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## Populations

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**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