Christine Muller
Wiess College
4/20/2001
Male Grackle Courtship Behavior
Objective: Male great-tailed grackles (frequenters of Rice University campus) perform complex courtship dances and calls for females during the mating season. Because the male of this species contributes little to no energy in the raising of the young and building of the nest, I hypothesize that courtship success will be positively correlated to length and complexity of dance.
Data Description: A total of 31 interactions were observed on or near Rice University campus. For each interaction, I recorded duration of courtship attempt, type of calling, posturing (yes or no), bobbing (yes or no), and any variation in the dance. Each behavior was given a point value based on energy/time expenditure(see below), and these points were added to give an overall quality/complexity rating.
Behavior / Point ValueCircled female / 5
--Two times or more / 7
Chased female / 5
Ran / 3
Whooping call / 4
Short Squawk / 2
Posturing / 3
Bobbing / 3
Fluffed up / 2
Flapped wings / 2
Wagged tail feathers / 2
The attempt was deemed a success when the female stayed near the male, or flew away with him. If the female left the site, or if the male flew away without her, the attempt was recorded as a failure.
Predictors:
Duration—duration of courtship ritual in seconds.
Quality rating—sum of all behavior point values as explained above.
Response Variable:
Success—given values of 0 (failure) or 1 (success) as defined above.
Methodology: In order to see if there was a correlation between mating ritual complexity and length with courtship success, I chose a binary logistic regression. (I chose this regression because my data is a mixture of binary and continuous data.)
Results and Analysis:
First I ran the binary logistic regression using duration and quality (complexity) rating as predictors with success as the response. The results are in the tables below:
Logistic Regression Table
Odds 95% CI
Predictor Coef StDev Z P Ratio Lower Upper
Constant -4.879 2.225 -2.19 0.028
Duration 0.16732 0.09533 1.76 0.079 1.18 0.98 1.42
Rating 0.1872 0.1943 0.96 0.335 1.21 0.82 1.76
Log-Likelihood = -12.067
Test that all slopes are zero: G = 8.462, DF = 2, P-Value = 0.015
Goodness-of-Fit Tests
Method Chi-Square DF P
Pearson 25.058 20 0.199
Deviance 24.135 20 0.237
The binary logistic regression is a success with a p-value of 0.015, so we can reject the Ho hypothesis that length and complexity of dance will have no affect on courtship success. The goodness-of-fit results yield insignificant p-values, which indicates that this model explains my data well (there is a high correlation present). In other words, duration and complexity rating are good predictors of courtship success. The p-value for duration (p=0.079) is not significant, so I ran another regression with duration alone, under the suspicion that rating and duration might not be independent predictors.
Logistic Regression Table
Odds 95% CI
Predictor Coef StDev Z P Ratio Lower Upper
Constant -3.1144 0.9946 -3.13 0.002
Duration 0.21414 0.08700 2.46 0.014 1.24 1.04 1.47
Log-Likelihood = -12.536
Test that all slopes are zero: G = 7.524, DF = 1, P-Value = 0.006
Goodness-of-Fit Tests
Method Chi-Square DF P
Pearson 13.700 8 0.090
Deviance 11.889 8 0.156
Hosmer-Lemeshow 1.299 4 0.862
Here you can see that when tested separately from quality, duration does indeed have a significant (p=0.006) affect on rate of success. Overall quality rating also shows a significant result when tested against success alone:
Logistic Regression Table
Odds 95% CI
Predictor Coef SE Coef Z P Ratio Lower Upper
Constant -5.009 2.037 -2.46 0.014
Rating 0.3319 0.1632 2.03 0.042 1.39 1.01 1.92
Log-Likelihood = -13.815
Test that all slopes are zero: G = 4.967, DF = 1, P-Value = 0.026
Goodness-of-Fit Tests
Method Chi-Square DF P
Pearson 14.892 9 0.094
Deviance 19.253 9 0.023
Hosmer-Lemeshow 14.700 5 0.012
To illustrate these results, I have included the following scatter plots:
Since success has only values of one or zero, it is difficult to see the distribution of points, as many are right on top of each other. To compensate for this, I dithered the values of success to yield the scatter plots below:
These graphs better show the correlation between duration and courtship success, and ritual complexity and courtship success. These predictors are more significant individually, so the model explains their effects on courtship success well.
I also graphed duration vs. rating to see if the two variables were related; the resulting scatterplot is shown below.
While the usual scattering appears from the random nature of my data, there seems to be a positive correlation between the two predictors, and I cannot assume that they are independent. A regression further supports the correlation with significant p-value of 0.001 (see table below).
Regression Analysis: Duration versus Rating
The regression equation is
Duration = - 3.00 + 0.990 Rating
Predictor Coef SE Coef T P
Constant -2.998 3.105 -0.97 0.343
Rating 0.9905 0.2777 3.57 0.001
S = 4.761 R-Sq = 31.2% R-Sq(adj) = 28.8%
Analysis of Variance
Source DF SS MS F P
Regression 1 288.29 288.29 12.72 0.001
Residual Error 28 634.67 22.67
Total 29 922.97
Unusual Observations
Obs Rating Duration Fit SE Fit Residual St Resid
5 13.0 20.000 9.878 1.073 10.122 2.18R
18 12.0 20.000 8.888 0.938 11.112 2.38R
R denotes an observation with a large standardized residual
Since the model I used proved a good fit, I decided to take my data and using a Logit transformation, design a model that predicts the probability of mating success for any given courtship attempt with a duration between zero and thirty seconds. (This model would be appropriate because very few courtship attempts were above twenty seconds, with only one exception, which was left out of this study as an outlier.) To get the log odd values, I used the coefficients from the regression run of –3.1144 and 0.21414. The probability of success was calculated in Minitab using the formula below:
Exp (duration in seconds)
1 + Exp (duration in seconds)
The model is shown here:
Discussion and Conclusions: While I created a model using duration alone, the best model to use to predict mating success would probably include both complexity rating and duration of mating ritual. The confidence intervals for this model do not contain zero ((0.98,1.42) and (0.82, 1.76)), and the p-value indicates significance (0.015).
While it is obvious that the two predictors are correlated with success, there may not necessarily be a causal relationship. To prove causation, many more studies would have to be done, controlling factors such as age, size, and coloring of both grackles involved. (Though in truth, science cannot prove, only disprove.)
The model included above should be tested on other species of birds with similar ancesteral backgrounds, or similar behavioral patterns in order to see if it is a useful tool for prediction. If the model fits, it is likely that duration of courtship ritual does indeed have a causal relationship with rate of courtship success.