Mathematical Psychology and Psychophysiology

By Stephen Grossberg | Go to book overview

TABLE 3
Viability, nurturance, and asymptotic frequency for k = -1
Genotypeuvw Frequency
A2A2 (altruistic) 1/9 3 1/3 1/16
A1A1 (neutral) 1 1 1 9/16
A1A2 (selfish) 16/9 3/4 4/3 6/16

Since ∣k∣ < 2, the selfish genotype should be favored, but, again, it is asymptotically less prevalent than the neutral genotype. For further consideration of "∣k∣ > 1/r," in the context of other models, see [13] and [14].

5. Genes and genotypes. Fitnesses of genes can be defined by averaging over genotypes in which they occur. In the classical case, the fitnesses of A1 and A2 are
w1. = w11pn + w12qn and w2. = w12pn + w22qn.

Although (4.2) and (4.3) do not imply positive selection of genotypes with above average fitness, they do imply positive selection of genes with above average fitness. Thus discussions of evolution in terms of genes rather than genotypes avoid the pitfall which this paper has been concerned.

Many discussions of evolution (e.g., parts of [15]) are, in fact, cast in terms of genes. A limitation of this approach is that the fitness of a gene is not as intuitive as the fitness of a genotype. It is frequency dependent, and, if the heterozygote is most (or least) fit, even the ordering of w1. and w2. is different for large and small pn. Discussions that ignore this frequency dependence implicitly (and perhaps unconsciously) rule out heterozygote superiority, which is the basis for the example considered repeatedly in this paper.


REFERENCES

1. M. F. Norman, A "psychological" proof that certain Markov semigroups preserve differentiability, these PROCEEDINGS.

2. E. O. Wilson, Sociobiology: the new synthesis, Harvard Univ. Press, Cambridge, Mass., 1975.

3. W. J. Ewens, Mathematical population genetics, Springer-Verlag, New York, 1979.

4. S. J. Gould, Ever since Darwin: reflections in natural history, Norton, New York, 1977.

5. J. Maynard Smith, "Evolution and the theory of games", Amer. Sci. 64 ( 1976), 41-45.

6. G. F. Oster and S. M. Rocklin, "Optimization models in evolutionary biology", Some Mathematical Questions in Biology, vol. 10 ( S. A. Levin, ed.), Amer. Math. Soc., Providence, R. I., 1979.

7. P. D. Taylor and L. B. Jonker, "Evolutionarily stable strategies and game dynamics", Math. Biosci. 40 ( 1978), 145-156.

8. J. Hofbauer, P. Schuster and K. Sigmund, "A note on evolutionary stable strategies and game dynamics", J. Theoret. Biol. 81 ( 1979), 609-612.

9. W. F. Bodmer, "Differential fertility in population genetics models", Genetics 51 ( 1965), 411-424.

10. T. Nagylaki, Selection in one- and two-locus systems, Springer-Verlag, New York, 1977.

-195-

Notes for this page

Add a new note
If you are trying to select text to create highlights or citations, remember that you must now click or tap on the first word, and then click or tap on the last word.
One moment ...
Default project is now your active project.
Project items

Items saved from this book

This book has been saved
Highlights (0)
Some of your highlights are legacy items.

Highlights saved before July 30, 2012 will not be displayed on their respective source pages.

You can easily re-create the highlights by opening the book page or article, selecting the text, and clicking “Highlight.”

Citations (0)
Some of your citations are legacy items.

Any citation created before July 30, 2012 will labeled as a “Cited page.” New citations will be saved as cited passages, pages or articles.

We also added the ability to view new citations from your projects or the book or article where you created them.

Notes (0)
Bookmarks (0)

You have no saved items from this book

Project items include:
  • Saved book/article
  • Highlights
  • Quotes/citations
  • Notes
  • Bookmarks
Notes
Cite this page

Cited page

Style
Citations are available only to our active members.
Sign up now to cite pages or passages in MLA, APA and Chicago citation styles.

(Einhorn, 1992, p. 25)

(Einhorn 25)

1

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

Cited page

Bookmark this page
Mathematical Psychology and Psychophysiology
Table of contents

Table of contents

Settings

Settings

Typeface
Text size Smaller Larger Reset View mode
Search within

Search within this book

Look up

Look up a word

  • Dictionary
  • Thesaurus
Please submit a word or phrase above.
Print this page

Print this page

Why can't I print more than one page at a time?

Help
Full screen
/ 320

matching results for page

    Questia reader help

    How to highlight and cite specific passages

    1. Click or tap the first word you want to select.
    2. Click or tap the last word you want to select, and you’ll see everything in between get selected.
    3. You’ll then get a menu of options like creating a highlight or a citation from that passage of text.

    OK, got it!

    Cited passage

    Style
    Citations are available only to our active members.
    Sign up now to cite pages or passages in MLA, APA and Chicago citation styles.

    "Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn, 1992, p. 25).

    "Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn 25)

    "Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences."1

    1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

    Cited passage

    Thanks for trying Questia!

    Please continue trying out our research tools, but please note, full functionality is available only to our active members.

    Your work will be lost once you leave this Web page.

    For full access in an ad-free environment, sign up now for a FREE, 1-day trial.

    Already a member? Log in now.