Supplemental Lecture (97/02/11 update) by Stephen T. Abedon (abedon.1@osu.edu)

  1. Chapter title: Populations
    1. A list of vocabulary words is found toward the end of this document
    2. Malthus and exponential population growth:
      1. As Malthus noted, an unbounded population simply tends to increase in size geometrically.
      2. A geometric (or exponential, logarithmic, etc.) progression is one in which the value at a subsequent time is a direct, multiplicative function of the value at a previous time. Thus, the progression 2, 4, 6, 8, 10, 12, 14, . . . is an arithmetic progression (which is achieved by adding the number 2 to the previous value), while the progression 2, 4, 8, 16, 32, 64, 128, . . . is a geometric progression (i.e., each number is equal to the previous number multiplied by two).
      3. Unchecked population growth consequently has very simple mathematics. Particularly, such a population doubles in size at an unvarying rate (thus, if a dynamic population growing without limits had 10 members at time 0, a population of 20 members after 10 years and 40 members after another 10 years, then we would predict that it would have 80 members after another 10 years of growth).
      4. Malthus, however, noted that unchecked population growth cannot be maintained for long because limits on growth inevitably arise.
      5. Because of the existence of various environmentally imposed limits, the structure of populations tends away from simplicity (e.g., most populations are neither randomly distributed nor geometrically increasing in size). In this lecture we will consider various population concepts which embody this complexity.\
  2. Population
    1. A population is an interbreeding group of individuals.
    2. Defining characteristics:
      1. Populations have various defining characteristics including:
        1. species of organism
        2. time (historical)*
        3. place where they live*
        4. their number (size)
        5. their density
        6. their distribution in space (dispersion)
        7. age structure/demographics**
        8. niche***
      2. *Populations are both spatial and temporal entities.
      3. **The ratio of older to younger individuals.
      4. ***The role their members play within the ecosystem they inhabit.
  3. Extinction
    1. Population size = 0:
      1. A population whose size has been reduced to zero is said to have gone extinct.
      2. A population size of zero is unique among population sizes in that subsequent recovery (increase in size) is not possible.
    2. Limits:
      1. Limits and extinction often go hand in hand.
      2. Thus, limits on population size, range, availability of nutrients, or abiotic requirements (e.g., as a consequence of over-specialization) can all result in an increased likelihood that a population will become extinct.
  4. Population size
    1. Population size has a direct effect on the magnitude with which genetic drift can affect populations. Particularly, smaller populations are more affected by random occurrences than are larger populations.
    2. Higher likelihood extinction:
      1. In the real world this means that random effects can far more easily lead to the extinction of a small population than large population.
      2. Mathematically, picture population size varying over time. If both large and small populations tend to vary in size over the same absolute magnitude over time, then such variations much more likely can lead to a population size of zero (extinction) in the small population than in the large population.
    3. Starting with a population consisting of 100 individuals ("large" population) and a second population consisting of 10 individuals ("small" population), a decline of 10 or more will bring the large population down to 90 or so individuals, but will bring the small population down to 0.
    4. Individual alleles are also likely to be lost from small populations with much higher likelihood (and for much the same reason) than from large populations.
    5. Another was of saying this is that large populations are able to sustain genetic variability (genetic polymorphisms, lot's of alleles) much more readily than small populations.
    6. Loss of genetic variability leads to a lack of evolutionary flexibility which in turn leads to a higher likelihood of extinction.
    7. Depending upon who you believe, a population may be considered small in this regard, and therefore highly likely to go extinct, if it effectively contains less than somewhere between 500 and a few thousand individuals.
    8. Man the terminator?
      1. The dominant effect of genus Homo on her environment is to set up conditions which lead to drastically reduced population sizes in a vast numbers of species.
      2. Though in the very short term the effects of such actions may appear to have only minor consequences, in the medium term they are likely to lead to the extinctions of large numbers of populations.
  5. Population distribution [dispersion]
    1. Typically not random distribution:
      1. Most populations are not randomly distributed through space (one-, two-, or three-dimensional depending on habitat).
      2. Instead, properties intrinsic either to the individuals making up the population or the environment(s) in which they exist tend to determine how individuals are distributed over the landscape.
