Population Dynamics: J and S Curves, Density Factors, R/K Strategies, and Controls

Population Dynamics and Life History Strategies

J-Shaped Population Growth Curve

• Definition: Describes populations growing forever, faster and faster, as if going up a ramp without end.
• Assumptions (Ideal Circumstances):
  • No Predators: Death (d) is equal to 0. No disease, no starvation.
  • Infinite Resources: Infinite amount of food, no competition for space, plenty of room for nests and reproduction.
  • Simplified Breeding Cycle: Every viable individual breeds once and then dies, simplifying mathematical models by not carrying individuals through multiple breeding cycles.
  • Maximum Reproduction: Every individual reproduces at the same maximum number (e.g., every female mouse produces a litter of 10 pups, not a variable number).
• Realism: This model describes an ideal, unrealistic world (e.g., from a mouse's perspective: no starvation, no predation, plenty of space/food – a paradise).
• Occurrence: Occasionally, natural populations approximate these ideal conditions and exhibit J-shaped growth for a period.

S-Shaped Population Growth Curve

• Definition: Describes populations that initially grow like a J-shaped curve but then the growth rate starts to level off and eventually plateaus.
• Plateau: At the plateau, births and immigration are exactly equal to deaths and emigration, meaning individuals are still born and die, but their numbers offset each other, resulting in a stable population size.
• Carrying Capacity (K): The population size at which the growth rate slows and plateaus. This value can fluctuate year to year based on resource and habitat availability.

Case Study: Wolf Reintroduction in the Northern Rockies

• Data Period: Wolf population data collected by scientists from 1982 to 2012. The minimum number of wolves is estimated using stacked bar graphs for three populations, including the Greater Yellowstone Area (GYA) and Central Idaho (CID).
• Reintroduction: Wolves were first reintroduced to the GYA in 1995, indicated by the first pink bar. Around the same time, wolves were introduced to Central Idaho (CID).
• Initial Conditions: Roughly 30 wolves or fewer were introduced to each area. The habitat was ideal for rapid growth:
  • Abundant Prey: Elk, deer, and moose numbers were extremely high because wolves, the apex predator, had been missing for 80 years.
  • No Competition: No other wolf packs were present, meaning no competition for habitat, dens, territories, or prey. Wolves are territorial and defend their space against other packs.
  • Federal Protection: Wolves were federally protected from hunting, a significant factor as humans are their primary predators.
• Population Trend: Initially, wolf populations in the Northern Rockies increased rapidly, consistent with an S-shaped curve, then began to level off around 2007. The population stabilized between 1,500 and 1,800 individuals. A recent New York Times article estimated between 1,300 and 1,500 individuals, suggesting it has remained constant or slightly declined. This leveling off suggests the carrying capacity (K) for wolves in the Northern Rockies is in this range.
• Reasons for Slowing Growth: From a wolf's perspective, the Northern Rockies became crowded. New habitats became scarce, and prey (deer and elk) numbers declined, making it harder for wolves to thrive and leading to population stabilization.

Factors Affecting Population Growth and Density

• Population Density: The number of individuals packed together. Both excessively high and low densities can cause problems.
  • High Density Issues: Limited habitat, limited food, increased competition, disease spread, etc. (Important exam material).
• Limiting Factors: Resources needed for survival that may be in short supply (e.g., habitat, food). Scarcity of these resources determines the carrying capacity (K).
• Resistance Factors: Factors that limit population size and growth, such as predation, competition, and disease.

Density-Dependent Factors

• Definition: Factors whose effect on a population increases in strength as the population size (density) increases. They are always limiting factors.
• Examples:
  • Competition: Becomes stronger as population density rises.
  • Disease: Spreads more easily and severely in denser populations. Example: Brucellosis, a fatal airborne lung infection affecting deer and elk in the Northern Rockies, is more prevalent when animals are at high density and weakened by food competition.
  • Predation: Predators often show preference for prey species that are at their highest density, focusing their efforts where prey is most abundant.

Density-Independent Factors

• Definition: Factors that affect a population regardless of its size or density.
• Examples:
  • Storms: Yellowstone experiences harsh spring storms that can devastate elk and bison populations, causing significant declines regardless of their overall density.
  • Forest Fires: Yellowstone is famous for fires. Initial effects: some individuals die, loss of food leading to population decline in the first year. Subsequent effects: In years 2-4 after a fire, new growth flushes, providing abundant food as trees die, opening the forest floor to light and water, which can lead to increased populations.

Life History Strategies: R-Adapted vs. K-Adapted Species

• Continuum: Species are not strictly R or K but exist along a continuum between these two extremes.

R-Adapted Species

• Strategy: Tend to increase quickly as resources become available; opportunistic.
• Life History Traits:
  • Short Lifespan: Quick turnover of generations.
  • Rapid Individual Growth: Reach maturity very quickly.
  • Early Maturity and Reproduction: Breed soon after birth.
  • Many Small Offspring: Produce a large number of offspring in a short period.
  • Generalists: Good at many jobs, not great at any one. Can thrive in various environments.
• Examples: Deer mice (reach reproductive age in 6 weeks, have 10 pups, live 3 years, produce hundreds of offspring), knackweed (common roadside weed), other species capable of rapid population increases.

K-Adapted Species

• Strategy: Tend to have low reproductive rates and respond slowly to environmental changes (increase and decrease slowly).
• Life History Traits:
  • Long Lifespan.
  • Slower Individual Growth Rates.
  • Late Maturity and Reproduction: Takes a long time to reach reproductive age.
  • Few, Large Offspring: Produce a small number of offspring over a longer period.
• Examples: Elk, spruce trees, bears (female black bear reaches reproductive age at 6 years, has 1-2 cubs every 4 years, lives up to 20 years, produces about 6 offspring in her lifetime), whales.

Humans: A Mix of R and K Strategies

• K-Adapted Aspects:
  • Late Sexual Maturity: Around age 13.
  • Long Parental Care: Infants reliant for 8-18 years.
• R-Adapted Aspects (Breaking the Mold):
  • Niche Generalists: Omnivore teeth allow diverse diets.
  • Technology: Brains enable creation of technology (clothing, shelter from infinite materials) to live in almost all habitats, unlike any other species.

Conservation Implications

• K-adapted species are generally more vulnerable and sensitive to environmental changes, particularly those caused by humans.
• Example: Whale populations, being K-adapted (long maturity, slow birth rates), collapsed due to historical human hunting and are very slow to recover even with protection.

Population Control: Top-Down and Bottom-Up

• Trophic Pyramid: Conceptual model of feeding levels.
• Top-Down Control: Occurs when a population is limited by predators that are higher on the trophic pyramid.
  • Example: Wolves (predators) limit elk (prey) populations.
• Bottom-Up Control: Occurs when a population is limited by the availability of producers (plants) or other resources at lower trophic levels.
  • Example: Elk populations are limited by the availability of their food supply (plants).
• Interconnectedness: Properly understanding population dynamics (e.g., elk in Yellowstone) requires appreciating both top-down (predation) and bottom-up (food supply) controls. When wolves were removed from Yellowstone early in the 20^{th} century, prey populations of elk and bison increased dramatically, causing significant ecosystem changes.