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

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.
Growth Rate: How fast or slow a population is growing.
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.
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

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).
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.
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.