      3. Often the size, trophic level, and inherent clumpiness of the environment that a population inhabits impacts distribution. For example:
        1. The smaller the organism, the closer individuals may be without impacting the ability of neighbor's to survive.
        2. The higher the trophic level, the more photosynthesis is required to sustain nutrient needs thus leading to widely spaced individuals or groups of individuals.
    2. Many populations tend toward high levels of cohesiveness (herds, etc.), deriving benefit from the proximity of conspecifics, and consequently such populations will tend toward a clumpy distribution.
    3. In addition, growing populations of limited mobility may appear to display a clumpy distribution.
    4. Sexual reproduction limits dispersion:
      1. Among sexually reproducing individuals, limits on dispersion include the need to find a second individual of the same species (and opposite gender) with which to mate.
      2. Asexually reproducing organisms don't have this problem and, indeed, one of the advantages of not requiring sex in order to reproduce is a greater potential for dispersion (such species require only a single individual to found a new population).
  6. Intrinsic rate of population growth [biotic potential]
    1. Lack of limits results in growth:
      1. All viable populations retain a capacity to increase in numbers.
      2. With constraints removed, the size of most populations would be expected to increase.
    2. Rate of increase population characteristic:
      1. The rate at which a population could increase under such circumstances (intrinsic rate of population growth or biotic potential) varies greatly among species.
      2. Some species have a large intrinsic rate of population growth, while other have a much lower intrinsic rate of population growth.
    3. Regardless of intrinsic rate of population growth, most populations exhibit relatively stable (or at least predictable) population sizes, at least in the short term.
    4. Births = deaths:
      1. A stable population size usually means that the rate of death of its members is equal to the rate of birth.
      2. For example, organisms with a tendency to produce large numbers of offspring also have a tendency to lose an equally large number of offspring whereas those which produce few offspring likely engage in a reproductive strategy which results in a much higher likelihood of survival for any given offspring.
    5. The size of a population growing at its biotic potential at a given time is dependent on its population size at a previous time by a multiplicative function. This is because unconstrained population growth occurs exponentially.
    6. In practice, biotic potential is realized only by small populations newly inhabiting an environment containing abundant resources and few predators.
    7. An imported plant or animal which exploits a resource either not exploited or not efficiently exploited by native fauna or flora, and which itself is not efficiently exploited by higher trophic level, local consumers. Such exotics can rapidly (exponentially) increase in numbers, sometimes resulting in profound negative alteration of their new ecosystems.
  7. Carrying capacity
    1. The size of a population which can exist indefinitely in a certain environment/place.
    2. Carrying capacities tend to be stable equilibria in that the presence of more individuals results in increased death due to some environmental limitation, whereas too few individuals leads to population growth (or migration into the environment) since that situation is one in which the net increase in a not entirely restrictive environment is possible.
    3. The maintenance of population size at carrying capacity is essentially equivalent to the maintenance of a salt solution at saturation. Dilution of the solution leads to dissociation of some fraction of the solid present thus increasing salt concentration back up to the maximum. Evaporation, in contrast, leads to an increase in salt concentration and compensatory precipitation reduces salt concentration back down to the same maximum.
  8. Maximal population growth
    1. Exponential growth vs. limits:
      1. The rate of population growth is influenced, generally, by two opposing factors, the intrinsic tendency of a given population to increase in numbers exponentially, and the imposition of cap on their total numbers imposed by some aspect of the environment (carrying capacity).
      2. Beginning with a population of minimal density, then, growth occurs exponentially. As limits begin to impose on the rate of growth, growth may continue though no longer at the same rate. That is, "instantaneous" exponential growth continues, but the overall rate of growth declines as absolute population size approaches that of the carrying capacity.
      3. A way of picturing this effect is to imagine that early during exponential growth, for example, each individual parents, on average, four individuals who all survive until adulthood. However, as carrying capacity is approached this rate of growth declines such that the average number of individuals parented declines to 3 then 2 then 1 (at which point each individual, on average, is essentially replacing themselves over the course of their reproductive life---the population size at which this occurs is another way of defining carrying capacity).
    2. Sigmoidal growth curve:
      1. A graph depicting the number of individuals as a function of time, during growth starting from few individuals and eventually reaching carrying capacity, takes on a sigmoidal shape.
