Webb et al, the paper that couldn't be more wrong

http://www.sciencedirect.com/science/article/pii/S0003347299912150
I discuss certain points here in this paper which seem utterly wrong to me and also  expres my disbelief at what all can get published. If i were to speak, game theory already developed quite nicely by 1960's was applied for the first time in biology in 1980's by Maynard Smith (that's why he is the father of biological game theory or something like that) and that too wrongly.
Seeing the lack of consistency for a long time is disheartening.
What were the reviewers doing.Or were they not trained in the subject. 
Points to discuss:
1. "

Although Maynard Smith’s model has been very influen-

tial, it cannot explain multiple patterns of care."

Because it was wrong.

2.

"

There are

three obvious ways in which multiple patterns of parental

care might appear. First, the ESS may consist of mixed-

strategy behaviours, that is, either or both of the parents

should desert with a probability between one and zero.

Second, behaviour may be time dependent with parents

changing their care decision during the breeding season.

Third, there may be differences in quality between indi-

viduals leading to different care decisions being made

depending on the qualities of both parents."

The first reason covers everything,by definition.

 3.

"

In Maynard

Smith’s ‘model 2’: (1) there are no mixed ESS solutions

since an individual’s behaviour can depend on its sex,

and the payoffs for care and desertion are fixed (Selten

1980; Maynard Smith 1982, page 107); (2) it describes a

single, time-independent decision; and (3) the individ-

uals in the population are identical."

Again the reasons are not necessary because he was wrong.

4.

“let us suppose that the population is following the strat-

egy of female care and male desertion. The condition for

male desertion to be optimal, given that all females in the

population are caring (y=0) and all males are deserting

(x=1), is V1 +rm(1,0)V2 >V2. However, with rm(x,y) given

by equation (5) we have rm(1,0)=0 since there are no

females available with which to mate. Thus for uniparen-

tal care by the female to be an ESS, it must be the case that

V1 >V2 which contradicts our original assumption that

biparental care is better than uniparental care. The failure

to satisfy the condition for uniparental female care is due

to our choice of functions for the remating probabilities. ”

They accept their mistake,in fact the whole formulation becomes wrong and still they continue talking about it.

5.

“If none of the females in the population participated in

the first breeding attempt (for example, because they had

not yet arrived on the breeding site), then some females

may be available even though the number of deserting

females is zero. ”

Who are you kidding?

If all females are caring,how the hell do you plan to get those additional females from. If from somewhere else,then sorry,your model has unknown elements coming in and going out which is terribly not acceptable.

Experiments cannot be always in experimenter's control but you cannot do that to a model.

6.

If Webb et al had chosen the matrix payoffs carefully,they would have gotten exactly the same results as our model 0.

And we wouldn't be doing that and reading it in their paper.

7."

In Appendix 2 we show that, in the standard replicator
dynamics (Taylor 1979), the corresponding polymorphic
populations with x* as the proportion of deserting
individuals are asymptotically stable under the same
conditions on V1/V2 as for the ESS solutions."

Why should they be any different ?Finding ESS is same as finding the fixed points of certain game which is stable (asympotically).

Replicator dynamic kind of analysis is enough.

In ESS kind of analysis ,people directly compare payoffs of different strategies ,which is essentially the same for replicator dynamics except that it gives you an additional structure and also a mechanism to generate the whole game being played in real time. like you can monitor the allele frequency change by iterating the game.