Photographs of spatial cognitive testing apparatus.

A. Side-view of one array suspended in the air. B. A mountain chickadee tagged with a passive integrated transponder (PIT) tag visiting the ‘smart’ feeder array. Motorized door is open. The blue band on the left leg of the bird is the PIT tag. C. View of the testing apparatus from below, depicting equidistant placement of eight ‘smart’ feeders. Data presented come from four independent feeder arrays.

Model predictions of the number of extra-pair young a male sired in a year by the mean number of location errors per trial over the first 20 trials.

The dashed line represents a zero-inflated model for all males, including those with no extra-pair young (N=280; 137 individual males), and the solid line represents the model prediction for males that sired at least one extra-pair young (N=41; 34 individual males). Points are slightly jittered on the y-axis to improve readability. Shading represents bootstrapped 95% confidence intervals. Inset depicts 8 nestlings at 16 days post-hatching. See model predictions for the number of extra-pair young a male sired in a year by total 4-day testing performance in Figure S5.

Comparing spatial cognitive performance (mean number of location errors per trial over the first 20 trials) of extra-pair (mean ± SE = 0.96 ± 0.07) and social fathers (mean ± SE = 1.17 ± 0.07, 71 comparisons).

Lines connect males by offspring: blue lines show comparisons where the extra-pair father performed better than the social father (49 of 71 cases or 69%), and purple lines show comparisons where the social father performed better than the extra-pair father (19 of 71 cases, or 26.7%; in 3 cases the extra-pair and social father had the same cognition score). Shaded distributions represent smoothed histograms of cognitive performance for each father type. The same analysis is presented for performance over the 4-day testing period in Figure S6.

Extra-pair (EPY) and within-pair (WPY) paternity rates across 3 years of data collection and two elevation sites.

Number insets represent the number of EPY and WPY for each year and elevation. EPY rates did not differ significantly by year or elevation.

Histogram plotting the distance of extra-pair male nests from the females’ nest.

Mean = 167 meters and Median = 136 meters. Range is 56 to 1022 meters between nestboxes.

High elevation extra-pair paternity relationships and cognition scores.

Maps show nests with genotyped offspring and the nests of males that sired extra-pair offspring. Red arrows show extra-pair paternity relationships. The direction of the arrow indicates a social male’s nest at the blunt end connected to the nest he sired extra-pair young in at the sharp end. Arrows that originate in open space show males that sired extra-pair young but did not breed in our nest boxes in that year (they likely bred in a natural cavity). Point colors represent the cognition scores of the social male at each nest. Gray circles represent males without cognition data. Only nests that included EPY are included on this map, which is a sample of the active nests in each year (Figure S4).

Low elevation extra-pair paternity relationships and cognition scores.

Maps show nests with genotyped offspring and the nests of males that sired extra-pair offspring. Red arrows show extra-pair paternity relationships. The direction of the arrow indicates a social male’s nest at the blunt end connected to the nest he sired extra-pair young in at the sharp end. Arrows that originate in open space show males that sired extra-pair young but did not breed in our nest boxes in that year (they likely bred in a natural cavity). Point colors represent the cognition scores of the social male at each nest. Gray circles represent males without cognition data. Only nests that included EPY are included on this map, which is a sample of the active nests in each year (Figure S4).

Heat maps of male spatial cognitive scores for high and low elevation nestboxes across the 3 years we have extra-pair paternity data from, including those nests that failed before day 16 or were not genotyped.

Each point represents a nestbox. Color gradient represents mean location errors of male on the first 20 trials of the spatial cognitive task. Gray circles indicate nestboxes with no cognitive data for the male. Data shows that nestboxes are not clustered by male cognitive performance. Some of the males on the maps did not participate in cognitive testing until after these breeding seasons, but since spatial cognitive ability does not change with age, we present their scores here as well.

Model predictions of the number of extra-pair young a male sired in a year by the mean number of location errors per trial over the 4-day testing period.

The dashed line represents a zero-inflated model for all males, including those with no extra-pair young (N=280; 137 individual males), and the solid line represents the model prediction for males that sired at least one extra-pair young (N=41; 34 individual males). Shading represents bootstrapped 95% confidence intervals. Note: data presented in figure do not account for total trials completed, which was accounted for in statistical analysis.

Comparing spatial cognitive performance (mean number of location errors per trial over the 4-day task) of extra-pair and social fathers (total of 71 comparisons).

Lines connect males by offspring: blue lines show comparisons where the extra-pair father performed better than the social father (34 of 71 cases or 47.9%), and purple lines show comparisons where the social father performed better than the extra-pair father (37 of 71 cases or 52.1%). Shaded distributions represent smoothed histograms of cognitive performance. Note that the data presented in the figure do not account for the total number of trials completed, which was accounted for in the statistical analysis.

There is a strong positive correlation between the number of location errors on the entire 4-day task and on the first 20 trials for males completing the task (Coef=0.27, F=121.72, P<0.001).

Representative learning curve of 19 males included in the extra-pair paternity analysis, from the 2021 breeding season.

Dotted line represented chance level performance on the task at 3.5 mean location errors. Curve includes performance on trials 1 – 20 and over the entire 4-day task. Errors bars represent standard error of the mean.

Comparisons of Trio LOD scores for 1st and 2nd ranked potential fathers for each offspring by elevation and year.

Note the mostly bimodal distribution in which 1st-ranked males (blue) consistently out-performed 2nd-ranked males (red). Offspring with low 1st-ranked male Trio LOD scores are cases where we did not sample the offspring’s genetic father.

Sample sizes for extra-pair paternity broken down by year and elevation for both the nest and offspring level.

Differences in extra-pair paternity rates between high and low elevations.

A likelihood ratio test indicated that an interaction between elevation and year improved the model, so years were run separately.

Relationship between spatial cognitive ability and extra-pair young sired.

Two models are presented for each spatial cognitive measure, a model that included a zero-inflation parameter for all observations and a model that only included male-years where the male sired at least one offspring.

Relationship between male and female spatial cognitive ability (mean location errors per trial over the first 20 trials) and breeding performance.

Test of whether siring extra-pair offspring affected the offspring in a male’s own nest.

Whether a male sired extra-pair offspring or not was compared to A) brood size, B) brood size controlled for clutch size, and C) mean nestling mass.

Test of whether offspring sired by extra-pair fathers differed in mass from offspring sired by social males.

Comparison of spatial cognition scores between social males and extra-pair males they were cuckolded by.

Log-transformed values are reported in Table 4B – entire task mean location error model.

Test of whether a male’s spatial cognition score was associated with whether he was cuckolded or not.

Test of whether the number of extra-pair young in nests with at least one extra-pair young is associated with spatial cognitive ability (performance on the first 20 trials).