      2. That is, one in which the number of individuals increases at a greater and greater rate (exponential growth---it would be a straight line if graphed on log-linear graph paper) until the rate of increase no longer increases with time (point of inflection) and then the rate of increase declines until equilibrium at carrying capacity is reached (a zero rate of increase in population size).
      3. In other words, first the curve increases in steepness until it reaches a point of maximal steepness, then it slowly bends over thus displaying less and less steepness until it is effectively horizontal. See figure 1540.1.
    3. The maximal rate of population growth in a given environment is the steepest point of the sigmoidal growth curve, the point of inflection.
    4. A very important equation:
      1. A differential equation approximating the sigmoidal growth curve of an ideal population is: dN/dt = rN(K - N) / K where r is the intrinsic rate of population growth, K is the carrying capacity of the environment, N is the number of individuals present in a population, and t is time.
      2. For those of you haven't had calculus, dN/dt stands for instantaneous change in N as a function of t, a slope.
      3. Thus, using this equation one can determine the instantaneous rate of increase of a reasonably well behaved population (change in N as a function of time) so long as one has knowledge of the population's biotic potential, actual size, and the carrying capacity of the environment in which the population lives.
  9. r strategist
    1. Adapted to exponential increases:
      1. An organism which is particularly well adapted to an exponential increase in population size is know as an r strategist (the r coming from the differential equation described above).
      2. r strategists are characterized by great rapidity in their developmental programs combined with an ability to produce large numbers of offspring.
      3. No organism is a pure r strategist. Most show at least some capacity to survive at equilibrium, i.e., in carrying capacity situations.
    2. Pioneer species:
      1. r strategists tend to be particularly good at finding disturbed environments and then rapidly producing large numbers of progeny in such environments.
      2. Often those offspring are ill-equipped for survival except under optimal conditions because of the small amount of parental resource put into their survival. However, the large numbers produced tend to both make up for low survivorship as well as allow for great dispersal.
      3. Wide dispersal allows at least some fraction of progeny to find and therefore exploit newly disturbed habitats.
    3. A plant which is an r strategists more likely than not we would call a weed.
  10. K strategist
    1. Adapted to limitation:
      1. In contrast to r strategists, many organisms show extreme potential to survive and prosper at or near carrying capacity, though often at the expense of their ability to display rapid population increases under most circumstance (i.e., their intrinsic rate of population growth is small). Such organisms are called K strategists.
      2. The variable K refers to carrying capacity (i.e., they display a bias in their adaptations toward maximizing carrying capacity).
    2. K strategists tend to be very good at surviving in mature (climaxed) ecosystems.
    3. K strategists also tend to put a great deal of resource into raising only a few young.
    4. A gorilla is a K strategist.
  11. Generation time
    1. The time between birth and propagation.
    2. Generation time is one aspect of the rate of growth of populations. That is, all else being equal, the shorter the generation time, the greater the intrinsic growth rate of a population.
    3. Other aspects that affect intrinsic growth rate include the number of offspring produced per reproductive episode and the number of reproductive episodes prior to death.
  12. Mortality
    1. Death rate:
      1. In the real world the timing of deaths also plays an important role in population growth.
      2. Mortality is the rate of death within a population.
  13. Survivorship
    1. The fraction of a population which reaches a certain age is described as the survivorship associated with that age.
    2. Characteristic survivorships:
      1. Different organisms, at different times (and different environments) show different survivorships at different ages. Often gross variations in survivorship between species reflect variations in reproductive strategies.
      2. For example, the longer individuals survive while living off of parental resources, the larger a drain they are on parental fitness if those individuals should die prior to reproducing (e.g., should there be an overabundance of such individuals). Organisms for which a high fraction tend to die prior to reproductive maturity (low pre-replicative survivorship) thus tend to invest fewer resources in those progeny (though this can be circular since the lower amount of resources invested also likely contributes to higher mortality).
      3. Three types of survivorship curves, types I, II, and III, are shown in figure 1540.2.
    3. Big evolutionary payoff potentially comes only upon survival to reproductive maturity (pre-replicative survivorship).
    4. Post-replicative survivorship:
      1. Following the achievement of reproductive maturity, additional survival is most obviously beneficial only if an organism is capable of further rounds of reproduction (though in some situations, e.g., humans, post-reproductive individuals may still contribute positively to the fitness of their offspring).
