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14.2 Measuring and Modeling Population Change Carrying capacity • The maximum number of organisms that can be sustained by available resources over a given period of time • Is dynamic because environmental conditions are always changing Population growth: factors Population dynamics: changes in population characteristics The main determinants are: – natality (birth rate) – mortality (death rate) – Immigration (individuals moving in) – Emigration (individuals moving out) Population change: [(births + immigration) - (deaths + emigration)] x100 initial population size [(B+I)-(D+E)/ n] x 100 CLOSED POPULATION • A population whose growth is influenced only by natality and mortality OPEN POPULATION • A population whose growth is influenced by natality, mortality and migrations Factors affecting Birth rate Fecundity: theoretical maximum number of offspring that could be produced by a species in one lifetime Fertility: the number of offspring actually produced by an individual during its lifetime. • affected by food supply, disease, mating success, etc. Type I survivorship • Type I: species that have a high survival rate of the young, live out most of their expected life span and die in old age. • Example: Elephants are slow to reach sexual maturity and have few offspring. They have a long life expectancy Type III survivorship • Type III: species that have many young, most of which die very early in their life. • Example: Plants, oysters and sea urchins. Type II survivorship • Type II :species that have a relatively constant death rate throughout their life span. Death could be due to hunting or diseases. • Examples:coral, squirrels, honey bees and many reptiles. Biotic potential • maximum reproductive rate under ideal conditions (intrinsic rate of natural increase) • Example: Under ideal conditions, a population of bacteria can grow to more than 10 in 24 h. • Limiting Factor: the name applied to an essential resource that is in short supply or unavailable, and prevents an organism from achieving this potential Geometric Growth - births take place at one time of the year (i.e., breeding season), but deaths may occur all year - population grows rapidly during breeding season, declines throughout year until next breeding season - constant growth rate must be compared by looking at same time each year - annual growth rate can be determined - line of best fit (on graph) produces J-curve - examples: seals, deer, salmon Geometric growth • A population that grows rapidly during breeding season, then declines through the year until the next breeding season • Populations with geometric growth curves experience a constant growth rate • Determine growth rate with formula: = N(t+1)/N(t) where (lambda) represents the geometric growth rate N(t+1) represents the population size in a given year N(t) represents the population size at the same time in the previous year. (See page 663) • This equation can be generalized and rearranged to find population size at any given time: • N(t) = N(0) t • See page 633-634, Sample Problem Exponential growth • reproduction is continuous throughout year (i.e., no breeding season) - constant growth rate - instantaneous growth rate can be determined, more complex than ageometric formula - examples: yeast, bacteria, humans • In natural populations, exponential growth does not continue indefinitely because of limited amounts of: energy, water, shelter, space • Can use a modified form of exponential growth formula to estimate doubling time. • See Sample Problem p.665 • Both geometric and exponential growth models produce similar graphs, known a J-curves. Logistic Growth Curve Stationary phase stabilizing Log phase – very rapid growth Lag phase – small population size, therefore slow population growth r- and k- species • Depending on their reproductive strategies, species can be characterized as r or k species. • r is the instantaneous rate of population increase while k is the carrying capacity. • The r-species possess characteristics of high biotic potential, rapid development, early reproduction, single period of reproduction per individual, short life cycle, and small body size. • Populations of r-species usually remain below the carrying capacity and are regulated by density-independent factors • k-species possess characteristics of low biotic potential, slow development, delayed reproduction, multiple periods of reproduction per individual, long life cycle and larger body size. • populations of k-species are usually maintained near the carrying capacity and regulated by density dependent factors • In disrupted habitats r-species are more common while k-species are common in stable habitats. Many of our agricultural pests are r-species. Most organisms however actually have attributes that fit both r and k species.