Population Ecology: Comprehensive Notes
Population Ecology: Comprehensive Study Notes
Population ecology is the study of how and why the number of individuals in a population changes over time.
Principles apply to all living systems (plants, animals, fungi, etc.).
Applies to natural systems, agricultural systems, managed systems, and human populations.
Disease epidemiology is part of population ecology (bacteria, viruses, fungi, parasites).
Population ecology projects (predicts) the size of future populations starting from various initial conditions.
Key Agencies and Applications
Agencies that depend on population biology studies:
US Department of Agriculture (USDA)
Department of Natural Resources (DNR) – environment, land usage (state)
US Geological Survey (USGS) – environment, land usage (federal)
National Institutes of Health (NIH)
Centers for Disease Control (CDC)
Wisconsin Department of Health Services (WDHS)
United States Department of Housing and Urban Development (HUD)
Budget context (example): APHIS outlays for pests and diseases exceeded $1 billion per year from 2003–2007; additionally, $15 billion spent annually on pesticides.
Population Sampling: Mark–Recapture Method
How to estimate population size in a natural system:
Capture, tag, and release a random sample of s individuals.
Allow marked individuals to mix back into the population.
Capture a second sample of size n and note how many are marked (x).
Estimate population size N.
Core idea: the proportion of marked individuals in the second sample should reflect the proportion marked in the population.
Proportion marked in second sample ≈ proportion marked initially. If s are marked initially and x are recaptured marked in a second sample of size n, then a common estimator is:
N \,\approx\, \frac{sn}{x}
This is one of many models used to estimate population size.
Assumptions (critical):
Nothing changes the proportions of marked vs unmarked (no births/deaths or immigration/emigration affecting marks).
Marked individuals are neither more nor less likely to be captured than unmarked ones.
Marking does not bias towards sex, age, or trap-shyness/happiness.
Sufficient time for marked and unmarked to mix.
Marks are not lost.
Marking Techniques and Equipment
Marking methods vary by species; common approaches include:
Box traps
Canon nets
Funnel traps
Electrofishing
Marking methods (examples):
Canon nets
Box traps
Mist netting
Funnel traps
Electro Fishing
Operculum punch (a marking method for certain fish)
Other species-specific tagging methods
Population Change: Simple Mathematical Models
Exponential model (the J-curve): population grows without bound as time progresses.
Logistic model (the S-curve): growth slows as carrying capacity is approached and eventually levels off.
Four Demographic Factors determine population size:
Births
Deaths
Immigration (into the population)
Emigration (out of the population)
Exponential model: key assumptions include a closed population, small population size, unlimited resources, and constant environment.
Basic relationship for population growth in the exponential model is:
\frac{dN}{dt} = rN
where the growth rate r is constant.
Population ecologists ask: How many individuals will be in the next generation?
A population will grow when: B > D
A population will shrink when: B < D
For simplicity, sometimes immigration and emigration are neglected, so change in population size is births minus deaths:
\Delta N = B - D
Per-capita rate of increase, r, is defined as:
r = b - d
If b > d, r is positive; if b < d, r is negative.
Exponential growth is independent of population size, given enough time:
Larger r leads to faster growth; smaller r leads to slower growth.
With higher r, populations become astronomically large faster.
Factors influencing per-capita rate of increase (r):
Age of first reproduction
Frequency of reproduction
Fecundity: average number of offspring
Length of reproductive lifespan
Survival rate of young
Life History Traits and Survivorship
Survivorship: patterns of mortality at different life stages across species.
Low mortality in young often leads to fewer offspring with parental care.
High mortality in young leads to many offspring with little parental care.
Intermediate survivorship is less common (seen in some invertebrates and rodents).
Fecundity: number of female offspring produced by each female in a population.
Age-specific fecundity: average number of female offspring by a female in age class x.
Survivorship curves (concept): illustrate how survivorship changes with age across species.
Population Growth and Carrying Capacity
Ultimate size of a population results from a balance between:
The rate of increase under ideal conditions
Environmental factors that restrict growth (food, space, resources)
Availability of food and resources
Interspecific and intraspecific competition
Interactions between species (predation, disease)
Density dependence: growth rate is a function of population size; carrying capacity (K) represents the maximum population size that the environment can sustain.
Early growth is rapid; later growth slows as N approaches K.