      2. Once reproduction is no longer likely, either in a physiological sense or a statistical one, survivorship can decline with little impact on fitness.
    5. Exponential decline:
      1. Some organisms show little variation over time (or past a certain time) in either reproductive potential or survivorship.
      2. In these organisms survival is statistical. That is, total survivorship declines exponentially with time (e.g., some constant fraction of a population dies per unit time, regardless of age).
  14. Type III survivorship
    1. Type III survivorship combines low pre-replicative survival with a reduced rate of exponential decline following the achievement of reproductive maturity (i.e., such organisms display bimodal survivorship curves).
    2. Organisms displaying type III survivorship typically produce large numbers of offspring few of which survive.
    3. Long lived fecundity:
      1. Once established in a stable environment, however, individuals from populations displaying type III survivorship show little decline in reproductive potential over time.
      2. Longer term survival thus leads directly to increased progeny production creating benefits for the long lived and therefore selecting against premature death.
    4. Premature death be accident and predation nevertheless occurs thus accounting for the gradual decline in survivorship.
    5. Sea turtles, with their extremely high post-hatching mortality, but long livedness given survival to adulthood, show type III survivorship.
    6. example: oak trees
  15. Type II survivorship
    1. Organisms displaying type II survivorship show simple exponential decline from day one: There is no enhanced mortality at any age, nor any significant decline in reproductive potential with age.
  16. Type I survivorship
    1. Type I survivorship starts out with simple exponential decline but shows bimodal kinetics whereby post-reproductive individuals display much more rapid exponential decline (a consequence of physiological limits on life span).
    2. Such limits actually may represent an optimization of type II survivorship whereby replicative potential early in life (when survivorship is relatively high) is optimized at the expense of long-term physiological robustness (when survivorship declines anyway due to random effects).
    3. K strategists which display physiological limits on reproductive capacity (e.g., humans) tend toward Type I survivorship.
  17. Demographics [age structure]
    1. Study of age structure:
      1. The study of the structure of populations.
      2. Note that age structure, the absolute number of individuals of each age group alive within a population, is affected by births, deaths, emigration, and immigration.
  18. Stable population
    1. A stable population is one which neither increases in size nor changes in age structure.
    2. The absolute number of individuals of every representative age does not change through time.
  19. Population pyramid
    1. Graphic representation:
      1. A population pyramid is a graphic representation of the age structure of a population at a given time.
      2. A population pyramid is a series of stacked bar graphs with each bar representing a given age cohort and the height of the bars representing the fraction of the population made up of members of that cohort.
    2. See figure 1540.3.
  20. Habitat destruction [habitat isolation, habitat fragmentation]
    1. Population size reduction:
      1. Destruction of habitats (e.g., as a consequence of development) leads directly to a reduction in the number of individuals present in a given population.
      2. For example, given a set number of individuals capable of surviving on a given area of habitat, less habitat translates directly into fewer individuals and therefore smaller population sizes).
    2. High probability of extinction:
      1. Following habitate destruction, resulting populations are left in small, isolated fragments.
      2. The probability of extinction among these isolated populations is high due to their inherently small size.
    3. The likelihood of repopulation from other fragments may be reduced due to the habitat isolation (and therefore population isolation), a second consequence of habitat destruction (habitat fragmentation).
    4. Habitat destruction also has a tendency to affect other, especially (literally) downstream ecosystems.
    5. Excessive errosion from clear cut forests clogs the steams in which salmon hatch and develop thus helping decimate salmon populations.
    6. Habitat destruction tends to turn mature ecosystems into disturbed ecosystems.
    7. Since some organisms are well adapted to growth in disturbed ecosystems (e.g., r strategists---weeds), habitat destruction tends to favor the growth of some organisms while disfavoring the growth of many others (particularly, K strategists).
    8. Thus, in a very real sense, the net effect of the impact of man on earth is to increase the relative representation of the species man considers undesirable (e.g., those which thrive in impoverished ecosystems including various rodents, insects, and weeds) while simultaneously destroying the species considered desirable (e.g., those which successfully compete in non-impoverished ecosystems including large mammals, trees, woodland flowers, etc.).
