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Population Dynamics I. Introduction

A. Adolph Murie studied wolf (Canis lupis) predation of Dall’s’s sheep (Ovis dalli) in Denali National Park (DNP) in the 1930s and 1940s. 1. The main purpose of his study was to determine whether wolves kill enough sheep

to justify the call for reducing the wolf population.

2. Murie pursued several lines of research. a. He directly observed wolves and sheep. b. He tracked wolves through snow to find their kills. c. Where wolves killed sheep, they often left the skulls. The skulls provided a

means of identifying gender, age, and general physical condition (via tooth wear).

3. Murie found 608 sheep skulls, which he used to explore causes and age of death. 4. Data from the skulls indicated that death within the Dall’s sheep population in

DNP fell mainly on the young and old. Most of the sheep could avoid predation by wolves.

B. Ahmad Hegazy studied an endangered plant, Cleome droserifolia, in the desert of eastern Egypt in the 1980s. At the time of the study, humans were heavily exploiting the plant for medicinal purposes and Hegazy was concerned that the heavy harvesting was leading to the plant’s extinction. 1. Hegazy painstakingly estimated patterns of survival

and reproduction, which means he keep track of and counted a huge number of plants and their seeds over time.

2. His analyses provided a means for managing the species that promotes its survival and allows its use in traditional medicine.

Population dynamics 2

C. The population studies done by Murie and Hegazy illustrate 2 of several approaches used and the types of data acquired in the study of the population dynamics of a species.

D. All populations continually increase and decrease in size. 1. In mathematical symbolism: Nt+1 = Nt + Bt – Dt + It – Et. That is, population size

(N) at time t+1 is equal to the population size at time t plus births (B) minus deaths (D) plus immigrants (I) minus emigrants (E).

2. If you were managing a business, you would be interested in knowing how much money was being paid out of the business relative to how much money was coming in. The net difference represents your profit.

3. The same is true for managing a wildlife population. By knowing the net change in the size of the wildlife population from 1 year to the next, you as a wildlife manager know whether the population is profitable (i.e., gaining in size) or headed toward bankruptcy (i.e., becoming smaller).

E. To organize our study of population dynamics, which is the change of populations over time, we will: 1. Consider patterns of survival in populations and then age distributions. 2. Acquire the quantitative tools for perceiving population changes. 3. Examine the effects of individuals’ moving into and out of populations.

II. Patterns of survival A. Introduction.

1. Patterns of survival vary a great deal from 1 species to another and, depending on environmental circumstances, can vary substantially even within a species.

2. In response to practical challenges of discerning patterns of survival, ecologists have invented bookkeeping devices called life tables that list both the survivorship and the deaths (or mortality) in populations. a. A life table summarizes the statistics of death and survival of a population by

age. b. An example of a life table for a murre population is shown below.

Age (x)

Survivorship (lx)

Mortality (dx)

Mortality rate (qx)

Life expectation (ex)

0 1000 550 0.55 (or 55%) 1.15 1 450 300 0.67 (or 67%) 0.94 2 150 100 0.67 (or 67%) 0.83 3 50 50 1.00 (or 100%) 0.50 4 0 -- -- --

c. The column headings are defined as follows:

1) The age at the beginning of the time interval is represented by x.


2) lx is survivorship, the number of individuals alive at the beginning of the time interval.

3) dx is mortality, the number dying within the time interval. 4) qx is mortality rate, the number dying within the time interval divided by

the number alive at the beginning of the time interval. 5) ex is life expectation, the mean time left to an individual at the beginning

of the time interval. d. In the table, we start out with 1000 individuals at the time they were born

(age 0). Such a group, all born at the same time, is called a cohort. For example, all of the grizzly bears born in Glacier National Park, Montana in February 2006 are a cohort.

e. About the only part of the life table that is not easy to understand is the calculation of ex, life expectation. The concept itself is quite simple; it is the mean additional time still left to individuals alive at a particular age.

B. There are 3 ways of estimating patterns of survival. 1. Cohort life table.

a. The first and most reliable way is to identify a large number of individuals that are born at about the same time and keep records on them from birth to death.

b. A group born at the same time is called a cohort. c. A life table made from data collected in this way is called a cohort life table. d. A cohort studied might be a group of plant seedlings that germinated at the

same time or all the lambs born into a population of mountain sheep in a particular year.

