Intro to Ecology: Populations (PDF for printing)

Estimation of Population Parameters
Density is a measure of the number of organisms per unit area or unit volume. The method of density determination depends on the size and motility of the organism. Density measures may be either absolute or relative (area one has more animals than area two). Absolute density may be determined through total counts (the human census, for example) or through indirect measures. Ornithologists can estimate a bird population by walking through the woods early in the spring and counting the number of singing males, others might count the number of animals in a breeding colony (fur seals), or the number of scats (feces), tracks, scratch marks on trees, etc. For some sessile animals a direct count is possible (barnacles, coral).

For other organisms, sampling techniques must be used. A common method is the use of quadrates. Quadrates may be of any size or shape, depending on the organism. For small creatures, a square meter is often used. Several quadrates are arranged in the environment and the researcher counts the total number of creatures in each of the quadrates. The population size is then extrapolated over the entire research area. The reliability of the estimate depends on (1) the population in each quadrate must be known exactly, (2) the area of each quadrate must be known and (3) the quadrates must be representative of the sampling area (you can't avoid areas that are boggy, with poison ivy, etc). Quadrates are commonly used to measure plant populations.

Take a peek at the sage population!

Another method used by plant biologists is the line-transect method: Researchers might set three line transects 106.7 m long (350 feet) into a forest and the count all trees more than 25 cm tall within a distance of one meter from the transect.   Each transect is a long, thin quadrate of 213.4 m² (about 0.0527 acre). Table 1 shows the results.

Mark and Recapture Techniques for Determining Population Size.

Often it is not possible to directly count all of the organisms in a habitat to determine the size of a population. In these cases an estimate of the population size can be made by marking a segment of the population at one time and later recapturing the organisms (hence "Mark and recapture techniques"). The ratio of marked to unmarked individuals in the second sample can then be used to estimate the total number of organisms in the population. In this section of the laboratory we will simulate a population of organisms to demonstrate the methods used in a mark and recapture experiment. If time and climate permit, your instructor may have you perform the experiment at a field site.

The procedure for estimating population size begins with the capture of individuals at the study site. The organisms are then marked in some way so that they can later be identified by the investigator. Typical marking methods include ear tags, leg bands, dyes or paints, and clipping of fins or toes (ouch!). These animals are then returned to the habitat and allowed sufficient time to mix with the other members of the population, thus establishing an as yet unknown ratio of marked to unmarked animals in the total population. After an appropriate period of time, a second sample is collected to determine the ratio of marked to unmarked animals in the total population. Since a record is kept of the number of marked individuals in the first sample and the number of marked and unmarked animals in the second sample, this information can be used to estimate the total number of individuals in the population by the following formula:  

N =    M_t (U_c + M_r)
                   M_r       
Where:

• N = The estimated population size.
• M_t  = The number of organisms marked, then released during the first sampling interval.
• U_c = The number of unmarked individuals captured during the second sampling interval.
• M_r = The number of marked individuals in captured during the second sampling interval.

As an example, assume that 50 animals were captured, marked, and returned to a population during the first sampling period (M_t = 50). On returning to the field, 60 animals are captured. Of these 60, 55 are unmarked (U_c = 55 and M_r = 5). Plugging these values into our formula:  

N = M_t (U_c + M_r)  = 50 (55 + 5) = 3000 = 600
               M_r                      5                 5

The estimated number of animals in the entire population is 600. 

There are three assumptions of the mark and recapture technique:

1. Marked and unmarked animals are captured randomly. Field mice may become trap-happy or trap-shy. If your marks make the animals more conspicuous, you may collect too many marked animals during the recapture phase of the survey.
2. Marked animals are subject to the same mortality rate as unmarked organisms. Fish marked at sea may be weakened and suffer higher mortality or marks may make your study animal more conspicuous to predators.
3. Marks must not be lost or overlooked. Leg rings can be lost by birds or arthropods may molt and lose the mark.

