Population Ecology

Population Ecology: Environmental Science

Introduction to Population Ecology

• Definition: Population ecology studies the factors affecting the size, density, distribution, sex ratio, and age structure of populations.

• Case Study: Whooping Crane: A significant conservation success story.

  • Initially, over $10,000$ individuals in the U.S.

  • By $1938$, numbers plummeted to only $15$ individuals.

  • Scientific intervention focused on identifying breeding areas and protecting them, leading to a population rebound.

Factors Influencing Population Size

• Population Growth (Increase):

  • Births: New individuals born into the population.

  • Immigration: New individuals moving into the population from elsewhere.

• Population Decline (Decrease):

  • Deaths: Individuals dying naturally or due to other factors.

  • Emigration: Individuals moving out of the population to another area.

• Intrinsic Growth Rate (r): Determines if a population is increasing or decreasing based on births, deaths, immigration, and emigration.

Other Population Characteristics

• Density: The number of individuals per unit area (e.g., $9$ rabbits in an area vs. $9$ rabbits in a smaller area having greater density).

• Distribution: How individuals are spaced within their habitat.

  • Random: Individuals are scattered without any particular pattern (e.g., randomly distributed rabbits).

  • Uniform: Individuals are evenly spaced.

  • Clumped: Individuals are grouped in specific areas.

• Sex Ratio: The proportion of males to females in a population.

• Age Structure: The distribution of individuals among different age groups (e.g., first-year female rabbits, second-year, third-year, and similar for males).

Limiting Factors to Population Growth

• Density-Dependent Factors: Factors that limit population growth based on the density of the population. Their impact intensifies as density increases.

  • Examples: Insufficient food, water, or shelter (these are called limiting resources).

  • Mechanism: As population density increases, competition for these resources rises, eventually causing the growth rate to level off.

  • Carrying Capacity (K): The maximum number of individuals that an area can sustainably support. Population growth often levels off at K.

  • Disease: As population density increases, disease transmission can become more prevalent, leading to increased deaths and leveling off the population size.

• Density-Independent Factors: Factors that limit population growth regardless of the population's density. These are often related to chance events.

  • Examples: Natural disasters like floods or fires that can kill a significant portion of a population irrespective of how dense it was.

Population Growth Models

• Exponential Growth Model (J-shaped curve):

  • Description: Describes a population that grows at a constant and accelerating rate, assuming unlimited resources and ideal conditions.

  • Appearance on Graph: Forms a 'J' shape, indicating rapid, unchecked increase.

  • Equation: $Nt = N0e^{rt}$

    • $N_t$: Population size at time $t$

    • $N_0$: Initial population size (population at time $0$)

    • $e$: Euler's number, a mathematical constant approximately equal to $2.718$ (for practical purposes, often approximated as $2.71$).

    • $r$: Intrinsic growth rate (calculated as the change in population divided by the initial population).

    • $t$: Time elapsed.

  • Example Calculation: If $N_0 = 10$, $r = 0.5$:

    • After $1$ year ($t=1$): $N_1 = 10 \times 2.71^{0.5 \times 1} = 10 \times 2.71^{0.5} \approx 10 \times 1.64 = 16.4$ (approx. $16$ rabbits).

    • After $2$ years ($t=2$): $N_2 = 10 \times 2.71^{0.5 \times 2} = 10 \times 2.71^1 \approx 10 \times 2.71 = 27.1$ (approx. $27$ rabbits).

    • After $3$ years ($t=3$): $N_3 = 10 \times 2.71^{0.5 \times 3} = 10 \times 2.71^{1.5} \approx 10 \times 4.46 = 44.6$ (approx. $45$ rabbits).

  • Implication: This model predicts indefinite growth, which is unrealistic in nature.

• Logistic Growth Model (S-shaped curve):

  • Description: Initially shows exponential growth but then levels off as the population approaches its carrying capacity (K).

  • Appearance on Graph: Forms an 'S' shape.

  • Mechanism: Incorporates density-dependent limiting factors that slow down growth as the population density increases and resources become scarce.

  • Population Fluctuation: Real-world populations rarely perfectly level off; they often exhibit overshoots (exceeding K) followed by die-offs, eventually averaging around K.

Population Calculations

• Change in Population Size ($\Delta N$):

  • Formula: $\Delta N = (Births - Deaths) + (Immigration - Emigration)$

  • Example: Initial population $N_0 = 10$

    • Births: $3$

    • Deaths: $1$

    • Immigration: $1$

    • Emigration: $2$

    • $\Delta N = (3 - 1) + (1 - 2) = 2 + (-1) = 1$

    • This means an increase of $1$ individual.

• Growth Rate ($r$):

  • Formula: $r = \frac{\Delta N}{N_0}$

  • Example (using above data): $r = \frac{1}{10} = 0.1$

  • This represents a $10\%$ growth rate for that period.

Life History Strategies: r-selected vs. K-selected Species

• K-selected Species: Traits favor competitive ability and survival in stable, high-density environments near carrying capacity (K).

  • Characteristics:

    • Few offspring per reproductive event.

    • High parental care (investing significant resources in each offspring).

    • Longer lifespan.

    • Population size typically increases and stabilizes near K.

  • Examples: Whooping Cranes, Humans.

• r-selected Species: Traits favor rapid reproduction and colonization in unstable or low-density environments.

  • Characteristics:

    • Many offspring per reproductive event.

    • Little to no parental care.

    • Shorter lifespan.

    • Population undergoes