2. Static life table. a. A second way to estimate patterns of survival in wild populations is to record

the age at death of a large number of individuals. b. This method differs from the cohort approach because the individuals in your

sample are born at different times. c. This method produces a static life table. d. The table is called “static” because the method involves a snapshot of survival

within a population during a short interval of time. e. This is the kind of life table Murie constructed for Dall’s sheep in DNP and the

kind of life table illustrated for the murre population above. 3. Age distribution.

a. A third way of determining patterns of survival is from the age distribution. b. An age distribution consists of the proportion of individuals of different ages

within a population. For example, a population of 1000 elk in July consists of:


300 calves (30% of the population); 200 yearlings (20%); 175 2-year-olds (18%); 175 3-year-olds (18%); 140 4-year-olds (14%); 10 ≥5-year-olds (1%).

c. You can use an age distribution to estimate survival by calculating the

difference in proportion of individuals in succeeding age classes. For example, in the elk population above, 20% of the herd are yearlings and 30% are calves. If you assume that the difference in numbers of individuals in 1 age class and the next is the result of mortality, then calves have a 33% mortality rate (300-200/300), or a 67% survival rate.

C. High survival among the young. 2. Murie estimated survival patterns by collecting the skulls of 608 sheep that had

died from various causes. 3. He determined the age at which each sheep in his sample died by counting the

growth rings on their horns and by studying tooth wear. 4. Figure 1 (Top) shows the data in Murie’s life table.

a. Notice that although Murie studied only 608 skulls, the numbers in the table are expressed as numbers per 1,000 individuals.

b. This adjustment is made to ease comparisons with other populations. 5. Figure 1 (Bottom) summarizes the survival patterns for Dall’s sheep based on

Murie’s sample of skulls. a. Plotting number of survivors per 1,000 births against age produces a

survivorship curve. b. A survivorship curve shows patterns of life and death within a population.

6. In Murie’s sample of Dall’s sheep skulls, he deduced there are 2 periods when mortality rates are highest: during the first year and during the period between 9 and 13 years. Mortality in the middle years is relatively lower.


Figure 1. Dall’s sheep life table (Top) and survivorship curve (Bottom). Figure from Molles (1999), page 189.


7. The overall pattern of survival and mortality among Dall’s sheep is much like that for a variety of other large vertebrates, including red deer (Cervus elaphus), Columbian black-tailed deer (Odocoileus hemionus columbianus), East African buffalo (Syncerus caffer; Figure 2), plains zebra (Equus burchelii; Figure 2), and humans.

Figure 2. Survivorship curves for selected African ungulates. Figure from Feldhamer et al. (2004), page 385.

8. This pattern of survival has also been observed in populations of annual plants and small invertebrates (Figure 3).


Figure 3. Relatively high rates of survival among young and middle-aged plants (Top) and rotifers (Bottom). Note the different time scales on the x-axes. Figure from Molles (1999), page 190.

D. Constant rates of survival. 4. The survivorship curves of many species are nearly straight lines. 5. In these populations, individuals die at approximately the same rate throughout

life.


6. This pattern of survival has been commonly observed in birds, such as the American robin (Turdus migratorius; Figure 4—Top) and the white-crowned sparrow (Zonotrichia leucophrys nuttalli; Figure 4—Top). It has also been found in the mud turtle (Kinosternon subrubrum; Figure 4—Bottom).

Figure 4. Relatively constant rates of survival. Figure from Molles (1999), page 190.

7. Life expectancy remains relatively constant over the whole period a cohort is in existence.


E. High mortality among young. 1. Some organisms produce large numbers of young with very high rates of

mortality. 2. The eggs produced by

marine fish such as the king mackerel, Scomberomorous cavalla, may number in the millions. Out of 1 millions eggs laid by a mackerel, more than 999,990 (99.99%) die during the first 70 days of life either as eggs, larvae, or juveniles.

3. Survival rates are similar in populations of the common prawn, Leander squilla, off the coast of Sweden. For each 1 millions eggs laid by Leander, only about 2,000 individuals (0.0002%) survive the first year of life.

