Racing data

We obtained racing data from the public website of the Chinese Racing Pigeon Association (CRPA, http://www.crpa.net.cn/). For each race, data include city of the home loft and the city of release site, release time, arrival time of each pigeon, average beeline distance from the release site to the home lofts, number of pigeons released and number of pigeons successfully returned. The homeward direction from the release site to the centre of the home lofts was calculated and categorised as North, Northeast, East, Southeast, South, Southwest, West and Northwest. The distance (in km) of each race was calculated as the average of all returned pigeons.

Data focused the North China Plain, an area with the worst air pollution and for which the new Air Quality Index (AQI)1 – which integrates the most important haze source – PM2.5 – has been available since 2013. We focused on racing data from the fall of 2013 and 2014 because this is the time of year with the worst air quality30 and over half of the racing events are held during the fall. More importantly, pigeons behave differently between seasons31 and thus to eliminate variation, we focused on fall racing events. Since racing pigeons fly at an average of 60 km/h and they are released mostly in the early morning, we eliminated races over 470 km to ensure that most pigeons potentially could return to their home lofts in the same day. The shortest race was 160 km long. Distances between different lofts were thus usually small compared to the race length, i.e., within 30 km. With these criteria, we created a data set of 415 races (Supplemental file 1).

Air Quality Index

We obtained Air Quality Index (AQI) data from the Data Centre of the Ministry of Environmental Protection of the People’s Republic of China (MEP, http://datacenter.mep.gov.cn/), or from related provincial or city meteorological departments. Based on established criteria (GB3095-2012), AQI is calculated for six major air pollutants separately: particle matter <10 microns in diameter (PM10), particle matter <2.5 microns in diameter (PM2.5), ground-level ozone level (O 3 ), carbon monoxide (CO) level, sulphur dioxide level (SO 2 ) and nitrogen dioxide level (NO 2 ). An individual score is assigned to the level of each pollutant and the final AQI is the highest of those 6 scores. AQI values range from 0 to 500 and can be classified into six categories (Good: 0–50, Moderate: 51–100, Unhealthy for Sensitive Groups: 101–150, Unhealthy: 151–200, Very Unhealthy: 200–300, Hazardous: 301–500). In China, particulate pollution poses the greatest threat to human health in China and AQI is well predicted by the concentrations of PM10 (r = 0.988, P < 0.01) and PM2.5 (r = 0.983, P < 0.01, Supplemental file 2).

Since all races were held in North China Plain, which is a broad plain without any geological obstructions and the air quality is similar in adjacent cities32, we recorded the AQI at both the sites of release and the home lofts (if there were no AQI reports at either the release site or home lofts, we used AQI of the closest city; a distance <50 km). AQI levels at the release site and home lofts were positively correlated (r = 0.424, P < 0.01), so we used the average AQI to represent the pigeon’s air environment during a race.

Meteorological variables

We obtained meteorological data from a public weather website (http://www.tianqihoubao.com/). We collated weather conditions, wind direction and ground air temperature (°C) at both the release and home lofts. Based on these data, we defined the weather conditions at the time of each race as: sunny, if both sites were sunny; cloudy, if either site was cloudy; and overcast or rainy (hereafter “rainy”), if either site was overcast or rainy. Precise information on wind speed was unavailable, so we focused on wind direction, which was classified into three categories: tailwind, when wind direction was the same as the direction of the birds’ flight at both release and home sites; headwind, a wind direction opposite to the birds’ flight directions at both sites; and variable, which included all other possible combinations of directions. We assumed that temperature increased smoothly from the lowest at sunrise (06:00 in September; 06:30 in October; 07:00 in November) to the highest at 14:00 and then decreased similarly. Then we calculated the average temperature of each race using the corresponding average homing times.

Data analysis

We tested two hypotheses: under conditions of low visibility and olfactory interference associated with air pollution, pigeons would 1) increase their homing time and 2) decrease their homing rate (the percentage of pigeons successfully homed). To avoid a ratio-correlation problem that inevitably occurs when searching for relationships between speed (distance/time) and distance where distance appears on both sides of the equation33, we fitted a linear model using average homing time of each race as the dependent variable. Average beeline distance, weather, wind, AQI, temperature were defined as independent variables and the intercept was set at 0. In the second linear model, we used the homing rate (percentage) as the dependent variable and distance, weather, wind, AQI and temperature as independent factors. For categorical variables, we defined weather as sunny = 1, cloudy = 2 and rainy = 3, which indicated an increase of clouds cover and wind as tailwind = 1, variable = 0 and headwind = −1, which indicated an effect of wind direction on flight difficulty. We did not include home city, homing direction and year in the final regression model, because we found no effects of city (F 6,397 = 1.692, P = 0.12) or homing direction (F 3,397 = 1.302, P = 0.27) on homing time in a preliminary analysis. Year (2013, 2014) explained significant variation in homing time (F 1,397 = 9.885, P < 0.01), but since it was not the aim of our study to predict homing time in specific years, we excluded it from the final model. Individual pigeons vary in homing experience and some pigeons are probably trained for uni-direction, which might bias their directional decision. Since we knew nothing about prior homing or training experience, we focused on homing time and homing rate, which are characteristics of a race, not an individual. Finally, we plotted the relationship between average actual homing speed and AQI and we estimated the homing speed (beeline distance/homing time) using our regression model for three distances (200 km, 300 km, 400 km), under three weather conditions (sunny, cloudy, rainy) and three wind conditions (tailwind, headwind, variable). We reported coefficient values ± standard error. All analyses were conducted with SPSS 18.0.

Ethics statement

Data on homing pigeon races were collected from public sources; no ethics approval was required for this study.

Data availability

Data used for all analyses are available as electronic supplementary material.