Characteristics of Populations POPULATION ECOLOGY Characteristics of Populations Two important characteristics of any population are density and the spacing of individuals Demography is the study of factors that affect the growth and decline of populations

Equations to know for the AP Biology Exam

Introduction A population is a group of individuals of a single species that simultaneously occupy the same general area. The characteristics of populations are shaped by the interactions between individuals and their environment.

1. The characteristics of populations are shaped by the interactions between individuals and their environment Populations have size and geographical boundaries. The density of a population is measured as the number of individuals per unit area. The dispersion of a population is the pattern of spacing among individuals within the geographic boundaries.

Density is the result of a dynamic interplay between processes that add individuals to a population and those that remove individuals from it Births and immigration add individuals to a population. Births Immigration PopuIation size Emigration Deaths Deaths and emigration remove individuals from a population.

Measuring density of populations is a difficult task. We can count individuals; we can estimate population numbers. Fig. 52.1 Copyright © 2002 Pearson Education, Inc., publishing as Benjamin Cummings

Unfortunately, it is usually impractical to attempt to count individuals in a population. One sampling technique that researchers use is known as the mark-recapture method. Individuals are trapped in an area and captured, marked with a tag, recorded, and then released. After a period of time has elapsed, traps are set again, and individuals are captured and identified. This information allows estimates of population changes to be made.

A past grid-in problem on the AP exam A past grid-in problem on the AP exam. What factors might affect the validity of this method?

2. Demography is the study of factors that affect the growth and decline of populations Additions occur through birth, and subtractions occur through death. Demography studies the vital statistics that affect population size.

Reproductive rates. Demographers that study populations usually ignore males, and focus on females because only females give birth to offspring. A reproductive table is an age-specific summary of the reproductive rates in a population. For sexual species, the table tallies the number of female offspring produced by each age group.

Table 52.2 Copyright © 2002 Pearson Education, Inc., publishing as Benjamin Cummings

Survivorship Curves A survivorship curve is a graphic way of representing the data in a life table Survivorship curves plot the proportion or numbers of a cohort still alive at each age 12

Survivorship curves can be classified into three general types Type I: low death rates during early and middle life and an increase in death rates among older age groups Type II: a constant death rate over the organism’s life span Type III: high death rates for the young and a lower death rate for survivors Many species are intermediate to these curves

Number of survivors (log scale) Figure 40.16 1,000 I 100 II Number of survivors (log scale) 10 Figure 40.16 Idealized survivorship curves: types I, II, and III III 1 50 100 Percentage of maximum life span 14

The following terms are used to describe population growth: Biotic potential - is the maximum growth rate of a population under ideal conditions, with unlimited resources and without any growth restrictions. For example, some bacteria can divide every 20 minutes. At that rate, one bacterium could give rise to over a trillion bacteria in 10 hours. In contrast, elephants require nearly two years of gestation of a single infant.

The following factors contribute to the biotic potential of a species: Age at reproductive maturity Clutch size (number of offspring produced at each reproductive event) Frequency of reproduction Reproductive lifetime Survivorship of offspring to reproductive maturity

“Trade-offs” and Life Histories Organisms have finite resources Which may lead to trade-offs between survival and reproduction

EXPERIMENT 100 80 60 40 20 Reduced brood size Normal brood size Enlarged brood size Parents surviving the following winter (%) Male Female Researchers in the Netherlands studied the effects of parental caregiving in European kestrels over 5 years. The researchers transferred chicks among nests to produce reduced broods (three or four chicks), normal broods (five or six), and enlarged broods (seven or eight). They then measured the percentage of male and female parent birds that survived the following winter. (Both males and females provide care for chicks.) Conclusion?????

The traits that affect an organism’s schedule of reproduction and survival make up its life history. Life histories are a result of natural selection, and often parallel environmental factors. Some organisms, such as the agave plant, exhibit what is known as big-bang reproduction, where large numbers of offspring are produced in each reproduction, after which the individual often dies. Other examples??? Fig. 52.4

POPULATION ECOLOGY Population Growth The exponential model of population growth describes an idealized population in an unlimited environment The logistic model of population growth incorporates the concept of carrying capacity

Video: Population Ecology

Per Capita Rate of Increase Change in population size can be defined by the equation If immigration and emigration are ignored, a population’s growth rate (per capita increase) equals birth rate minus death rate − Change in population size Births Immigrants entering Deaths Emigrants leaving   23

The population growth rate can be expressed mathematically as  B −D where N is the change in population size, t is the time interval, B is the number of births, and D is the number of deaths 24

Births and deaths can be expressed as the average number of births and deaths per individual during the specified time interval B  bN D  mN where b is the annual per capita birth rate, m (for mortality) is the per capita death rate, and N is population size 25

The population growth equation can be revised  bN −mN 26

The per capita rate of increase (r) is given by r  b − m Zero population growth (ZPG) occurs when the birth rate equals the death rate (r  0) 27

Change in population size can now be written as  rN 28

Instantaneous growth rate can be expressed as dN dt  rinstN where rinst is the instantaneous per capita rate of increase 29

Exponential (EX-poe-NEN-shul) Growth Exponential population growth A pattern of population growth in which the number of individuals increase in doubling increments: (2,4,8,16,32,64….) Is population increase under idealized conditions Under these conditions The rate of reproduction is at its maximum, called the intrinsic rate of increase Occurs when the birth rate remains even slightly above the death rate.

