#### 2.5.7; vignette work

 ... ... @@ -3688,15 +3688,56 @@ For the Bozic model [@Bozic2010], however, the birth rate is set to 3688 3688 In the original model of @McFarland2013, the effects of drivers 3689 3689 contribute to the numerator of the birth rate, and those of the 3690 3690 (deleterious) passengers to the denominator as: $\frac{(1 + 3691 -s)^d}{(1 - s_p)^p}$, where $d$ and $p$ are, respectively, the total 3691 +s)^d}{(1 + s_p)^p}$, where$d$and$p$are, respectively, the total 3692 3692 number of drivers and passengers in a genotype, and here the fitness 3693 3693 effects of all drivers is the same ($s$) and that of all passengers 3694 -the same too ($s_p$). However, we can map from this ratio to the 3695 -usual product of terms by using a different value of$s_p$, that we 3696 -will call$s_{pp} = -s_p/(1 + s_p)$(see @McFarland2014-phd, his 3697 -eq. 2.1 in p.9). This reparameterization applies to v.2. In v.1 we 3698 -use the same parameterization as in the original one in 3699 -@McFarland2013. 3694 +the same too ($s_p$). Note that, as written above, and as explicitly 3695 +said in @McFarland2013 (see p. 2911) and @McFarland2014-phd (see 3696 +p. 9), "(...)$s_p$is the fitness disadvantage conferred by a 3697 +passenger". In other words, the larger the$s_p$the more 3698 +deleterious the passenger. 3699 + 3700 +This is obvious, but I make it explicit because in our 3701 +parameterization a positive$s$means fitness advantage, whereas 3702 +fitness disadvantages are associated with negative$s$. Of course, 3703 +if you rewrite the above expression as$\frac{(1 + s)^d}{(1 - 3704 +s_p)^p}$then we are back to the "positive means fitness advantage 3705 +and negative means fitness disadvantage". 3706 + 3707 + 3708 +As @McFarland2014-phd explains (see p.\ 9, bottom), we can rewrite 3709 +the above expression so that there are no terms in the 3710 +denominator. McFarland writes it as (I copy verbatim from the fourth 3711 +and fifth lines from the bottom on his p.\ 9) 3712 +$(1 + s_d)^{n_d} (1 - s_p^{'})^{n_p}$where$s_p^{'} = s_p/(1 + s_p)$. 3713 + 3714 + 3715 +However, if we want to express everything as products (no ratios) 3716 +and use the "positive s means advantage and negative s means 3717 +disadvantage" rule, we want to write the above expression as 3718 +$(1 + s_d)^{n_d} (1 + s_{pp})^{n_p}$where$s_{pp} = -s_p/(1 + s_p)$. And 3719 +this is actually what we do in v.2. There is an example, for 3720 +instance, in section \@ref(mcf5070) where you will see: 3721 + 3722 +{r mcflparam} 3723 +sp <- 1e-3 3724 +spp <- -sp/(1 + sp) 3725 + 3726 + 3727 +so we are going from the "(...)$s_p$is the fitness disadvantage 3728 +conferred by a passenger" in @McFarland2013 (p. 2911) and 3729 +@McFarland2014-phd (p. 9) to the expression where we have a product 3730 +$\prod (1 + s_i)$, with the "positive s means advantage and negative 3731 +s means disadvantage" rule. This reparameterization applies to 3732 +v.2. In v.1 we use the same parameterization as in the original one 3733 +in @McFarland2013, but with the "positive s means advantage and negative 3734 +s means disadvantage" rule (so we are using expression 3735 +$\frac{(1 + s)^d}{(1 - s_p)^p}$). 3736 + 3737 + 3738 + 3739 + 3740 + 3700 3741 3701 3742 For death rate, we use the expression that @McFarland2013 (see their 3702 3743 p. 2911) use "(...) for large cancers (grown to$10^6$cells)":$D(N) =