Possible Test Questions • Explain how biotic potential and/or carrying capacity produce the J-shaped and S-shaped population growth curves. • Draw the three main survivorship curves and relate them to r selection and K selection in animals. • 3. Explain how a single child born in the United States can have a greater effect on the environment and natural resources than a dozen or more children born in a developing country.
Biotic Potential The Biotic Potential is the maximum rate at which a population could increase under ideal conditions. Different species have different biotic potentials..
Exponential Growth Growth = dN/dt = rN where: r = biotic potential (per cap. rate of increase) N = population size When N is small, growth is small When N is large, growth is large When r is larger, the more rapid the growth
Exponential Growth • Think of exponential growth in terms of making money. How much you increase your earnings will depend on: • How much principle you have (population size) • The interest rate at which you are earning money (the biotic potential)
Density-dependent Growth Compared to Exponential Growth Populations will not increase forever. Ignoring all interactions with other species (competition, predation, parasites, herbivory), resources will still limit growth - food resources and space resources. (Remember the flies data from previous slide - In just 10 years, we would be swimming in several meters of flies if exponential growth continued.)
Characteristics of Density-dependent Growth Resources will limit growth - Food and/or Space Carrying capacity= the maximum number of individuals of a species that can be sustained by an environment without decreasing the capacity of the environment to sustain that same amount in the future.
K r J-Shaped Compared to S-Shaped Growth Curves growth = dN/dt = rN [(K-N)/K] where r = biotic potential N is the population size and K = carrying capacity So (K-N)/K = opportunity to grow
Example of Growth Data growth = rN [(K-N)/K] Imagine that r = 1.0 K=100 N (t+1) N (t ) r rN (K-N)/K dN/dt N (t+1) if no K 1 1 1 99/100 0.99 1.99 2 50 1 50 50/100 25 75 100 75 1 75 25/100 8.75 93.75 150 95 1 95 5/100 4.75 99.75 190 99 1 99 1/100 0.99 99.99 198 100 1 100 0/100 0 100 200
growth = rN [(K-N)/K] Imagine that r = 1.0 K=100 N (t+1) N (t ) r rN (K-N)/K dN/dt N (t+1) if no K 1 1 1 99/100 0.99 .99 2 50 1 50 50/100 25 75 100 75 1 75 25/100 8.75 93.75 150 95 1 95 5/100 4.75 99.75 190 99 1 99 1/100 0.99 99.99 198 100 1 100 0/100 0 100 200 (K-N)/K = opportunity to grow Three possible outcomes: 1. When N (population) is small, (K-N)/K ~ K/K ~ 1 so exponential growth at small pop. size. 2. Both K and r have an effect. Intermediate growth. 3. When N is large, K-N ~ 0 so the population doesn’t change in size
Population Strategiesr-Strategy Compared to K-Strategy r-strategy: high intrinsic growth rates - focuses on reproduction, not on competition with other individuals in the population. K-strategy: focuses on population at or near carrying capacity—must be able to compete with other individuals in the population. K-strategy r-strategy
Reproductive Strategies r-strategy K-strategy
Demography Demography = study of population change Natality = production of new individuals Mortality = death rate (+ migration contributes to local numbers) Factors affecting natality and mortality: (1) Age composition of population (2) Environment
Life Expectancies Change With Age • Type I: humans and other large mammals; high mortality when reach old age • Type II: birds (seagulls); probability of death is unrelated to age. • Type III: aquatic organisms that release fertilized eggs. High mortality of very young individuals. • Which is r-strategy? Which is K-strategy?
r-strategy K-strategy Survivorship curves: Type I related to K, Type III related to r.
Reproduction changes with age - proportion of individuals in each reproductive class can have a large effect on population growth. • Expanding: Population momentum: when young make large proportion of the population, potential for rapid increase in natality when young reach reproductive age. ‘Bottom heavy’ • Stable: stationary phase. Mortality such that each class goes to the next class at the size the next class was at. The population is at replacement numbers for births. • Diminishing: natality has fallen below replacement numbers. ‘Top heavy’.
HUMAN POPULATION 2000 years ago 300 million people 200 years ago under a billion people 40 years ago 3 billion people 1999 6 billion people Now, the population is growing by almost 78 million more people each year. Two possible causes: Life expectancy (age at mortality) Fertility
Mortality and death rates: The primary cause of population growth has been declining mortality. In the last 100 years, average life expectancy has risen by about 25 years - due to modern medicine, better food, and better sanitation (environment changed).
Comparison Population USA 2000 with 2050 Post-repro Reproductive Pre-repro 2000 2050
Columbia River Salmon - Carrying Capacity Estimates as Pounds Caught.
Conclusion By changing the salmon’s environment (DAMS), we have changed the carrying capacity for salmon. Are we doing the same thing with the earth for human beings?
Economics and Life Expectancy Although life expectancy is predicted well by annual per capita income, the correlation is good only up to about $4000.
Birth Rates and Fertility Rates • Crude birth rates are the number of births per 1000 people. It is crude because it is not adjusted for the number of women of reproductive age. • Total fertility rate is the number of children born to an average woman in a population during her reproductive life. • Obviously only women give birth, so women must be considered specifically.
Why are fertility rates so high in sub-Saharan Africa? Infant mortality rates strongly correlated with high fertility rates.
Other Correlations with Infant Mortality Rates? Can increased female literacy decrease infant mortality, and so decrease fertility rates?
EMPOWER WOMEN? What would this mean for some societies? Fertility Rates and Female Literacy Fertility Rates and Birth control (linked to literacy?)
Religious Beliefs Cultural Norms Religious Beliefs Cultural Norms