There are a lot of different versions of bird banding, tagging, and tracking. I've participated in bird banding and tagging as well as photographed it. The injury rate is very low - but does exist.
Songbirds are normally captured in fine nets. The birds are tangled in the net and can't get away. It's possible for an inexperienced person to damage the bird's leg or leg's during removal. For experienced banders, the risk of injury is very low. Once removed from the net, they are moved to a banding station for data gathering and banding. If it's windy or if temperatures are outside a safe range, banding is cancelled for the day. Banding is always supervised by a lead staff member as well as experienced banders. If there are injuries, they notice immediately. My guess from participating in this process is the injury rate is in the range of 0.1-0.3% - 1-3 per thousand birds.
While many of the people involved in banding are volunteers - and therefore hobbyists - they are not unskilled or untrained. There are many jobs involved, and the most experienced people are in senior roles while the novices are doing things like keeping the log book or carrying birds from nets to the banding station. The general skill level is higher than Master Gardeners or similar hobbyists. All volunteer banding that I am aware of is under direct supervision of licensed banding experts who are working directly under supervision of the Department of Natural Resources or an expert ornithologist responsible for the project. Many of the volunteers have been participants in banding projects for more than 10 years.
It's relatively uncommon for a bird to be caught and banded more than once. It happens, but the number of banded birds are so small compared to a population that it's probably in the 1-2% range.
Migrating birds like red knots and ruddy turnstones are sometimes captured in nets fired by canons. The Cape May survey of red knots is one of the biggest projects going back more than 20 years. They are very strict about handling of birds, and injuries or fatalities are in the 1-3 per thousand range. Birds are kept in the shade in insulated coolers to prevent overheating while they are being processed. This is only for a period of about 10-15 minutes. When ambient temperatures rise, they stop banding. The monitor the respiration rate and heart rate of birds being captured and handled.
Banding is an important way to track bird migration over time. There is a process for reporting band numbers (and colors and letters) so anyone can find out where a bird was originally banded. It's very helpful for photographers who capture photos of banded birds to report the band numbers. Some of these birds are part of large migrations and may be threatened or endangered.
Radio transmitters are used for some birds to aid in tracking. For example, whooping cranes migrate for long distances and are threatened/endangered. Most populations in the US were raised in captivity and released. Almost all are banded and many have radio transmitters. Most of the bands and transmitters were attached before the bird was released into the wild.
Raptor chicks are normally banded (and transmitters attached if appropriate) in the nest before they fledge. Nesting sites are identified, monitored, and chicks are safely banded before leaving the nest.
I know that from a photography standpoint, bands and transmitters are in the way. But I tend to view it as a small sample of the overall population, and overall is a good idea to support the birds and their habitat. Data on birds, migration routes, and population counts is critical to protecting species that need help.
My suggestion is to photograph birds with bands or transmitters, record the data or the band in the EXIF, report banding numbers where possible, and use those photos for education or editorial rather than art.
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