Mark and recapture techniques will also allow you to estimate the age structure of the population if data are collected over several years (Figure 2)

• Between times 7 and 8 the marked population can only decrease due to deaths and immigration. The survival rate is the percentage of animals that survive the time interval:

Survival Rate (%) - (M8/M7)*100

• The estimated survival is the total population size times the survival rate.
• The loss rate (emigration and death) = 100% - survival rate.
• The dilution rate (immigration and births) is obtained indirectly as in the following example:

• The estimated survival rate for time 8 is calculated by assuming that the survival rate for the unmarked animals is the same as the marked.
• The dilution is estimated since we can account for only 1200 (400 + 800) of the 1400 observed. The other 200 must be due to births and immigration.

Measuring Relative Density
A survey of relative density depends on collection of samples that represent some relatively constant, but unknown relationship to the true population size. Relative measures provide only an index of abundance. Relative measures include:

• Traps: Number of organisms trapped depends not only on the population density, but the activity, range of movement, and skill in placing the traps. Under most circumstances, trapping only gives you a rough idea of the population size.
• Number of fecal pellets.
• Vocalization frequency.
• Pelt records.
• Catch per unit effort (fishing).
• Number of artifacts (mud chimneys for crayfish, tree-squirrel nests, pupa cases),

Measuring Natality
Populations increase due to natality (birth, hatching, germination, or fission). Fertility is the actual level of performance in the population based on the number of individuals produced. Fecundity is the potential level of performance (a physiological capacity) of the population. The fertility rate for a human population may be one birth per 8 years per female while the fecundity rate is one birth per female per 9~11 months.

The natality rate is usually expressed as the number of offspring per female per unit time. The time measurement is dependent on the species (yearly, per breeding season, etc.). Note that males aren't important in calculating the nattily rate.

Fecundity varies vastly among species. Oysters produce 55-114 million eggs, birds between one and 20 eggs, mammals usually have a litter less than 10. In general, fecundity is inversely proportional to the amount of parental investment.

Mortality
How many organisms die, when they die, and why are important to an understanding of population dynamics.Two types of survivorship have been identified: physiological longevity (organisms die of senescent) vs. ecological longevity (most are cut down by predators, disease, and other hazards before they reach old age). The differences between these two types of survivorship can be extraordinary. Most European Robins, for example, only survive for a year in the wild, while captive birds can live to be 11 years old.

Mortality can be measured directly by marking animals as individuals (perhaps with a numbered leg band) and then determining exactly when they dies. Indirect measures of survivorship usually depend on capturing a whole series of organisms, all of differing age, and then determining from the age structure of the population the mortality rates for each age group. An example using a fish catch curve is shown in figure 3.

The survival rate for ages 2 - 3 =    Relative Abundance of 3-yr. fish   = 147/192 = 0.50
                                                            Relative Abundance of 2-yr. fish

The assumptions of this method are that the  initial number of fish in each of the two age groups was the same and that the survival rate is constant over time for the two age groups.

Immigration and Emigration
Immigration and emigration rates are not usually measured in populations because of the difficulties involved in such studies. Usually, researchers assume these effects are negligible, that the two components are equal and therefor cancel out or that your study site acts as an "island habitat" where the importance is reduced. Obviously, for high vagility creatures (such as birds and dandelions), such assumptions would ignore an important component of population dynamics.

If, however, the area is properly samples, it is possible to separate births from immigration and deaths from emigration (Figure 4). This way the researcher can avoid only having loss rates (deaths and emigration) and dilution rates (births and immigration).

The researcher lays out a sampling area as a large quadrate equally divided into four smaller squares (Figure 4). The size of the small squares is set so that the dispersal rate is not too large (determined by trial and error and depends on your organism).