4. Similar patterns of survival are shown by other marine invertebrates and fish and by plants (Figure 5) that produce immense numbers of seeds.

Figure 5. High rates of mortality among the young of Cleome droserifolia. Figure from Molles (1999), page 191.

F. Types of survivorship curves. 1. It is conventional and, to a degree, useful to recognize 3 general categories of

survivorship curves, as outlined by E.S. Deevey (1947). They are called Type I, II, and III, or better, convex, diagonal, and concave, respectively.


a. A type I, or convex, curve indicates high survivorship up to a particular age when most of the population dies (Figure 6). This could happen if environmental factors were unimportant and most of the organisms lived out their full physiological longevity.

b. A type II, or diagonal, curve indicates a constant probability of dying; that is, the same percentage of the population is lost each time period (Figure 6).

c. A type III, or concave, curve indicates high juvenile mortality and then low mortality as the survivors slowly succumb to environmental factors and, eventually, senility. This high juvenile mortality would result from such factors as inexperience in foraging and avoiding predators and lack of immunity to disease (Figure 6).

Figure 6. Survivorship curves. Figure from Molles (1999), page 191.

2. Probably no organism for which adequate birth-to-death information is available

actually fits any 1 of the 3 curves exactly. The most frequent pattern found in the real world seems to be one in which there is a juvenile segment of high mortality, followed by an adult segment of low, nearly constant, mortality, and a final senile segment in which mortality again rises.

3. III. Age distribution.

A. Introduction. 1. Ecologists can learn a great deal about a wildlife population just by studying its age

distribution. 2. Age distributions indicate periods of successful reproduction, periods of high and

low survival, and whether the older individuals in a population are replacing themselves or if the population is declining.


B. Stable and declining tree populations.

1. In 1923, R.B. Miller published data on the age distribution of a population of white oak, Quercus alba, in a mature oak-hickory forest in Illinois. a. He found that most of the white oaks in his study area were concentrated in

the youngest age class of 1 to 50 years, with progressively fewer individuals in the older age classes (Figure 7). The oldest white oaks were >300 years old.

b. What might we infer from this age distribution?

Figure 7. Age distribution of a white oak population in Illinois. Figure from Molles (1999), page 192.

2. The age distribution of Rio Grande cottonwoods, Populus deltoids, in central New

Mexico, differs markedly from the age distribution of the white oak forest in Illinois. a. In contrast to the white oak population in Illinois, the Rio Grande cottonwood

population is dominated by older individuals (Figure 8). b. What might we infer from this age distribution?


Figure 8. Age distribution of a Rio Grande cottonwood population in New Mexico. Figure from Molles (1999), page 193.

C. A dynamic population in a variable climate.

1. Rosemary Grant and Peter Grant (1989) have spent decades studying Galápagos finch populations.

2. The Galápagos Islands have a highly variable climate, which is reflected in the highly dynamic populations of the organisms living on the islands, including populations of the large cactus finch.

3. The age distributions of the large cactus finch during 1983 and 1987 show that the population can be very dynamic (Figure 9).


Figure 9. Age distribution of a population of large cactus finches on the island of Genovesa in the Galápagos Islands during 1983 (Top) and 1987 (Bottom). Figure from Molles (1999), page 193.


IV. Rates of population change. A. Introduction.

1. In addition to survival rates, ecologists are interested in another major influence on local population density—birthrates.

2. In mammals and other live-bearing organisms, the term birthrate means the number of young born per female in a period of time.

3. In birds, fish, and reptiles, births are usually counted as the number of eggs laid in a period of time.

4. In plants, the number of births may be the number of seeds produced annually. 5. Tracking birthrates in a population is similar to tracking survival rates.

a. The ecologist needs to know the mean number of births per female for each age class and the number of females in each age class.

b. The numbers of offspring produced by females of different ages are then tabulated.

c. The tabulation of birthrates for females of different ages in a population is called a fecundity schedule.

d. If we combine the information in a fecundity schedule with that in a life table, we can estimate several important characteristics of populations, such as whether a population is growing or declining.

B. Estimating reproductive rates for an annual plant. 1. Table 1 combines survivorship with seed production by the annual plant Phlox

drummondii.


