Population Growth, Life History, and Demography: Study Notes for General Biology

Population Growth Models

Logistic Growth Equation

The logistic growth equation models how populations grow in environments with limited resources. Unlike exponential growth, logistic growth accounts for a carrying capacity, which is the maximum population size the environment can sustain.

• Equation: $\frac{dN}{dt} = rN\left(1 - \frac{N}{K}\right)$

• Terms:

  • N: Population size

  • r: Intrinsic rate of increase

  • K: Carrying capacity

• Curve Shape: The logistic growth curve is S-shaped (sigmoidal). It starts with rapid growth, slows as resources become limited, and levels off at carrying capacity.

• Example: A population of bacteria in a petri dish initially grows rapidly, but as nutrients are depleted, growth slows and stabilizes.

Calculating Logistic Growth Over Generations

Population size changes over generations can be calculated using the logistic growth equation. For example, if at generation 0, N = 2, rmax = 2, and K = 10, the population size at subsequent generations can be determined.

Generation	N (Population Size)
0	2
1	Calculated using the equation
2	Calculated using the equation
3	Calculated using the equation

Additional info: To find N at each generation, substitute values into the logistic equation iteratively.

Overshooting Carrying Capacity

Populations can sometimes exceed their carrying capacity, a phenomenon known as overshoot. This typically occurs when resources are temporarily abundant or when population growth is very rapid.

• Consequences: Resource depletion, increased mortality, and population crashes.

• Example: Deer populations may overshoot carrying capacity after a mild winter, leading to food shortages.

Life History Traits and Trade-Offs

Life History Traits

Life history traits are the major biological decisions species make to maximize fitness, such as age at reproduction, number of offspring, and lifespan.

• Trade-offs: These traits are subject to trade-offs because resources are limited. For example, producing more offspring may reduce parental investment per offspring.

• Example: Birds may lay fewer eggs to ensure each chick receives enough food.

Recognizing Trade-Offs: The Kestrel Study

Studies such as the kestrel study examine how manipulating brood size affects parental investment and offspring survival.

• Methods: Researchers increase or decrease the number of chicks in a nest.

• Results: Larger broods often result in lower survival rates per chick, demonstrating a trade-off between quantity and quality of offspring.

• Implications: There is an optimal brood size that maximizes parental fitness.

Brood Size Manipulation and Trade-Offs

Manipulating brood size reveals the cost of reproduction. Increasing brood size may reduce parental survival or future reproductive success.

• Resulting Trade-Off: Parents with larger broods may have reduced survival or produce fewer offspring in subsequent years.

• Reason: Increased energy expenditure and resource allocation to current offspring.

Human Population Growth and Demography

Exponential Growth in Human Populations

Human populations have historically grown exponentially, but growth rates are changing.

• Exponential Growth Equation: $\frac{dN}{dt} = rN$

• Is r still positive? In many countries, r (the rate of increase) is declining due to lower birth rates and higher death rates, but global population is still increasing.

Demographic Transition

The demographic transition describes changes in birth and death rates as countries develop economically.

• Stages:

  1. High birth and death rates

  2. Death rates fall, birth rates remain high

  3. Birth rates fall

  4. Low birth and death rates

• Transition: Countries tend to go from high birth rates to low birth rates, and from high death rates to low death rates over time.

• Reason: Improved healthcare, education, and economic development.

Population Age Structure

Interpreting Age Structure

The age structure of a population can predict future growth trends.

• Rapid Growth: Broad base (many young individuals)

• Slow Growth: More uniform distribution across ages

• Zero or Halted Growth: Narrow base (few young individuals)

• Application: Age pyramids are used to visualize age structure and predict population trends.

Determinants of Species Distribution

Terrestrial and Aquatic Species

The distribution of species is determined by a variety of environmental factors.

• Terrestrial Species: Climate, availability of food and water, habitat structure, competition, and predation.

• Aquatic Species: Water temperature, salinity, oxygen levels, nutrient availability, and light penetration.

• Example: Tropical rainforests support high biodiversity due to warm temperatures and abundant rainfall.