  21. Cohort
    1. Group of individuals associated by some common characteristic.
  22. Jobs vs. owls
    1. Those of you who recall the owls versus jobs debate in the Pacific North West during the early 90s may or may not be aware that this debate was really about the saving of the last of the climaxed, large tree ecosystems in the Pacific North West versus the conversion of those ecosystems into vast tracts of weeds, erosion, and genetic impoverishment in order to give a few people a few more years of jobs implementing this destruction.
    2. Spotted owls entered into the debate because (a) they are K strategists specifically adapted to survival in the these climax forests, and (b) through the protection of specific, usually species of large animals (i.e., via the endangered species act), is one of the few ways whole ecosystems may be legally protected in this country short of outright private ownership by benign individuals.
    3. The probable extinction of spotted owls in the course of the logging of the majority of the remaining of the Pacific Northwest climax forest ecosystem was thus being used as a tool to effect the saving of the Pacific Northwest climax forest ecosystem.
    4. It was very obvious at the time to the environmentally aware that all those who framed this debate simply in terms of jobs versus owls (including a certain sitting president) were displaying an unforgivable biological naivet‚ as well as an unfortunate man over nature arrogance.
    5. Instead, the relevant question was not owls vs. jobs? Even stated more even handedly, is the short-term employment of people paid to destroy ecossystems more important than the survival of the spotted owl, the question misses the point. A far more truthly framing of the debate would in terms of the question, is the short-term employment of people paid to destroy ecosystems more important than the survival of the ecosystem they are paid to destroy?
    6. It would have been interesting to how such a rephrasing might have affected the owls vs. jobs debate. Particularly, in other countries when there is conflict between employment and gross environmental degradation (e.g., jobs vs. South and Central American rain forests) Americans appear to come close to achieving consensus in their condemnation of the choosing of employment over the environment. Is it therefore any wonder why the survival of the American North West big tree ecosystem debate was not framed in terms of cutting down the rain forests but instead in terms of saving an animal few have ever seen, but at the expense of American jobs?
  23. Vocabulary
    1. Age structure
    2. Biotic potential
    3. Carrying capacity
    4. Cohort
    5. Demographics
    6. Dispersion
    7. Extinction
    8. Generation time
    9. Habitat destruction
    10. Habitat fragmentation
    11. Habitat isolation
    12. Intrinsic rate of population growth
    13. Jobs vs. owls
    14. K strategist
    15. Maximal population growth
    16. Mortality
    17. Population
    18. Population distribution
    19. Population pyramid
    20. Population size
    21. r strategist
    22. Stable population
    23. Survivorship
    24. Type I survivorship
    25. Type II survivorship
    26. Type III survivorship
  24. Practice questions
    1. Convince me you know what exponential population growth is. [PEEK]
    2. Name three things associated with small population sizes (they need not all be completely independent but "small population size" itself may not be used as an answer). [PEEK]
    3. Describe an organism in terms of body size and trophic level which you might expect to exist at low numerical density in a given ecosystem. [PEEK]

    4. The above figure shows the growth of a population of organisms which initially finds itself in an environment lacking limits. Answer the following questions: What is A? How is the population growing at B? Why is the rate of population growth declining above the point of inflection, including in the area designated as C? [PEEK]
    5. Which population would you expect to grow the fastest? (growth is in terms of numbers of organisms; choose best answer) [PEEK]
      1. r strategist at population size near carrying capacity
      2. r strategist at low population size relative to carrying capacity
      3. K strategist at population size near carrying capacity
      4. K strategist at low population size relative to carrying capacity
      5. all of the above
      6. none of the above
    6. Humans display their reproductive potential relatively early (mid to early teens through mid to late thirties) within a life span which appears to be biologically (rather than environmentally) limited (at about 85+ years). Give me an evolutionary argument for why these two human survivorship characteristics might be as they are. [PEEK]
    7. Name the typical anthropogenic effect on the species composition of ecosystems. [PEEK]
    8. A K strategist finds itself in an ideal growth environment currently lacking in limits. Before carrying capacity is encountered in any way, shape or form, what limits the rate with which populations of this organism grow? [PEEK]
    9. Name three ecologically defining characteristics of a population of organisms (i.e., something other than the definition of a population of organisms, i.e., an interbreeding group of individuals). [PEEK]
    10. Name two things that affect biotic potential besides generation time. [PEEK]
    11. A plant which lives out its entire life span (germination through production of seed) in a single year is called an annual. Many weedy annuals produce abundant offspring, the vast majority of which fail to find suitable habitats, i.e., ones conducive to germination and growth. However, once established such plants typically survive the year with mortality due only to chance, e.g., by predation or accident, and independent of the age of the plant. Ignoring the complication that such plants inevitably die at the end of the season, what type of survivorship do they display? (circle best answer) [PEEK]
      1. type I.
