Population Dynamics Lecture 13

Lecture 13: Population Dynamics Over Time and Space

• Population size fluctuates naturally over time.

• Population dynamics describe variation in population size over time or space.

• Population dynamics can be relatively stable or widely fluctuating.

• Differences in body size, population response time, and sensitivity to environmental change affect population dynamics.

• Small organisms (e.g., algae) reproduce quickly (hours), allowing quick responses to environmental changes.

• Small organisms have a high surface-area-to-volume ratio, making them sensitive to environmental changes.

• Larger, longer-lived species have longer generation times and include many age classes.

• Fluctuations in birth rates have less impact on the growth of larger, longer-lived species.

• Populations maintain homeostasis (less sensitive to environmental change).

• Age structure can fluctuate.

• If a specific age group has unusually high or low numbers, the population experienced unusually high or low birth or death rates in the past.

• Example: whitefish (Coregonus clupeaformis).

Overshoots and Die-offs

• Populations can temporarily exceed carrying capacity (overshoot).
• Overshoots can occur when carrying capacity decreases.
• A die-off is a substantial decline in population density.
• Populations typically go well below carrying capacity after a die-off.
• Example: Reindeer on St. Paul Island (25 individuals introduced in 1911, exponential growth, massive die-off in 1938, now maintained at ~400 individuals).

Density Dependence with Time Delays

• Density dependence with time delays can cause population size to be inherently cyclic.
• Some populations experience regular patterns of fluctuations (population cycles).
• Example: Gyrfalcon exports match natural population cycles.
• Populations fluctuate above and below carrying capacity.
• At carrying capacity, populations are stable.
• When population decreases (predation, disease), growth starts.

Delayed Density Dependence

• Delayed density dependence occurs when density dependence occurs based on a past population density.
• It can be caused by factors related to carrying capacity, such as long gestation periods or predator response times.
• Example: Moose breed in fall but don't give birth in spring; available resources may be different by then.

Modeling Delayed Density Dependence

• Delayed density dependence can be modeled with a modified logistic growth model equation.
• Whether a population cycles depends on the time delay (τ) and the intrinsic growth rate (r).
• As time delay increases, density dependence is further delayed, making the population more prone to overshooting/undershooting carrying capacity.
• A high intrinsic growth rate increases the chance of overshoot.

Modeling Delayed Density Dependence: Cycling

• The amount of cycling depends on the product of r and τ.
• When rt is low (rt < 0.37), no oscillations occur. Example: a graph showing a gradually increasing growth.
• When rt is intermediate (0.37 < rt < 1.57), damped oscillations occur. There is ongoing fluctuation. Growth then reduces, and starts to grow again.
• When rt is high (rt > 1.57), stable limit cycle occurs. Large oscillations persist over time (a cyclical graph pattern).

Population Sizes Cycle in Laboratory Populations

• Example: Daphnia galeata; Bosmina longirostris.
• When population is low and food abundant, individuals store excess food droplets.
• Although growing, populations deplete resources but still reproduce because of stored food droplets.
• Causes the populations to overshoot, then die off.
• Bosmina longirostris do not store many lipid droplets, cannot reproduce beyond carrying capacity.

Extinction in Small Populations

• Small populations are more vulnerable to extinction than large ones.
• Small populations are vulnerable to both density-independent factors (e.g., natural disasters) and density-dependent factors (Allee effects).
• Relationship between population size and probability of extinction.
• Example: Birds in the Channel Islands, extinction rates were greater on smaller islands.
• Example: Plant populations in Germany, sampled over 10 years, smaller populations are likely to go extinct.

Extinction Due to Variation in Population Growth Rates

• Density-dependent population models show that small populations initially grow more rapidly than large ones.
• But, small populations are more likely to go extinct due to random environmental variation in birth/death rates.
• Stochastic models incorporate random variations in population growth rates.
• Stochasticity varies between demographic (differences among individuals) and environmental (changes in environmental conditions like weather).

Metapopulations

• Population dynamics vary over space.
• Populations are often divided into subpopulations.
• Subpopulations are smaller groups of conspecifics in isolated patches.
• Dispersal among subpopulations is infrequent; dynamics are independent.
• A collection of subpopulations forms a metapopulation.

The Fragmented Nature of Habitats

• Metapopulations can occur when habitat is naturally patchy.
• Example: Wetlands in North America; terrestrial habitat often inhospitable, minimal dispersal between water bodies.
• Metapopulations can also occur due to human activities.
• Example: Habitat fragmentation; breaking large habitats into smaller ones.

Conceptual Models of Spatial Structure

• Three models for spatial structure of subpopulations: Basic metapopulation model, Source-sink metapopulation model, Landscape metapopulation model.

The Basic Metapopulation Model

• Describes a scenario with patches of suitable habitat embedded in unsuitable habitat.
• All suitable patches are equally good.
• Some patches are occupied, others not.
• Unoccupied patches can be colonized by dispersers.
• The model emphasizes how colonization and extinction events affect the proportion of suitable habitats.

The Source-Sink Metapopulation Model

• Builds on the basic model, including variation in patch quality.
• Source subpopulations are high-quality habitats with dispersers.
• Sink subpopulations are low-quality habitats; outside dispersers maintain the subpopulation.

The Landscape Metapopulation Model

• Builds on the source-sink model by including variation in unsuitable habitat around patches.

The Basic Dynamics of Metapopulations

• Assume patches are equal quality. The same subpopulation size and the same number of dispersers.
• Some proportion of the habitats will be occupied (p).
• Fixed probability that a patch becomes unoccupied through extinction (e).
• Fixed probability of colonization (c).

Observing Metapopulation Dynamics in Nature

• Do we see a balance of colonization/extinction rates in nature?
• Example: Glanville fritillary butterfly (Melitaea cinxia); lives in isolated patches of dry meadows.
• Monitored extinction/colonization of 1600; 12-39% occupied over a 9-year period; ~100 colonized, ~100 extinct.

Patch Size and Isolation

• Habitat patches rarely have equal quality.
• Larger patches typically support more individuals.
• Example: California spotted owl (Strix occidentalis occidentalis).
• Smaller patches experience higher extinction rates.
• Distance between patches affects the rate of patch colonization.
• Less isolated patches could be supported by nearby dispersers = rescue effect.
• Example: skipper butterflies (Hesperia comma).

This quiz focuses on the concepts of population dynamics over time and space, highlighting natural fluctuations in population size. It explores the factors influencing these dynamics, including body size, reproductive rates, and environmental sensitivity. Test your understanding of how different species respond to changes in their environment and maintain homeostasis.