Table 1. Estimating net reproductive rate, Ro, for Phlox drummondii. Table from Molles (1999), page 195.

2. Note column headings. The first column, x, does not contain time periods of

equal length. 3. We have already used the data in column 3, lx, to construct the survivorship curve

for this species (Figure 3—Top). Let’s now combine those survivorship data with the seed production for P. drummondii, mx, to calculate the net reproductive rate, Ro.

4. In general, Ro is the mean number of offspring produced by an individual in a population (or the mean number of seeds left by an individual).

5. Calculate Ro by adding the values in the final column. 6. To calculate the total number of seeds produced by this population of P.

drummondii, during the year of study, multiply 2.4177 by 996, which was the initial number of plants in this population. The result, 2,408, is the number of seeds that this population will begin with the next year.

7. Since P. drummondii has nonoverlapping generations (i.e., it is an annual plant), we can estimate the rate at which its population is growing with a quantity known


as the geometric rate of increases, λ, which is the ratio of the population size at 2 points in time:

λt

1+t

NN

= .

8. In this equation, Nt+1 is the size of the population at some future time, and Nt is the size of the population at some earlier time (Figure 10).

Figure 10. The geometric rate of increase. Figure from Molles (1999), page 195.

9. The initial number of plants in the population was 996 (this is Nt). The number of

individuals (seeds) in the population at the end of a year of study was 2,408 (this is Nt+1). Therefore,

λ 2.4177.996

2,408= =

10. This is the same value we got for Ro, but that is simply coincidental. 11. What does λ=2.4177 mean? 12. How long do you think this plant can continue to reproduce at that rate?

C. Estimating rates when generations overlap. 1. A life table for the common mud turtle, K.

subrubrum, is located in Table 2. Let’s calculate the net reproductive rate, Ro.

2. The researchers found that about half (0.507) of the female turtles nest each year. Of those females that do nest, most nest once during the year. Some nest twice and a few nest 3 times.


3. The mean number of nests per year for the nesting turtles is 1.2, which means that 0.2, or 20%, of the turtles produce a second nest each year.

4. The mean clutch size, which is the number of eggs produced by a nesting female, is 3.17.

5. Therefore, the mean number of eggs produced by nesting females each year is 3.17 eggs per nest x 1.2 nests per year = 3.8 eggs per year. However, remember that only about half of the females in the population nest each year. Therefore, the number of eggs per female per year is 0.507 x 3.8 = 1.927 eggs per female per year.

6. On average, half of these eggs develop into males and half into females. Thus, since the sex ratio in this turtle population is 1:1, we multiply 1.927 by 0.50 to calculate the number of female eggs per adult female in the population, which equals 0.96 female eggs. This value is listed in column 3 of Table 2.

7. ∑ xx ml provides an estimate of Ro. We can interpret this number as the mean number of daughters produced by each female in this population over the course of her lifetime.

8. What value of Ro would produce a stable turtle population? In a stable population, Ro would be 1.0, which means that a female would replace just herself during her lifetime. In a growing population, such as the population of phlox, Ro would be >1.

D. Ecologists are also interested in other characteristics of populations, such as generation time, T, which is the mean length of time from egg to egg or seed to seed. 1. We can use the information in Table 2 to calculate mean generation time for the

common mud turtle:

.∑

o

xx

Rmxl

=T

2. In this equation, x is age in years. To calculate T, sum the last column and divide the result by Ro.

3. The result shows that common mud turtles have a mean generation time of 10.6 years. How doe this compare to other animals? See Figure 11.


Table 2. A life table for the common mud turtle, Kinosternum subrubrum. Table from Molles (1999), page 196.


Figure 11. Relationship between body size and generation time for a variety of organisms. From Molles (1999), page 197.

E. Knowing Ro and T allows us to estimate r, the per capita rate of increase for a population:

.TRln

=r o

1. ln is the base of the natural logarithms. 2. We can interpret r as birth rate minus death rate: r = b - d. 3. Using this method, the estimated per capita rate of increase for the common mud

turtle population in Table 2 is:

=10.60.601ln

=r -0.05

4. The negative value of r in this case indicates that birthrates are lower than death rates and the population is declining. A value of r > 0 would indicate a growing population; r = 0 would indicate a stable population.

