CURM Fifteenth Meeting, 12/9/2008

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Contents

Agenda

New Business

I have a pamphlet from Lisa, asking that we get signed up for the Mathematical Contest in Modeling by the 19th of December.

I want to talk about a new story, which I've built into our paper.

Action Items

  • Action items from our thirteenth meeting:
    • Grayson:
      • Write up the Tale of the Decimated Female Cicada Killers!
    • Katie:
      • Use indicator variables to see if some populations can be combined to give a single population to model.
      • Write up the story of the the mass/rwl non-linear model for the Cicadas, including for species-specific models. Make sure that you do it in the article we're writing.
      • Include some of the data you've been using in the article data section (including meta data).
      • The moving-window or kernel-smoother with bandwidth 3.4 looked good. We now want to feed that into the story that Grayson's telling. Summarize the kernel-smoothing process.
      • Consider registering for the Nebraska Conference for Undergraduate Women in Mathematics -- you didn't actually agree to this, but I'm suggesting you do!;)

Problem of the Week

Something interesting

Some interesting linear regression insights, from Edward Tufte (and F. J. Anscombe -- The American Statistician, Vol. 27, No. 1. (Feb., 1973), pp. 17-21.):

Anscombe's Quartet
Anscombe's Quartet

Anscombe's Quartet shows four extremely different data sets, all with the same best linear model (linear regression model).

Something fun(ction):

Old Business

  • Further discussion of Peter Grant's article as we work towards An article in response to Grant
    • Introduction
      • Fisher's Equal Investment model: "In the absence of local mate competition the expected sex ratio of sexually dimorphic species is the ratio produced when maternal investment in the two sexes is equal( Fisher, 1930; Trivers & Willard, 1973; Myers, 1978 ). As female wasps are larger than males, males should be produced in greater numbers than females."
      • "As female wasps are larger than males, males should be produced in greater numbers than females." [As Jon is fond of noting, however, the males may not live as long, as they are constantly fighting and causing trouble -- typical males!;). This should be factored into any census, of course.]
      • "Therefore, to produce an excess of male offspring, a female could prey selectively on small prey. At variance with this expectation, however, wasps are believed to hunt selectively for large, and therefore usually female, prey and lay female eggs on them, because female prey outnumber male prey ( Lin, 1979b ). This would tend to yield a female-biased sex ratio."
      • Three, non-exclusive, hypotheses of selective predation are tested.
        • The first hypothesis is that wasps prey preferentially on one sex of their prey, the more valuable sex ( Trivers & Hare, 1976; Charnov, 1982 ), without specifying a priori whether this is male or female; Lin’s (1979b) argument implicitly assumes it is female.
          • We can test this: we would want to include dates, however, because we may be seeing a preponderance of females simply because the males came out earlier.
        • The second hypothesis is that wasps choose prey on the basis of the size of their prey (e.g. Kobayashi & Shimada, 2000 ).
          • This is basically our hypothesis, so far, only we add in the component of transition to opportunistic as "unsuccessful hunt time" increases. Grayson has provided some initial examples of such a transition on his page.
        • The third hypothesis is that wasps prey preferentially on larger, more conspicuous and hence easier to detect species of cicadas.
      • Opportunistic predation, resulting in prey taken at random with respect to their traits, is the default hypothesis to account for data if they are not explained by selective predation.
      • Determining whether predation is selective or opportunistic requires estimating prey captured in relation to prey availability. This is difficult to achieve by direct observation because the attacks usually take place at the tops of tall trees.
        • This is not true. We don't need an accurate census to prove certain kinds of selectivity. For example, if field studies show that there is a super-abundance of small cicadas, but large wasps never take them, then we're sure that the cicada-killers are selective -- even though we don't know the actual abundances of the prey available.
      • As a further extension, weights of individual wasps and of the cicadas they carried were used to test for a positive relationship between the two ( Lin & Michener, 1972 ), as this has so far not been done. [Andy's emphasis]
        • We can test this: Strategy: paired t-test
      • "...on average [cicada killers'] prey burden is almost twice as heavy as the wasps ( Coelho, 1997 )."
        • We can test this: only we have rwl, rather than mass. So we need to model cicada mass based on rwl, and then do a conversion on all pairs.

Recent Business

Let's talk about Sex Allocation in Solitary Bees and Wasps (Vol. 146, No. 2. The American Naturalist. August 1995, and cited in Peter Grant's article). Frank has other papers available at his website, http://stevefrank.org/reprints-pdf/, including this paper which provides background on the one we're looking at.

"I develop a simple theory that predicts an increasing F/M allocation ratio with increasing F/M size ratio."

Why is it important?

  • It gets to the question of why -- or whether -- wasps use a "one if by male, two if by female" strategy for allocating their eggs (or even a "four if by male, seven if by female" strategy!); or how they might behave under resource limitation (all males?).
  • It helps us to understand "the psychology of the wasp".

Results related to Frank's paper Sex Allocation in Solitary Bees and Wasps

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