Population Ecology

Fundamentals of Population Ecology

• Definition of Population Ecology: The study of populations in relation to their environment, including environmental influences on density and distribution, age structure, and population size.
• Definition of a Population: A group of individuals of one species simultaneously occupying the same general area, utilizing the same resources, and influenced by similar environmental factors.     * Populations cannot continue to grow indefinitely.     * Many remain relatively stable over time.     * Others show dramatic increases followed by equally dramatic decreases.

Factors Affecting Population Size

• Four Main Factors:     1. Natality: The number of new members of the species due to reproduction (birth rate).     2. Mortality: The number of deaths. Factors include predation and old age.     3. Immigration: The rate at which individuals move INTO the population.     4. Emigration: The rate at which individuals move out or EXIT the population. Factors include leaving for another habitat, lack of food, etc.     * Population Change Formula:         $\text{Population change} = (\text{natality} + \text{immigration}) - (\text{mortality} + \text{emigration})$

Characteristics of a Population

1. Population Density: The number of individuals per unit of area.     * It is dynamic (ever-changing).     * Determined through counts, sample size estimates, indirect indicators, or mark-recapture methods.
2. Growth Rate: How fast or slow a population is growing.
3. Population Dispersion/Distribution: The pattern of spacing among individuals within the boundaries of the population.     * Random Dispersion: Unpredictable, patternless spacing.     * Clumped Dispersion: Patchy aggregation (most common).     * Uniform Dispersion: Even spacing, often resulting from direct interactions between individuals.
4. Age Structure: The relative number of individuals of each age in the population.

Measuring Population Density: The Mark-Recapture Method

• Counting all individuals is often impractical or impossible.
• Mark-Recapture Formula:     $N = \frac{(\text{number marked 1st time}) \times (\text{total catch 2nd time})}{\text{number of marked recaptures}}$
• Assumptions: The method assumes that marked individuals have the same probability of being trapped as unmarked individuals, though this is not always valid.

Population Growth Models and Curves

• Growth Rate Calculation:     $\text{Growth rate} = \frac{\text{Change in number of individuals}}{\text{Time period}}$
• General Growth Model: Shows changes in population size against time. When a new species spreads into an area, growth is often S-shaped (sigmoid-shaped).
• Exponential Model (J-curve):     * Represents an idealized population in an unlimited environment.     * Associated with r-selected species ($r = \text{per capita growth rate}$).
• Logistic Model (S-curve):     * Includes carrying capacity (K), the maximum population size that a particular environment can support.     * Associated with K-selected species and limited resources.

Stages of Population Growth

1. Exponential Growth Phase (Logarithmic Phase):     * The number of individuals increases at a faster and faster rate.     * Causes:         * Natality rate is higher than mortality rate.         * Population doubles per unit time.         * Unlimited resources and ideal conditions (abundant food, space, light, nutrients, oxygen).         * Few or no predators regularly present.         * Rare disease occurrence.         * Little or no competition from other inhabitants.         * Favorable abiotic factors (e.g., temperature, dissolved oxygen levels).
2. Transitional Phase:     * Growth rate slows down considerably, though the population is still increasing.     * Causes:         * Natality rate starts to fall (but remains higher than mortality).         * Mortality rate starts to rise due to crowded conditions allowing diseases to spread.         * Increasing competition for resources due to high population density.         * Predators move into the area, attracted by the growing food supply.
3. Plateau Phase (Stationary Phase):     * The number of individuals stabilizes; growth ceases.     * The population reaches carrying capacity.     * Causes:         * Natality and mortality are equal ($\text{Natality} + \text{Immigration} = \text{Mortality} + \text{Emigration}$).         * Limited resources (less space for seeds/germination, less food, less nutrients/oxygen).         * Increased predators, disease, and parasites.         * Lowered reproduction rates result from resource scarcity.

Carrying Capacity and Environmental Resistance

• Carrying Capacity ($K$): The maximum population of a particular species that a given habitat can support over a given period of time.
• Intrinsic Rate of Increase: No real population can grow at its intrinsic rate indefinitely because of limiting factors.
• Environmental Resistance: All factors that act to limit the growth of a population.
• Relationship: Biotic potential and environmental resistance together determine $K$.

