Population Dynamics and Growth Patterns

By the end of this section, you will be able to:
- Explain the characteristics of and differences between exponential and logistic growth patterns.
- Give examples of exponential and logistic growth in natural populations.
- Give examples of how the carrying capacity of a habitat may change.
- Compare and contrast density-dependent growth regulation and density-independent growth regulation, providing examples.

Population ecologists utilize various methods to model population dynamics.
An accurate model should describe the changes in a population and predict future changes.

The two simplest models of population growth utilize deterministic equations (do not account for random events).
- Exponential Growth Model
- Describes populations increasing in numbers without growth limitations.
- Logistic Growth Model
- Introduces limits to growth as population size increases.
Neither model perfectly describes natural populations but serve as points of comparison.

Influenced by Thomas Malthus, who published a book in 1798 stating that populations with unlimited resources grow rapidly (exponential growth) and decrease as resources become limited (logistic growth).
Example of Exponential Growth: Bacteria
- Bacteria reproduce mainly by binary fission.
- Division occurs approximately every hour in many species.
- If 1000 bacteria are placed in a flask with abundant nutrients:
- After 1 hour: 1000 → 2000
- After 2 hours: 2000 → 4000
- After 3 hours: 4000 → 8000
- After 24 cycles: population increases from 1000 to over 16 billion.
- Growth Rate Equation: Population Growth = rN where:
- N = Population size
- Growth rate determination:
- r = B - D (where B is the birth rate and D is the death rate)
- Possible values for r:
- Positive: Population grows
- Negative: Population declines
- Zero: Stable (zero population growth)

Logistic Growth Equation: Population Growth = rN \left[\frac{K - N}{K}\right] where:
- K = Carrying capacity
- N = Current population size
Exponential growth can only happen with infinite resources, which is unrealistic.
Charles Darwin discussed the “struggle for existence,” highlighting competition for limited resources.
Carrying Capacity (K):
- Maximum population size sustainable by the environment.
- Real populations may overshoot carrying capacity, leading to increased death rates.
- Population fluctuates around carrying capacity rather than being constant.
- As N approaches K, growth approaches 0 and is represented graphically as S-shaped curve.

Logistic model assumes equal resource access among individuals in a population (equal survival chances).
Important resources:
- Plants: Water, sunlight, nutrients, space.
- Animals: Food, water, shelter, mates.
Intraspecific competition occurs when individuals compete for limited resources.
- Not significant when population size is low; becomes crucial as size increases, leading to increased competition and potentially reduced individual success rates.
- Resource depletion (waste accumulation) can affect carrying capacity.

Yeast: Exhibits classical S-shaped growth in nutrient-rich environments.
- Growth levels off as nutrients deplete.
Wild Populations: Examples include sheep and harbor seals, which experience fluctuations in population size around carrying capacity.

The logistic model simplifies realistic population dynamics.
Carrying Capacity (K) is not constant; it changes annually due to climatic conditions and other factors.
- Examples: Variability between summer and winter conditions.
Populations do not exist in isolation but interact with others, leading to interspecific competition.

Biological factors influencing growth rates based on population density:
- Predation, competition (intra- and interspecific), parasites.
High-density populations typically have:
- Increased mortality rates due to competition and disease spread.
Example from wild donkey populations in Australia, showing a significant difference in juvenile mortality rates due to food scarcity in a high-density environment.

Physical factors causing mortality irrespective of population density:
- Weather, natural disasters, pollution.
For example, a deer dying in a forest fire has the same likelihood regardless of the population size.

Complex interactions exist in real-life situations.
An example of deer affected by a harsh winter highlights that a higher population density can lead to different recovery rates.

Woolly mammoths began their extinction around 10,000 years ago due to:
- Climate change and human hunting.
A study estimates a decline in habitat range from 3,000,000 to 310,000 square miles over 42,000 years.
Important factors in extinction:
- Climate change
- Reduction of habitat
- Migration of human hunters
Complexity of population maintenance is underscored by various interacting factors.

Population ecologists propose characteristics that evolve in species affecting population growth such as:
- Birth rates
- Age at first reproduction
- Number of offspring
- Death rates
Life History Strategies:
- K-selected Species:
- Adapted to stable environments.
- Example: Elephants.
- Features include fewer offspring with more parental investment.
- r-selected Species:
- Adapted to unstable environments.
- Example: Jellyfish, dandelions.
- Features include many offspring with little parental investment.
These strategies exist on a continuum, encompassing various species with divergent life histories.