Lecture 18

Topics

• Examining the nature of r as N increases.

• Testing the assumptions about r in the laboratory with Daphnia.

• The idea of "age-specific" variables

• Net Reproductive Rate

• Fecundity, Survivorship and the lxbx Curve

Study Sources

• Ricklefs: Chapter 16

  If you enjoy arithmetic, this chapter is for you. Ricklefs develops most of the ideas that demographers use to devlelop Life Tables for populations. He starts with some simple examples and then works through some examples from nature.

• Ricklefs: Chapter 16 (especially pp.318 - 323 and Figs. 16-9 and 16-10)

  Also see pp. 314-320 and Figs. 16-1, 16-2, 16-3 and 16-4.

• Study Guide: Biology of Single Populations

The Main Points

• Does the linear decrease of r_a with an increase in N have a clear connection to biological reality?

• What it specifies is that each addtional member of the population causes the biotic potential (b - d) to decrease by an amount that is equal over all densities. This would have to be a pretty "mechanical" process. Somehow the production of newborn would have to be precisely connected to the available energy and that this energy is being reduced in equal increments as individuals are added to the population.

• Several important studies (see pp. 319-320) have indicated that Daphnia (D. pulex in the studies summarized by Ricklefs) is an excellent example of rather precise effects of density upon reproductive potential. Why is Daphnia used in these experiments and why does it seem to respond in such a "mechanical or deterministic" way?
  1. Some species of Daphnia are particularly easy to raise in the laboratory and their short generation time makes it possible to gather data in a short time.

  2. Their carapace is transparent so one can easily count the young about to be released. This count is a direct measure of fecundity.

  3. All individuals in the population during these low density experiments are females and reproduction is parthenogenetic. This means that females give rise to females over many generations.

  4. Since the Daphnia are filter feeders they are removing food from the culture medium in a direct proportion to the density of the algal cells they are filtering. The density of algal cells is determined by the number of animals filtering the water.

  5. After food is eaten and assimilated, the first order of business for the animals is to "pay the metaboloic costs of living and gathering food." Energy in excess of this cost can go to growth and reproduction (in earlier work we called this Production). In a rather direct way then, higher densities of animals result in less food available to produce eggs. In other work (note cited by Ricklefs), Slobodkin had shown that increasing levels of food supply to the cultures would result in higher K-vlaues (at least over a finite range of densities). He had called these animals "food-limited" in direct, density-dependent way.

• The upshot of all this is that we can find organisms that can be modeled pretty well by the logistic equation and its assumptions.

• Organisms that have to find mates for reproduction may have a very different problem turning energy into young. At very low to low densities, mates may be hard to find and reproduction may be very "inefficient" with respect to the amount of food available. Therefore, at low densities, r_a may also be low; as N increases and mates become more plentiful, mating becomes more efficient and r_a rises rapidly. At higher densities, the advantages of mating efficiency are finally overcome by the disadvantages of growing food scarcity and r_a may decrease along the familiar density-dependent curve

• The Net Reproductive Rate is the "replacement" rate of a population. Specifically, it is the number of offspring left by the average female in her lifetime. The symbol used for this rate is R_o.

  In the human population, for instance, a replacement rate of 2.1 offspring per female will eventually yield a stable population size (zero population growth).

  1. R_o is directly related to the Fecundity or age-specific birth rate of a population (b_x). This can be stated as the average number of offspring left by females at a given age.

  2. Since there is a decreasing probability of a female being alive at a given age, we must weight each value of b_x by this probablility. This probability of being alive is called Survivorship and is symbolized by l_x.

  3. Survivorship is another age-specific variable and is derived from a survivorship curve which plots, in its simplest form, the number of individuals of a cohort alive at each age. This curve is called the l_x curve.

  4. To calculate R_o, one sums the products of l_xb_x over all ages. Ricklefs shows a simple example of this calculation in a Table15-4 on the bottom of p. 310, in Chapter 15.
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