From: Alan Rogers

From: Alan Rogers To: Jeffrey Epstein <[email protected]> Subject: Re: Date: Mon, 25 Nov 2013 22:48:34 +0000 My paper was about the evolution of menopause. George Williams had argued years before that as women age, the risk of childbirth mortality increases. Eventually, that risk outweighs the potential fitness gain from another child. My paper showed that this doesn't work--the risk of childbirth mortality is too low. I saw more promise in a hypothesis having to do with opportunity cost. To do these calculations, I needed an age-structured theory of kin selection with a time delay between the investment (forgone pregnancy) and the return on that investment (ability to care for one's previous children). So the model had economic pretensions, and I eventually used it to study the evolution of time preference. It was the time preference work that brought me into contact with Gordon G. Alan On Mon, Nov 25, 2013 at 2:20 PM, Jeffrey Epstein <[email protected]> wrote: risk of death in childbirth? On Mon, Nov 25, 2013 at 5:05 PM, Alan Rogers < > wrote: Charlesworth and Charnov published an age-structured theory of kin selection in 1981 (JTB 88:103) and Taylor and Frank did it a different way in 1996 (JTB 180:27). I added time delays to the Charlesworth- Charnov model in 1993 (Evollutionary Ecology 7:406). These models all grow out of the ideas that Hamilton introduced in his "Moulding of senescence" paper in 1966. But Hamilton 1966 didn't do kin selection. He did however argue that reproductive value is not the right way to formulate the problem. His model (and also those mentioned above) use the numerator of reproductive value, but the normalization is different. To put this differently, the reproductive value at age x needs to be weighted by l_x, the probability of surviving to that age. This weighting is missing from the formulation directly in terms of reproductive value. Alan 2013/11/25 Gordon Getty The information contained in this communication is confidential, may be attorney-client privileged, may constitute inside information, and is intended only for the use of the addressee. It is the property of Jeffrey Epstein Unauthorized use, disclosure or copying of this communication or any part thereof is strictly prohibited and may be unlawful. If you have received this communication in error, please notify us immediately by EFTA00977627 return e-mail or by e-mail to [email protected] and destroy this communication and all copies thereof, including all attachments. copyright -all rights reserved EFTA00977628