Is using a Binomial GLM correct for comparing two groups probability of doing something?

Question

I'm currently a biology student and we use R occasionally for statistics. I'm currently looking at two groups chances of mating based on their size. I am using my own generated data for this and only the large group mates and the small group does not. My lecturer suggests using a Binomial GLM but using their code doesn't work and, to be honest, I am not sure what it is testing for. I need a test that compares chances of mating and if the difference is statistically different I think. This is the code that I am using. It works fine until the last line.

#this is 35 males who were chosed, with a mean claw size of 15
not.chosen.size<-rnorm(n=65,mean=5,sd=1.5)
#this is 65 males who were not chosen, with a mean claw size of 5

population.size<-c(chosen.size,not.chosen.size)
population.size


#add a column indicating whether they were chosen or not
yes<-rep(1,35)
no<-rep(0,65)
#combine them
chosen<-c(yes,no)

dat<-data.frame(population.size,chosen)
dat

mod<-glm(chosen~population.size,family=binomial,data=dat)

I would appreciate any help you can offer.

EDIT:

I've gotten these results by implementing the changes suggested by @EdM.

    Min       1Q   Median       3Q      Max  
-1.4430  -0.8965  -0.4957   0.9204   2.4367  

Coefficients:
                Estimate Std. Error z value Pr(>|z|)    
(Intercept)      -4.4769     0.9991  -4.481 7.44e-06 ***
population.size   0.7105     0.1675   4.243 2.21e-05 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 133.75  on 99  degrees of freedom
Residual deviance: 107.94  on 98  degrees of freedom
AIC: 111.94

Number of Fisher Scoring iterations: 4

EDIT: New Code:

chosen.size<-rnorm(n=35,mean=7,sd=1.5)
#this is 35 males who were chosed, with a mean claw size of 7
not.chosen.size<-rnorm(n=65,mean=5,sd=1.5)
#this is 65 males who were not chosen, with a mean claw size of 5

population.size<-c(chosen.size,not.chosen.size)
population.size

#add a column indicating whether they were chosen or not
yes<-rep(1,39)
no<-rep(0,61)
#combine them
chosen<-c(yes,no)

dat<-data.frame(population.size,chosen)
dat

mod<-glm(chosen~population.size,family=binomial,data=dat)

Answer 1

This thread goes into extensive detail about how to interpret the output from a logistic regression model.

Briefly, in logistic regression (generalized linear model, binomial family, logit link) intercepts and regression coefficients are in log-odds scales.

With default coding in R, the (Intercept) is the baseline log-odds, estimated when all continuous predictors are at values of 0 and categorical predictors are at their reference values. A regression coefficient is then the change in log-odds from the (Intercept) associated with a predictor.

In your case, the (Intercept) is the estimated log-odds of mating success when population.size = 0. That might not be a realistic value but that doesn't matter. You just use that to start the calculations. The population.size coefficient is the change in log-odds per unit change in population.size. For example, if population.size = 6 the log-odds of success are -4.4769 + (6 * 0.7105) = -0.2139.

Log-odds can be hard to think about but they are very useful for these models. To put the estimate into a somewhat easier form to grasp, first exponentiate the log-odds to get the odds of success: exp(-0.2139) = 0.807, the estimated odds of success at population.size = 6.

If $p$ is the probability of success, the the odds are $p/(1-p)$. You can then solve for $p$ as odds/(1+odds); you get an estimated probability of success of 0.447 at population.size = 6.

Statistical software can make these predictions for any set of predictor values, along with confidence intervals based on the estimated (co)variances among the regression coefficients. For more complicated models, particularly when there are interactions, it's wise not to focus on the apparent "significance" of the individual coefficients. Look instead at the overall quality of the model and predictions for particular sets of predictor values of interest.