At what time was the test tube a quarter of the way full? See if you and your table partner can solve the problem below? Be able to explain your answer. Say that you transfer one bacteria to a test which has the optimal conditions for growth. The single bacteria can divide on its own (a process called fission). At optimum conditions it takes some bacteria (like E.coli) a time span of about 20 minutes to go through fission. So at 20 minutes you have 2 bacteria. After 40 minutes you have 4. After 60 minutes you have 8…etc. Because you do not have a life you decide to return back to the lab and found to your surprise that at midnight the entire test tube was 100% full. From your conceptual understanding of this rate of growth, calculate the exact time that the test tube only half full (half empty for you pessimist out there:). At what time was the test tube a quarter of the way full?

Exponential Growth (cont) Exponential (EX-poe-NEN-shul) population growth is population increase under idealized conditions Under these conditions, the rate of increase is at its maximum, denoted as rmax The equation of exponential population growth is dN dt  rmaxN 32

Exponential population growth results in a J-shaped curve 33

2,000 dt dN  1.0N 1,500 dt dN  0.5N Population size (N) 1,000 500 5 Figure 40.17 2,000 dt dN  1.0N 1,500 dt dN  0.5N Population size (N) 1,000 500 Figure 40.17 Population growth predicted by the exponential model 5 10 15 Number of generations 34

The J-shaped curve of exponential growth characterizes populations in new environments or rebounding populations For example, the elephant population in Kruger National Park, South Africa, grew exponentially after hunting was banned 35

Figure 40.18 8,000 6,000 Elephant population 4,000 2,000 Figure 40.18 Exponential growth in the African elephant population of Kruger National Park, South Africa 1900 1910 1920 1930 1940 1950 1960 1970 Year 36

Introduction Why do all populations eventually stop growing? What environmental factors stop a population from growing? The first step to answering these questions is to examine the effects of increased population density.

Limiting factor Are those elements that prevent a population from attaining its biotic potential. Limiting factors are characterized into density-dependent and density- independent factors.

Density-dependent Factors are those agents whose limiting effect become more intense as the population density increases. This is a type of negative feedback. Examples? Transmission rates of parasitism and disease Competition for resources (food, space, water, light etc.) Toxic effects of waste products. Increased rates of predation

Territoriality, defense of a space, may set a limit on density. Intraspecific competition for food can also cause density-dependent behavior of populations. Territoriality, defense of a space, may set a limit on density. Predation may also be a factor because it can cause mortality of prey species. Fig. 52.15 Copyright © 2002 Pearson Education, Inc., publishing as Benjamin Cummings

Waste accumulation is another component that can regulate population size. In wine, as yeast populations increase, they make more alcohol during fermentation. However, yeast can only withstand an alcohol percentage of approximately 13% before they begin to die. Disease can also regulate population growth, because it spreads more rapidly in dense populations.

Density-independent factors occur independently of the density of a population and there is no feedback to slow population growth. Natural disasters (fires, earthquakes, volcanic eruptions, tsunamis, cyclones, meteorite impacts, etc.) and extremes of climate are examples.

Carrying Capacity Exponential growth cannot be sustained for long in any population A more realistic population model limits growth by incorporating carrying capacity Carrying capacity (K) is the maximum population size the environment can support Carrying capacity varies with the abundance of limiting resources 43

The Logistic Growth Model In the logistic population growth model, the per capita rate of increase declines as carrying capacity is reached The logistic model starts with the exponential model and adds an expression that reduces per capita rate of increase as N approaches K dN dt  rmaxN (K −N) K 44

Table 40.2 Table 40.2 Logistic growth of a hypothetical population (K = 1,500) 45

The logistic model of population growth produces a sigmoid (S-shaped) curve 46

Exponential growth 2,000 dt dN  1.0N 1,500 K  1,500 Logistic growth Figure 40.19 Exponential growth 2,000 dt dN  1.0N 1,500 K  1,500 Logistic growth dt dN (1,500  N) 1,500 Population size (N)  1.0N 1,000 Population growth begins slowing here. Figure 40.19 Population growth predicted by the logistic model 500 5 10 15 Number of generations 47

Number of Paramecium/mL Figure 40.20 1,000 180 150 800 120 Number of Daphnia/50 mL Number of Paramecium/mL 600 90 400 60 200 30 5 10 15 20 40 60 80 100 120 140 160 Figure 40.20 How well do these populations fit the logistic growth model? Time (days) Time (days) (a) A Paramecium population in the lab (b) A Daphnia (water flea) population in the lab 48

The logistic model fits few real populations but is useful for estimating possible growth Conservation biologists can use the model to estimate the critical size below which populations may become extinct 49

Grid-in: quantitative reasoning Answer the following problem- show your work.

Other populations have regular boom-and-bust cycles. There are populations that fluctuate greatly. A good example involves the lynx and snowshoe hare that cycle on a ten year basis. Fig. 52.19 Copyright © 2002 Pearson Education, Inc., publishing as Benjamin Cummings

50 2,500 Wolves Moose 40 2,000 30 1,500 Number of wolves Figure 40.24 50 2,500 Wolves Moose 40 2,000 30 1,500 Number of wolves Number of moose 20 1,000 10 500 Figure 40.24 Fluctuations in moose and wolf populations on Isle Royale, 1959–2011 1955 1965 1975 1985 1995 2005 Year 52

Grid-in: quantitative reasoning practice