45.1 Population Demography

Population ecology studies how groups of organisms interact with their environment and with each other. Understanding how populations are measured, how they grow, and what limits that growth gives you the foundation for predicting ecological changes. This section covers the tools ecologists use to quantify populations, the patterns they observe, and the mathematical models that describe population change over time.

Population Ecology

Methods for population measurement

Population size is the total number of individuals in a population. Counting every single organism is rarely practical, so ecologists rely on sampling techniques to estimate this number.

Mark and recapture is one of the most common methods for mobile animals. Here's how it works:

1. Capture a sample of individuals from the population and mark them (with tags, paint, bands, etc.).
2. Release the marked individuals back into the population and allow time for them to mix back in.
3. Capture a second sample and count how many of those individuals carry marks.
4. Use the Lincoln-Petersen formula to estimate total population size:

$N = \frac{M \times C}{R}$

• $N$ = estimated population size
• $M$ = number of individuals marked in the first capture
• $C$ = total number of individuals in the second capture
• $R$ = number of marked individuals recaptured

This method assumes that marked and unmarked individuals mix randomly, that marks don't fall off or affect survival, and that the population is closed (no immigration or emigration between captures).

Quadrat sampling works well for organisms that don't move much, like plants or sessile invertebrates. You divide the habitat into equal-sized plots (quadrats), randomly select several of them, count the individuals in each, then multiply the average count per quadrat by the total number of quadrats in the area.

Population density is the number of individuals per unit area or volume. You calculate it by dividing population size by the total area or volume the population occupies. For example, 500 trees across 10 hectares of forest gives a density of 50 trees per hectare.

Patterns of population distribution

How individuals are spread across their habitat falls into three main patterns:

• Uniform distribution: Individuals are evenly spaced. This typically results from competition or territorial behavior. Nesting penguins, for instance, space themselves at roughly equal distances because each pair defends the area around its nest.
• Random distribution: Individuals are scattered with no predictable pattern. This happens when resources are abundant and there's no strong attraction or repulsion between individuals. Dandelions sprouting across a meadow are a classic example.
• Clumped distribution: Individuals cluster together in groups. This is the most common pattern in nature and results from patchy resource distribution or social behavior. Schools of fish and herds of elephants both show clumped distribution for different reasons: fish school for predator defense, while elephants cluster near water sources and for social bonding.

Life tables and mortality rates

A life table tracks survival and reproduction across different age classes in a population. Think of it as a demographic spreadsheet for a species. The key columns include:

• $l_x$: proportion of individuals surviving to age $x$
• $d_x$: proportion of individuals dying between age $x$ and age $x+1$
• $q_x$: age-specific mortality rate (probability of dying between age $x$ and $x+1$), calculated as $q_x = \frac{d_x}{l_x}$

Mortality rate is the proportion of individuals that die within a specific time period. Life tables let you calculate age-specific mortality rates, such as infant mortality or adult mortality, which reveal when a species is most vulnerable.

Fecundity refers to the reproductive output of an individual or population, often measured as the number of offspring produced per individual per unit time. Life tables frequently include a fecundity column ($b_x$) showing how reproduction varies with age.

Survivorship curves across species

Survivorship curves plot the proportion of individuals surviving at each age on a log scale. They fall into three general types:

• Type I: Low mortality in early and middle life, then a sharp increase in death rates in old age. Large mammals, including humans, follow this pattern. These species invest heavily in fewer offspring and provide extensive parental care.
• Type II: A roughly constant mortality rate throughout life, producing a straight diagonal line on a log-scale graph. Many birds, small mammals, and some reptiles show this pattern.
• Type III: Extremely high mortality early in life, but those few individuals that survive past the vulnerable stage have much lower death rates afterward. Most fish, marine invertebrates, and plants fit here. An oak tree may produce thousands of acorns, but only a handful survive to become saplings.

These curves reflect fundamentally different life history strategies. Type I species produce few offspring with high parental investment; Type III species produce enormous numbers of offspring with little or no care, relying on sheer numbers for some to survive.

Population Dynamics

Factors affecting population growth

Four processes drive changes in population size:

• Natality (birth rate): Influenced by both intrinsic factors (genetics, physiology, age at reproductive maturity) and extrinsic factors (resource availability, predation pressure, competition).
• Mortality (death rate): Shaped by intrinsic factors like genetic susceptibility to disease and senescence, plus extrinsic factors like predation, competition, and abiotic stressors such as temperature extremes.
• Immigration: Movement of individuals into a population from elsewhere.
• Emigration: Movement of individuals out of a population to other areas.

Net migration is the difference between immigration and emigration. A simple way to express overall population change is:

Exponential and logistic growth models

Exponential growth describes what happens when a population has unlimited resources. The per capita growth rate stays constant, and population size increases faster and faster over time, producing a J-shaped curve:

$N_t = N_0 e^{rt}$

• $N_t$ = population size at time $t$
• $N_0$ = initial population size
• $r$ = intrinsic rate of increase (per capita growth rate)
• $t$ = time

This model works well for populations colonizing new, resource-rich environments (like bacteria in fresh culture media), but it can't hold indefinitely. No real environment has infinite resources.

Logistic growth adds realism by incorporating a ceiling on population size. Growth starts out exponential, then slows as the population approaches the carrying capacity ($K$), producing an S-shaped (sigmoidal) curve:

$N_t = \frac{K N_0}{N_0 + (K - N_0)e^{-rt}}$

• $K$ = carrying capacity (the maximum population size the environment can sustain)

The logistic model has its own limitations: it assumes $K$ is constant, it doesn't account for time lags in population response, and it can't capture oscillations like those seen in predator-prey cycles.

Carrying capacity and population growth

Carrying capacity ($K$) is the maximum population size an environment can support indefinitely given available resources like food, water, space, and shelter.

As a population approaches $K$, density-dependent pressures intensify:

• Competition for limited resources increases
• Predation rates may rise as prey become easier to find
• Disease and parasites spread more readily in crowded conditions
• Waste products accumulate

When a population overshoots $K$, it can experience a dramatic crash. The reindeer population on St. Matthew Island, Alaska, is a well-known example: introduced in 1944, the herd grew to about 6,000 by 1963, then crashed to 42 animals by 1966 after overgrazing their food supply.

Population regulation factors

• Density-dependent factors scale with population density. As density increases, their effects become stronger. Examples include competition for food, predation, parasitism, and disease transmission.
• Density-independent factors affect populations regardless of how crowded they are. Natural disasters (hurricanes, volcanic eruptions), severe weather events, and habitat destruction by human activity all fall into this category.

Most real populations are regulated by a combination of both types of factors.

Population characteristics and dynamics

• Age structure: The distribution of individuals across age groups (pre-reproductive, reproductive, post-reproductive). A population with many young individuals is likely to grow; one dominated by older individuals may decline. Age structure diagrams (population pyramids) are a common way to visualize this.
• Generation time: The average time between the birth of an individual and the birth of its offspring. Species with shorter generation times (like bacteria) can evolve and grow in number much faster than species with longer generation times (like elephants).
• Life history strategy: The evolved pattern of growth, reproduction, and survival for a species. This includes trade-offs like producing many small offspring vs. few large ones, or reproducing once vs. multiple times over a lifetime.
• Population projection: Estimating future population size and structure using current demographic data. Ecologists combine age structure, survivorship, and fecundity data to model how a population will likely change over time.