Limiting factors:
Density-independent factors: affect population size regardless of density.
Weather (frost, drought) can limit annual plant and insect populations.
Human activities (pollution, pesticides, habitat destruction).
Density-dependent factors: become more effective at higher densities.
Predator–prey dynamics: more prey can support more predators, which can then reduce prey populations.
Density-independent regulation example: mosquito populations show seasonal, weather-driven fluctuations that are not tightly tied to population density.
Predator-prey boom and bust cycles (classic examples):
Snowshoe hare and lynx cycles show alternating high/low abundances.
Isle Royale: wolves and moose populations demonstrate predator–prey interactions over decades.
Disease Ecology and R0 (Basic Reproduction Number)
R0: a numerical representation of how likely a disease will spread when an infectious individual enters a completely susceptible population.
Formula: R_0 = c \cdot t \cdot d
c = average rate of contact between infected and susceptible individuals
t = transmissibility (probability of infection given contact)
d = duration of infectiousness
Interpretation:
If R_0 > 1, each infection causes more than one new infection; disease can spread widely (outbreak/epidemic).
If R_0 = 1, the disease persists at a constant level (endemic).
If R_0 < 1, the disease will decline and eventually die out.
Examples of R0 values for human diseases:
Hepatitis C: ~2
Ebola: ~2
HIV: ~4
SARS: ~4
Mumps: ~10
Measles: ~18
SARS-CoV-2 (COVID-19) estimates: R0 ≈ 5.7 (range ~3.8–8.9) as reported by Sanche et al. (2020).
Herd immunity and vaccination:
Threshold of vaccinated individuals is needed to reduce disease outbreaks.
When vaccination reduces the effective reproduction number below 1, disease spread is interrupted.
Diagrams show scenarios with different vaccination coverage leading to varying spread dynamics.
Practical takeaway:
Understanding R0 helps predict outbreak potential and informs vaccination strategies and public health interventions.
Measles Case and Vaccine Impact
Measles in the United States (1950–2001): cases show a dramatic decline after vaccine introduction and licensure.
Measles vaccination dramatically reduces incidence; vaccines are a cornerstone of herd immunity.
Note: Visuals in the transcript indicate historical case counts and vaccine licensing milestones.
Real-World Case Studies
Asian Carp Invasion (Bighead Carp, Hypophthalmichthys nobilis)
Invasive fish in the Mississippi/Missouri Rivers and Great Lakes region; threaten native fish and wildlife.
Characteristics:
Bighead carp: breeders with large heads and specific dorsal/ventral features; adults can exceed 60 lbs and 4 ft in length.
Silver carp: smaller head, upturned mouth, potential to jump when disturbed by boats.
Population dynamics:
Asian carp presence since the early 1990s; population density rose dramatically post-1995 floods.
By 1994–1996, rapid increases observed; long-term data show exponential growth in density.
Reproductive capacity:
One female can produce ~1.9 million eggs per oviposition and can reproduce up to 3 times per year.
Management and public health implications:
Risk of entry into the Great Lakes and potential wipe-out of commercial fisheries.
Public engagement: identify and report new sightings, preserve specimens, and contact appropriate wildlife authorities.
Population projection example (hypothetical): If starting with 4 individuals and assuming r = 1 (doubling per time unit), time to reach 200,000 by discrete doubling is approximately 16 years (2^t growth reaching 50,000 from 4). This illustrates how rapid growth can threaten new ecosystems.
Notable real-world event: June 22, 2017, a live Asian carp was found 9 miles from Lake Michigan, prompting intensified monitoring and barriers.
Reindeer on St Matthew Island (1944–1980s)
Initial introduction: 29 reindeer released on St Matthew Island as a backup food source; island had abundant lichen but few predators.
Population explosion:
By 1957, population grew to about 1,350 individuals in 13 years.
By 1963, population expanded to ~6,000.
Resource depletion and crash:
Overgrazing led to depletion of lichen; population began to rely on sedge grass.
Winter conditions worsened as resources declined; by 1966 skeletons and a dramatic crash occurred.
By the 1980s, the population collapsed to near extinction (only a few individuals remained for some time).
Lesson: population overshoot and crashes can occur when carrying capacity is overestimated or resources are depleted faster than replenishment, illustrating density-dependent regulation and the consequences of overshoot.
Predator–Prey Dynamics: Isle Royale
Classic predator–prey dynamics observed as wolves and moose interact over decades.
