Data Analysis and Mathematical Models

Size is usually designated as N (total number of individuals) Density – total number of individuals per area or volume Dispersion – how individuals in a population are distributed

Age structure – is a description of the abundance of individuals of each age Rapid growth – many young, few elderly; developing countries Slow growth – larger at the bottom that slowly narrow; the US Zero growth – tiers of equal width; Italy

About 1,000 years ago the human population began population growth thanks to increasing the carrying capacity of our environment Increase in food supply Reduction in disease Reduction in human waste Expansion of habitat

Survivorship Curves describe how mortality of individuals in a species varies during their lifetimes 3 types of curves Type 1 Type 2 Type 3

Type 1 Survivorship describe species in which most individuals live to middle age; after that mortality is high Examples: Humans, Elephants

Type 2 Survivorship describes organisms in which the length of survivorship is random, that is, the likelihood of death is the same at any age – constant death rate Examples: Rodents and invertebrates

Type 3 Survivorship describe species in which most individuals die young, with only a relative few surviving to reproductive age and beyond Examples: oysters, plants, free-swimming larvae, frogs

Biotic Potential is the maximum growth rate of a population under ideal conditions Take into consideration the following: Age at reproductive maturity Clutch size Frequency of reproduction Reproductive lifetime Survivorship of offspring to reproductive maturity

Limits to Growth Density-Dependent factors are those factors whose limiting effect becomes more intense as the population density increases Examples – parasite & disease transmission; competition for resources; predation

Limiting Growth Factors Density-Independent factors occur independently of the density of the population Examples – natural disasters such as fires, earthquakes, volcanic eruptions; extreme climates such as storms and frosts

Exponential Growth in a population occurs whenever the reproductive rate is greater than zero. Producing a J shaped curve G=rN G stands for growth, r stands for the per capita rate of increase, and N stands for the population size

Logistic Growth occurs when limiting factors restrict the size of the population to the carrying capacity of the habitat Producing a S shaped curve G=rN*(K-N)/K K stands for the carrying capacity; as N approaches K the growth rate is slowed, eventually reaching zero growth

Exponential and logistic growth patterns are associated with two kinds of life-history strategies: R-selected species K-selected species

R-selected species – Rapid growth (J shaped curve) Opportunistic species – grasses and insects Quickly invade a habitat and reproduce immediately (after reproducing they die) Produce many offspring that are small, mature quickly and require little if any parental care

K selected species Population size remains relatively constant at carrying capacity, K – s shaped curve Produce few offspring that are larger in size and require extensive parental care Reproduction occurs repeatedly during their lifetime