F. Population dynamics are clearly influenced by patterns of survival and reproduction. Birth and deaths, however, are not the only processes that make populations dynamic. As we will see below, population dynamics are also influenced by the movements of organisms.


V. Dispersal. A. Dispersal is an important aspect of population dynamics.

1. The seeds of plants are dispersed with wind or water or may be transported by a variety of mammals, insects, or birds.

2. Young mammals and birds often disperse from the area where they were born and may join other local populations.

3. Because of movements such as these, wildlife managers attempting to understand local population density must consider dispersal into (immigration) and out of (emigration) the local population. Remember: Nt+1 = Nt + Bt – Dt + It – Et.

4. It is interesting to note that, in spite of its importance, dispersal is one of the most least-studied aspects of population dynamics.

B. Dispersal of expanding populations. 1. Africanized honeybees (AHB).

a. AHB produce swarms that disperse to form new colonies at a much higher rate than do European honeybees.

b. Their rate of dispersal has ranged from 300-500 km/yr. c. Within 30 years, AHB occupied most of South America, all of Central

America, and most of Mexico (Figure 12). 1) They reached south Texas in 1990 and southern Arizona and New Mexico

in 1994. 2) They stopped spreading southward through South America by about 1983,

stopping at about 34o S latitude.


Figure 12. The range expansion of Africanized honeybees from South America through Central America and North America. Figure from Molles (1999), page 198.


Figure 13. Spread of Africanized honey bees by year and county in the southern U.S. as of January 2007. Africanized honey bees were first found in Texas in 1990. They were first found in Miller and Lafayette counties, Arkansas in 2005, and in Columbia, Union, Bradley, and Clark counties, Arkansas, in 2006.

2. Collared doves. a. Collared doves (Streptopelia decaocto) began to spread from Turkey into

Europe after 1900.


Figure 14. The range expansion of collared doves across Europe. Figure from Molles (1999), page 199.

b. Adult collared doves are highly sedentary, and dispersal is limited to young

doves. Most dispersing young stay within a few km of their parent’s nest, but some disperse hundreds of km (Figure 14).


Figure 15. Dispersal distances by collared dove fledglings. Figure from Molles (1999), page 199.

C. Range changes in response to climate change. 1. In response to climate change following retreat of glaciers northward in North

America, organisms of all sorts began to move northward from their ice age refuges.

2. Temperature forest trees have left a particularly good record of northern dispersal (see Figure 15).

Figure 16. The range expansion of maple (left) and hemlock (right) in North America following glacial retreat. From Molles (1999), page 200.


3. Maple colonized the northern part of its present range from the lower Mississippi Valley region, while hemlock colonized its present range from a refuge along the Atlantic coast.

4. The pollen preserved in lake sediments indicates that forest trees in eastern North America spread northward following the retreat of the glaciers at the rate of 100 to 400 m per year. This rate of dispersal is similar to that of some large mammals such as North American elk.

D. These examples illustrate dispersal by populations in the process of expanding their ranges. Significant dispersal also takes place within established populations whose ranges are not changing. Movements within established ranges can be an important aspect of local population dynamics. We will consider 2 examples. 1. Dispersal in response to changing food supply.

a. Predators show several kinds of responses to variation in prey density. b. In addition to functional responses, predators respond numerically.

1) Numerical responses are changes in the density of predator populations in response to increased prey density.

2) C.S. Holling (1959) studied populations of mice and shrews preying on insect cocoons and attributed the numerical responses he observed to increased reproductive rates (Figure 17). Holling commented that “because the reproductive rate of small mammals is so high, there was an almost immediate increase in density with increase in food.”

Figure 17. Populations of shrew (Sorex) and deer mouse (Peromyscus) increase in size, up to a point, as food supply increases. Shrews of the genus Blarina, however, show no response to increased food supply (sawfly cocoons, photo at right). Thus, their numbers must be limited by some other resource. Figure from Feldhamer et al. 2004.


3) Other predators, with much lower reproductive rates than mice and shrews, also show strong numerical responses. These responses to prey density are almost entirely due to dispersal.

c. Let’s look at the contribution of dispersal to local populations of kestrels and owls.

1) In some years in northern landscapes, vole (Microtus spp.) populations are extremely high. Go to the same place during other years and it may be difficult to find any voles.