Boom–bust cycles illustrate density-dependent regulation and the feedback between predator abundance and prey availability.
Human Population Growth and Global Projections
Human population growth has followed an exponential trend in many historical periods, punctuated by events (e.g., pandemics like the Plague) that can alter trajectories.
World population statistics (contemporary estimates in the lecture context):
U.S. population around 305–326 million depending on year; world population in the billions (6–7.5+ billion in the examples).
Projections (1950–2050):
1992 projections for 2050 suggested higher population than 2002 projections did, largely due to AIDS and other factors not fully captured earlier.
Projections by fertility scenario (high, medium/low, low) show different 2050 population estimates:
High fertility: ~12.5 billion
Medium: ~10.15 billion
Low: ~7.8 billion
Norman Borlaug quote underscores the Green Revolution idea: science and agriculture can prevent famine in the future.
Fisheries and Population Management: Maximum Sustainable Yield (MSY)
Concept: MSY is the largest catch that can be taken from a species stock indefinitely without compromising future yields.
Discussion prompt in the material: If a previously unexploited species is at carrying capacity, relative to that size, what proportion should be harvested to achieve MSY? (Conceptual choices A–E.)
Takeaway: MSY aims to balance exploitation with maintaining population viability; this requires understanding carrying capacity and growth dynamics.
Daphnia Culture Case Study: Population Dynamics and Carrying Capacity
A culture experiment demonstrates rapid growth and subsequent stabilization around the carrying capacity.
Observations:
Population experiences negative growth briefly when overshooting carrying capacity, then stabilizes near the predicted carrying capacity.
In periods following overshoot, deviations from the predicted values can occur due to resource limitation and density-dependent regulation.
Key reasoning questions addressed in the slides:
Did the population overshoot carrying capacity?
What explains negative growth rates during specific intervals?
Why did the population stabilize below carrying capacity for a period after overshoot?
Interpreting these results reinforces the concept of carrying capacity and density dependence in real populations.
Daphnia and Carrying Capacity Visualization (Time Series)
A time-series graph indicated a carrying capacity (K) that the population tended to approach or stabilize around.
Interpretation questions stem from the timing of overshoots and the lag in resource regeneration or death rates relative to birth rates.
Practical Takeaways and Real-World Relevance
Population ecology informs land management and invasive species tracking, disease control, and conservation strategies.
Understanding growth models, carrying capacity, and limiting factors helps predict responses to environmental changes, policy decisions, and management actions.
R0 and herd immunity concepts are essential for epidemiology and public health planning (vaccination strategies and outbreak control).
The study of historical case studies (St Matthew Island, Isle Royale) provides concrete examples of theoretical concepts like overshoot, carrying capacity, and predator–prey dynamics.
Mathematical Recaps (Key Formulas)
Mark–recapture population size estimator:
N \,\approx\, \frac{sn}{x}
s = size of first (marked) sample, n = size of second sample, x = number of marked recaptures in second sample.
Exponential growth model:
\frac{dN}{dt} = rN
Solution: N(t) = N_0 e^{rt}
Logistic growth model (carrying capacity K):
\frac{dN}{dt} = rN\left(1 - \frac{N}{K}\right)
Per-capita growth rate:
r = b - d
Basic reproduction number (R0) for infectious diseases:
R_0 = c \cdot t \cdot d
c = contact rate, t = transmissibility, d = duration of infectiousness
R0 interpretation thresholds:
If R_0 > 1: outbreak potential exists
If R_0 = 1: endemic equilibrium
If R_0 < 1: disease declines
Quick Reference: Key Concepts by Topic
Mark–recapture: population size estimation via marking and recapture; critical assumptions must hold.
Growth models: exponential vs logistic; carrying capacity; density dependence.
Demography: births, deaths, immigration, emigration; per-capita growth rate; life history traits.
Disease ecology: R0; herd immunity; vaccination impacts; Measles historical decline; SARS-CoV-2 specifics.
Invasive species case studies: rapid growth, reproduction rates, ecosystem impact, management actions.
Historical population dynamics: overshoot and collapse (St Matthew Island) and predator–prey cycles (Isle Royale).
Human population and policy: MSY concept; famine prevention; fertility scenarios and projections.
Practical applications: land management, invasive species monitoring, public health planning, fisheries management.