females 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 shrub Age Structure Age class - individuals whose ages fall within a specified range Age structure - describes proportions of the population in each age class
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Age structure influences how rapidly population grows or shrinks In general, population with more individuals of reproductive age will grow more rapidly 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 rate 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 environment 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
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λ is the geometric population growth rate or the per capita finite rate of increase When λ is between 0 and 1, the population decreases over time A second geometric equation is Nt = λt N0 where N0 is the initial population size (population size at t=0) Use 1st equation if population size in current and previous time periods is known Use the second equation to predict size of population after any # of discrete time periods Populations grow exponentially when reproduction occurs continuously and where generations can overlap Exponential growth - Change in population size by a constant proportion at each instant in time and forms J-shaped curve when plotted on a graph Exponential growth can be described in 2 equations: 1) dN/dt = rN 2) N(t)=N(0)ert - here e=2.718 and ert can be calculated using function ex dN/dt represents rate of change at each instant in time N(t) is the population size at each instant in time. r is called the exponential population growth rate or the per capita intrinsic rate of increase r is a multiplier that gives a measure of how rapidly a population can grow Exponential curve can be drawn through discrete points of geometrically grown population Since these 2 types of growth curves overlap, both are sometimes lumped together and referred to as "exponential growth" Geometric and exponential curves are similar except that λ is replaced by ert So we can calculate λ from r and vice versa using these equations: λ=er or r=ln(λ) Note that ln(λ) is loge(λ) and can be plotted on a graph versus time to show whether population is growing exponentially (or geometrically). Straight line means exponential (or geo) growth When λ0), population will decline to extinction When λ>1 (or r