      2. type II.
      3. type III.
      4. type IV.
      5. type V.
      6. type VI.
    12. Most organisms are neither pure K strategists nor pure r strategists. For example, many trees produce abundant progeny even though the few surviving progeny are long lived. However, even among trees it is possible to distinguish tendencies toward K strategies or toward r strategies. These differences are seen particularly in terms of the kind of environments in which seeds best germinate and in which seedlings grow best. In either positive or negative terms, describe the general environment in which you would expect the seeds of an r selected tree to germinate with high probability, and also in which its seedlings would grow best. (hint: would you expect a shade tolerant seedling to be the offspring of an r strategist tree or a K strategist tree?) [PEEK]
    13. Sketch two population pyramids, one corresponding to a growing human population, and the other corresponding to stable population of humans. Be sure to label axes and to indicate gender. [PEEK]
  25. Practice question answers
    1. future population size dependent on past population size by a multiplicative factor, which is constant per unit time in a unchanging environment. For example, the following progression shows an exponential increase of three-fold per entered digit: 1, 3, 9, 27, 81, 243, . . . Generally, if N is defined as a previous value of N multiplied by a constant (such as r), then N increases as a multiplicative function of both r and N (in the example, r was set equal to 3).
    2. higher potential for extinction of population, genetic impoverishment (i.e., higher potential for extinction of alleles), greater consequences of genetic drift.
    3. large and high (i.e., body size and trophic level, respectively).
    4. A is the carrying capacity; at B the population is displaying exponential growth; at C and other areas above the point of inflection the population is showing decreased growth due to environmentally imposed impositions on growth (i.e., limits).
    5. ii, r strategist at low population size relative to carrying capacity
    6. The human type I survivorship curve (post-reproductive limits on life span) may represent an optimization of type II survivorship given evolution in the face of random and detrimental environmental effects which limit life span to some extent independent of biology (i.e., random death). That is, we maximize our early reproductive potential at the expense of our long term reproductive potential (and robustness, and therefore biologically controlled survival).
    7. Impoverishment (genetic, total number of species, nutrients in ecosystem, etc.)
    8. the biotic potential of the organism (intrinsic rate of growth)
    9. (i) species the population consists of, (ii) time the population exists, (iii) place where the population exists, (iv) the population size, (v) the density in which the population lives, (vi) the populations spatial distribution (dispersion), (vii) the populations age (etc.) demographics, (viii) the role(s) the population members play within their ecosystem.
    10. number of offspring produced per reproductive cycle and number of reproductive cycles prior to death.
    11. iii, type III.
    12. Something other than the environment in which the adult tree grows; e.g., pine trees tend not to sprout within pine forests; e.g., something other than a climaxed forest.
    13. The x axis is some measure of frequency (starting at zero at a center line and increasing positively in both directions), the y axis is some measure of age. Typically population pyramids are bar graphs indicating the frequency of genders at different ages, starting with 0 at the bottom and going upward with age. Each gender is indicated separately, with males pointing in one direction (e.g., left) and females the other. A growing population particularly has an exaggerated, wide base signifying that there are more new humans than there are older ones (particularly the parent's age cohort). A stable population, in contrast, resembles a type I survivorship curve with little difference between age cohort sizes until an older age is reached, where the curve takes on a bimodal shape showing an accelerated rate of decline in survivorship.
  26. References
    1. Benjamin, C.L., Garman, G.R., Funston, J.H. (1997). Human Biology. The McGraw-Hill Co., Inc., New York, pp. 556-586.
    2. Raven, P.H., Johnson, G.B. (1995). Biology (updated version). Third Edition. Wm. C. Brown publishers, Dubuque, Iowa. pp. 450-460.