Sex Ratio Forecast

["Maladorno, Dionigi \(DRUG;Nutley\)" <DIONIGI.MALADORNO@roche.com>]

Jota Melgar  wrote: 
<<<<<
Looking at you water parameters and comparing them to Romer's results
you=

should have gotten close to 50:50 ratio. Why you didn't get it? I
couldn'=
t
tell you, just like I couldn't tell you if the "hard water" Peruvians
are=

subject to Romer's results. Unfortunately his experiments did not go
beyo=
nd
a pH of 6.5 but if you compare the results he got at 26 C and 29 C at pH
5.5 you see an increase in the number of males from 62.7% to 83%. If you
look at a 26 C and pH 6.5, his results show a 43.3%. Now, it is safe to
s=
ay
that at 26 C and pH 7.0 the ratios would have been a little lower but,
wh=
at
if he would have raised the temperature to 29 C (closer to what we found
=
A.
cacatuoides at).  Maybe the ratio could've been closer to 50:50. =>>>>>>



I think that in order to understand how to interpret the data from
Romer's study, it may be helpful to also clarify some statistical
concepts.
I do not want to complicate the issue just to sound important, but
rather to help understanding what to expect on the basis of a given
study, and avoid frustrations to hobbyists who get somewhat different
results, and wonder if they are doing anything wrong (when instead they
aren't).

Point 1: 
Say that a scientist like Romer performs a study on the sex ratio of
Apistos in relationship to pH and temperature.
He or she will use a given number of pairs to replicate a given number
of spawns for each specific water condition, from which the average of
the sex ratio for each will be calculated. Given perfect study
conditions, this average will be very realistic if it is based on an
adequately large number of pairs for each pH and temperature condition,
because each individual spawn will have a different sex ratio, but all
together, when averaged, they will provide a good GENERAL description of
the situation. The mean will in other words summarize the variability of
the individual spawn observations. 
 
Point 2:
Now, say that a week later Mr. Scientist receives a donation of another
large batch of pairs of apistos, he/she has free time, and it is decided
to duplicate the experiment.
Well, this time not only as before each individual spawn (replicated in
exactly the same condition) will have a sex ratio different from each
other, but also their mean will not be absolutely identical the one
previously found. It will be in fact different, on the basis of the
number of pairs used in this second experiment, and on the basis of the
intrinsic variability of the phenomenon being investigated.    This is
due to the fact that there is also a variability in the sample mean.


The morale of the story is that when we hear: "in such conditions I have
seen such and such sex ratio", it is not necessarily true that if we
duplicate the same conditions, we will see the same sex ratio.
Especially if we obtain only one or two spawns, it will be actually very
unlikely (still possible though, but not frequent) that we will get
exactly the same.

This is way there are indeed statistical procedures that allow the
scientist to say  (instead of  "in such conditions you should see such
and such sex ratio"), "if you duplicate my conditions you have a very
high probability to observe a sex ratio comprised between ....(low end
of the ratio) and .... (upper limit of the ratio)", which gives a much
more realistic presentation of what to expect. Depending on how large
the original study is, and the natural variability of the event, these
intervals of probability can be very narrow (say, between 1:1 and 1:1.2)
or very large (say, expect between 5:1 and 1:30). 

I do not have Romer's paper (is there anyone available to fax or mail it
to me, if it is in English? E-mail me, thanks), but unless the study was
extremely large, it is unlikely that the estimates calculated allow a
very precise forecast. They may however provide a useful guidance of the
general rules and trends of the gender ratio determination, which is
still an extremely important discovery. 

I hope to have helped to prevent bad feelings.....


Dionigi Maladorno