Population Dynamics and Carrying Capacity

Population growth is characterized by fluctuations. - The population increases with each birth and decreases with each death.
- A population does not maintain a constant size as deaths do not always equal births.
Carrying Capacity - Example: Red deer population on certain islands.
- Estimated carrying capacity: ranges between 250 and 350, averaging around 300.
- Despite fluctuations, the population remains within a narrow range around the carrying capacity.
Populations vary in stability. - Example of algae species in Lake Erie.
- Algal populations exhibit extreme fluctuations over time.
- Nutrient availability impacts growth rates.
- Algae can double rapidly due to high reproduction rates, leading to crashes when nutrients deplete.
- Dynamics of nutrient pulses significantly influence algal population growth.

Reproductive Output Variability - Example: Whitefish in Lake Erie.
- Study shows a notable reproductive spike in 1944 that impacted future populations and age classes.
- Fish from the 1944 cohort dominated catches for years until 1950.
Population dynamics affect generation representation. - Not all years yield the same reproductive output, thus affecting population structure.

Moose population dynamics: fluctuates cyclically. - Example from Isle Royale, Lake Superior.
- Moose population grows until a harsh winter leads to starvation due to high population density.
Wolf population relies on the available moose population. - Wolves arrive on the island when an ice bridge forms.
- Observed lag: wolf population peaks slightly after moose population peaks.
Example of reindeer on Saint Paul Island. - An exponential growth leads to overgrazing of lichens, resulting in extinction due to lack of food.

Use of parasitoids for pest control in citrus agriculture. - Introduction of Aphidus parasitoids effectively controlled the red scale pest.
Experimental Design - Three treatments: treated trees with and without scales, and a control group.
- Sampling methodology included periodic checks over 12 weeks and selective trapping.
Study Results - Population oscillation of parasitoids and hosts documented over time.

Changes in carrying capacity impact population dynamics. - Example: Three grass populations in Finland show predictable trends due to similar food sources and weather.
Mathematical modeling of population growth includes variations in carrying capacity over time. - Logistic Growth Equation:
- Expressed as: dN/dt = rN(1 - (N/K)) - where r is the intrinsic growth rate, N is the population size, and K is the carrying capacity.
Delayed Density Dependence - Affects population reactions to changes in carrying capacity.
- Introduces a time lag (tau) in response to changes and affects population stability.

Overall, reproduction rate affects the frequency and magnitude of population fluctuations. - High reproductive rates and long lag times lead to significant fluctuations.
- If intrinsic reproduction rate multiplied by lag time exceeds 1.37-1.57, it induces oscillating population patterns.
Small versus large populations: larger populations less likely to experience extinction during fluctuations.

Deterministic vs Stochastic Models - Deterministic Models: Predictable without accounting for randomness.
- Stochastic Models: Incorporate randomness, acknowledging demographic or environmental variations.
- Stochasticity leads to variations in reproductive output and survival rates.
Probability of extinction increases with time and smaller population sizes. - Smaller populations less resilient to fluctuations, making them more vulnerable to extinction.
- Over time, the likelihood of experiencing negative events that cause extinction rises as variability compounds.