2) In northern latitudes, vole populations usually reach high densities every 3 to 4 years. Between these peak times, population densities crash.

3) Population cycles in different areas are not synchronized (i.e., while vole population density is very low in one area, it is high elsewhere).

4) Korpimäki and Norrdahl (1991) conducted a 10-year study of voles and their predators in western Finland. a) The study began in 1977 during a peak in vole densities (1,800/km2)

and continued through 2 more peaks: 1982 (960/km2) and 1985-1986 (1,980 and 1,710/km2, respectively).

b) Between these population peaks vole densities fell to as low as 70/km2 in 1980 and 40/km2 in 1984. Interestingly, during this same period,

European kestrel (Falco tinnunculus)—left; American kestrel—right.

Short-eared owl (Asio flammeus)

Long-eared owl (Asio otus)

Microtus pennsylvanicus


the densities of European kestrels, short-eared owls, and long-eared owls closely tracked vole densities (Figure 18).

Figure 18. Numerical response of kestrels and owls to changes in vole densities. From Molles (1999), page 201.

c) How do kestrels and owl populations track these variations in vole densities? What mechanisms produce the numerical responses by kestrels and owls to changing vole densities? Look closely at Figure 18 for clues.

d) The peaks in raptor densities in 1977, 1982, and 1986 match the peaks in vole densities almost perfectly. If reproduction was the source of numerical response by kestrels and owls, there would probably be more of a delay, or time lag, in numbers, such as what has been observed between snowshoe hares and lynx (Figure 19).

Figure 19. Cycles in the numbers of a predator and its prey for over 90 years. From Bush (1997).


e) Korpimäki and Norrdahl (1991) proposed that kestrels and owls must move from place to place in response to local increases in vole populations. But do they have any supporting evidence for such high rates of movement by kestrels and owls? • Korpimäki (1988) marked and recaptured 217 kestrels, a large

proportion of their study population. • Because European kestrels have an annual survival rate of 48%-66%,

Korpimäki predicted a high rate of recapture of the marked birds. He recaptured only 3% of the female and 13% of the male birds, however.

• These low recapture rates indicated that kestrels were moving out of the study area, moving from place to place, probably in response to changing vole densities.

2. Dispersal in rivers and streams. a. Dispersal has a major influence on local populations in streams and rivers. b. How are stream populations affected by current? Why doesn’t the flowing

water of streams eventually wash all stream organisms, including fish, insects, snails, bacteria, algae, and fungi, out to sea? 1) All stream organisms have a variety of characteristics that help them

maintain their position in streams. 2) Body shapes and behaviors are 2 important groups of characteristics.

c. Stream organisms, however, do get washed downstream as drift. d. Why doesn’t drift eventually eliminate organisms from the upstream sections

of streams? 1) K. Müller (1954, 1974) hypothesized that drift would eventually wash

entire populations out of streams unless organisms actively moved upstream to compensate for drift.

2) He proposed that stream populations are maintained through a dynamic interaction between downstream and upstream dispersal that he called the colonization cycle (Figure 20).

Figure 20. The colonization cycle as proposed by Karl Müller.


3) The colonization cycle is a dynamic view of stream populations in which upstream and downstream dispersal, as well as reproduction, have major influences on stream populations.

4) Many studies provide support for Müller’s idea, especially among aquatic insects. However, these dynamics are difficult to observe because they occur so quickly, within the substratum, or at night, or they involve microorganisms. A snail (Neritina latissima) that lives in a tropical stream in Costa Rica, however, provides a well-documented example of the colonization cycle (Figure 21).

5) After the larvae metamorph into small snails, they reenter the Rio Claro River and begin dispersing upstream in huge dispersal aggregations of up to 500,000 individuals (Figure 21a).

6) The population of Neritina consists of a mixture of dispersing and stationary subpopulations, with exchange between them.

7) Individual snails disperse upstream for some distance and leave the dispersing wave and enter a local subpopulation. At the same time, individuals from the local subpopulation enter the dispersing wave and move upstream.

Figure 21. The colonization cycle in action. (a) A wave of dispersing snails in the Rio Claro River, Costa Rica. (b) A close-up of the dispersing snails.

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