Overshoot and Population Dieback

• Overshoot: When populations use up resource supplies and exceed carrying capacity.     * Reproductive Time Lag: It takes time for the birth rate to fall and death rate to rise once $K$ is reached (e.g., animals may be pregnant when food runs out).
• Population Dieback or Crash: If members do not switch resources or move, the death rate increases dramatically.
• Case Study: Sheep Population: Logistic growth of sheep showed an overshoot followed by stabilization around $1.5$ million sheep between $1850$ and $1925$.
• Case Study: Reindeer: Population on an island overshot carrying capacity (approx. $2,000$ individuals) and crashed to near zero by $1950$.

Limiting Factors of Population Growth

• Density-Dependent Factors: Factors that depend on population size.     * Intraspecific Competition: Reliance of individuals of the same species on the same limited resource; intensifies as population size increases.     * Predation, Disease, and Toxic Waste Buildup.     * Intrinsic Factors: Stress syndrome at high densities can cause hormonal changes that suppress the immune system, reducing birth rates and increasing death rates.
• Density-Independent Factors: Affects all populations regardless of size.     * Weather, Climate, and Natural Disasters: May control population size before density-dependent factors become relevant.     * Human Activity.

Ecology Mathematical Formulas (AP Biology)

• Rate:     $\frac{dY}{dt}$     where $dY = \text{amount of change}$ and $dt = \text{change in time}$.
• Population Growth:     $\frac{dN}{dt} = B - D$     where $N = \text{population size}$, $B = \text{birth rate}$, and $D = \text{death rate}$.
• Exponential Growth:     $\frac{dN}{dt} = r_{max} N$     * $r = b - d$ ($b = \text{per capita birth rate}$, $d = \text{per capita death rate}$).     * Zero Population Growth (ZPG) occurs when $r = 0$.     * If r > 0, population increases; if r < 0, population decreases.
• Logistic Growth:     $\frac{dN}{dt} = r_{max} N \left( \frac{K - N}{K} \right)$     * $K = \text{carrying capacity}$.     * $\frac{K - N}{K}$ represents the percentage of $K$ available for growth.
• Simpson's Diversity Index:     $D = 1 - \sum \left( \frac{n}{N} \right)^2$     * $n = \text{total number of organisms of a particular species}$.     * $N = \text{total number of organisms of all species}$.     * AP Bio uses the "infinite" formula version: $D_s = 1 - \sum \left( \frac{n}{N} \right)^2$.     * A "finite" version exists: $D_s = 1 - \frac{\sum n(n-1)}{N(N-1)}$.

Demography and Life History Strategies

• Demography: The study of vital statistics affecting population size.
• Demographic Transition: A dramatic change in birth and death rates in modern societies where education and standard of living are high; birth rates fall to meet death rates.
• Generation Time: Average span of time between the birth of individuals and the birth of their offspring, typically related to body size.
• Sex Ratio: Proportion of each gender; the number of females is usually directly related to the expected number of births.
• Life Tables: Describe how birth and death rates vary with age over a maximum life span; constructed by following a cohort (a group of individuals of the same age).
• Survivorship Curves:     * Type I: Flat during early/middle life, drops suddenly in old age. (e.g., humans and large mammals).     * Type II: Intermediate, constant mortality over life span. (e.g., Hydra, gray squirrels, lizards).     * Type III: High death rate for young, lower rate for survivors. (e.g., oysters, plants).     * Stair-stepped Curve: Shown by invertebrates with high mortality during molts (e.g., crabs).
• Strategy Comparison:     * r-strategy: Disposable offspring, high death rate, short life span, early maturity, small body size, reproduce once (e.g., insects, spiders).     * K-strategy: Nurturing strategy, low death rate, long life span, late maturity, large body size, reproduce multiple times (e.g., large animals).

Principle of Allocation

• Resource Acquisition: Resources are divided among homeostasis, defense, growth, and reproduction.
• Conditions:     1. Typical Conditions: Homeostatic needs met first; remaining resources divided among growth, defense, and reproduction.     2. Abundant Resources: More resources available for all activities after homeostasis is met.     3. Stressful Conditions: More resources expended on homeostasis; fewer available for growth, defense, and reproduction.