• The large square perimeter = 8 units; area = 4 square units.
• The small square perimeter = 4 units; area = 1 square unit.
• The ratio of perimeter to area for large squares is 2.
• The ratio of perimeter to area for the small squares is 4.
• Death rates and birth rates should be the same for the small squares and the large squares, but the immigration and emigration rates of the small squares should be twice that of the large square if dispersal movements occur at random in all directions since small squares have twice the perimeter relative to the area of the large square).

Example:

1. Large square loss rate (death and emigration) = 15% per month.
2. Small square loss rate (death and emigration) = 20% per month
3. Subtracting for estimates of the large square: Emigration rate is 5% per month, Death rate is 10% per month (remember, death rates should be the same).

Immigration and emigration rates can also be determined exactly by marking animals in two adjacent areas and noting the movement between the areas.

Life Tables and Demographics

Table 2 shows an example life table for the barnacle, Balanus glandula. Unlike most animals, barnacles are sessile as adults (they remain plastered down in a single place and do not move). This makes them easy to follow over long periods of time. During the first year researchers mapped out the distribution of 142 animals on a rocky coastline. They then return to the site for nine years and determined which individuals died (any missing from the map were known dead since barnacles cannot move as adults. Their data are shown below. 

• The first column (x) is the age of the animals in years. Depending on the beast, this may change. Mice, for example, may be better followed on a monthly basis, while long-lived animals (such as ourselves, crocodiles, and turtles) may be better followed in five-year intervals.
• The observed number of alive (n_x) is the actual number of barnacles counted each year (x). The researchers used half-counts during years 4 and 6 since they determined that the animals recently died (within the past week). They could determine this since there were "scars" still visible at the map positions of the individuals.
• The third column (l_x) is the number of surviving individuals adjusted to a standard population size of 1000. The value at 1 year is calculated as the current n_x divided by the original population size, then multiplied by 1000. For example, year 1 is (62/142)*1000 while year 2 is (34/142)*1000. The values are rounded to the nearest whole number.
• The number dying (d_x) represents the change in population size from year x to year x+1. The number dying during year 0 is 1000-437=563. For year 1 the number dying is 437-239=198.
• The mortality rate (q_x) is calculated by dividing the current year’s d_x by the current year’s l_x. For year 0, 563/1000=0.563. For year 1 the mortality rate is 198/437=.453.
• The average number alive during any particular year (L_x; don’t confuse with the number surviving) is calculated by adding together l_x +l_x+1 and dividing by 2. Thus, for year 0 the average number alive is (1000+437)/2=718.5! For year 1: (437+239)/2=338.
• The seventh  column (T_x) is an intermediate value for calculating the life expectancy. It is calculated by cumulatively adding the L_x values from the bottom up. Thus, for year 8, T₈= L₈+L₉ (T₈=0+7=7). For year 7, , T₇= L₇+L₈ (T₈=14+7=21).
• The life expectancy (e_x) is the average life expectancy of barnacles of age x in barnacle-years. It is calculated by dividing T_x by l_x. For year 0, the average barnacle is expected to live for only another 1.577 years (1577/1000). If they survive the first year, their life expectancy is an additional 1.9 years (858.5/437). Note that once the animals get past the first few years, the ones that survive get to live for a longer time.
• The last column is used to calculate a survivorship curve. It is simply the log of the number surviving (log(l_x)). The graph for the above data is shown in figure 5.:

A live calculation worksheet in Excel format can for the Balanus population can be found here. A further discussion on life tables is at this link. The human life table assignment is here!

Run the Population Growth Simulation. (Pop Growth PDF is here) VISTA USERS READ THIS TO RUN THE PROGRAMS

Run the Competition Simulation. (Competition PDF is here) VISTA USERS READ THIS TO RUN THE PROGRAMS

Run the Predator-Prey Simulation. (Predation PDF is here) VISTA USERS READ THIS TO RUN THE PROGRAMS

Game Theory. (Game Theory PDF is here) VISTA USERS READ THIS TO RUN THE PROGRAMS