Dear List,

Again the birds....

So far, I wanted to test if the breeding success in season t influences
mate- and site-fidelity of a individual (Bird) in season t+1.

My lmer model with Bird as a random effect was overparameterized (I have 55
Birds, i.e. individuals, and 64 observations), thus I used glm without the
random effect Bird instead.

lmer:

fm<-lmer(SameSite~BreedSuc1+(1|Bird), family="binomial") - model
overparameterized
fm1<-lmer(SameSite~1+(1|Bird), family="binomial"


glm
fm4 <- glm(SameMate ~ BreedSuc1, binomial, DSS1)
fm5 <- glm(SameMate ~ 1, binomial, DSS1)

However, the problem is that Bird A and Bird B form a pair (Pair 1), Bird C
and D form Pair 2, etc. This means that the breeding success (BreedSuc1) in
season t will always be the same for Bird A and B, because they are a pair
(same egg that doesn't hatch or same chick that dies). Thus, without the
term Bird in glm, wouldn't I be pseudo-replicating my data due to this
(didn't think of this before...)?

In addition, if Bird A and B remain together in season t+1 (mate-fidelity
=1), then the value for SameMate will be the same for Bird A and B and the
value for site-fidelity will also be the same for Bird A and B, i.e. for
pair 1 ("0", if the pair changes site, "1" if they remain at their nest
site).

BUT:
 If Bird A and B no longer form a pair in season t+1 (mate-fidelity=0 for
Bird A and B), then site-fidelity will have different values for Bird A and
B, because Bird A may remain at the nest site (site-fidelity=1) and Bird B
changes nest site (site-fidelity=0). However, even if the pair divorces in
season t+1, the value for the breeding success in season t is still the same
for Bird A and B.

A better example:

   Bird Sex Pair in Season t BreedSuc1  SameMate  SameSite  A F 1 0 1 0  B M
1 0 1 0  C F 2 1 1 1  D M 2 1 1 1  E F 3 0
0 0  F M 3 0 0
1  G F 4 1 0 1  H M 4 1 0 0

Note: Pair 3 (Bird E and F) was unsuccessful in breeding in season t
(BreedSuc1=0). In season t+1 they no longer form a pair (SameMate=0). Bird E
changes nest site (SameSite=0), while Bird F stays at its nest (SameSite=1).


To the questions (long way to get here, sorry):

1. If I want to test if BreedSuc1 influences SameMate and SameSite,
shouldn't I account for the fact that the BreedSuc1 value of Bird E and F is
exactly the same, since they are a pair?

2. Shall I use lmer with Pair as a random effect? What about the individual
Bird? If I look at site-fidelity (and mate-fidelity?), I'm looking at the
behaviour of the individual, rather than the behaviour of the pair. Could I
use a lmer model including Pair and Bird? But how can I relate the random
effect "Pair" to "BreedSuc1" and "Bird" to "SameMate", "SameSite"? Crossed
random effects?

Thank you all

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