Sorry for the delay in replying, I started from scratch to cleanly replicate this problem, and it took a while for it to re-occur. Here's an extract of the log, with a ton of Avira messages deleted, but everything else retained. Looks like it's reporting errors deleting old backups.
3/17/16 11:51:52.367 AM com.apple.backupd[10194]: Starting automatic backup
3/17/16 11:51:52.000 AM kernel[0]: nspace-handler-set-snapshot-time: 1458229914
3/17/16 11:51:52.789 AM com.apple.mtmd[250]: Set snapshot time: 2016-03-17 11:51:54 -0400 (current time: 2016-03-17 11:51:52 -0400)
3/17/16 11:51:53.000 AM syslogd[46]: ASL Sender Statistics
3/17/16 11:51:53.983 AM com.apple.backupd[10194]: Backing up to /dev/disk2s2: /Volumes/IanTimeMachine/Backups.backupdb
3/17/16 11:51:57.393 AM com.apple.mtmd[250]: Failed to remove /.MobileBackups.trash, error: Error Domain=NSCocoaErrorDomain Code=513 "“.MobileBackups.trash” couldn’t be removed because you don’t have permission to access it." UserInfo={NSFilePath=/.MobileBackups.trash, NSUserStringVariant=(
Remove
), NSUnderlyingError=0x7fd478e15bb0 {Error Domain=NSPOSIXErrorDomain Code=1 "Operation not permitted"}}
3/17/16 11:51:57.394 AM com.apple.mtmd[250]: Failed to delete /.MobileBackups.trash, error: Error Domain=NSCocoaErrorDomain Code=513 "“.MobileBackups.trash” couldn’t be removed because you don’t have permission to access it." UserInfo={NSFilePath=/.MobileBackups.trash, NSUserStringVariant=(
Remove
), NSUnderlyingError=0x7fd478e15bb0 {Error Domain=NSPOSIXErrorDomain Code=1 "Operation not permitted"}}
3/17/16 11:51:57.825 AM com.apple.backupd[10194]: Event store UUIDs don't match for volume: Macintosh HD
3/17/16 11:51:58.040 AM com.apple.backupd[10194]: Deep event scan at path:/ reason:must scan subdirs|new event db|
3/17/16 11:51:58.040 AM com.apple.backupd[10194]: Running event scan
3/17/16 11:51:58.643 AM com.apple.mtmd[250]: attempting to thin because of low free space on Macintosh HD ✅ by removing 2016-03-17 11:47:47 -0400, estimate 0 bytes to recover, 1 snapshot can be thinned
3/17/16 11:53:52.659 AM launchservicesd[85]: SecTaskLoadEntitlements failed error=22
3/17/16 11:53:52.715 AM launchservicesd[85]: SecTaskLoadEntitlements failed error=22
3/17/16 11:53:52.719 AM launchservicesd[85]: SecTaskLoadEntitlements failed error=22
3/17/16 11:53:52.743 AM launchservicesd[85]: SecTaskLoadEntitlements failed error=22
3/17/16 11:54:10.632 AM uxupdate[10236]: Update started.
3/17/16 11:54:12.120 AM appleeventsd[55]: SecTaskLoadEntitlements failed error=22
3/17/16 11:54:15.466 AM Microsoft Excel[8906]: Stream 0x84afa5e0 is sending an event before being opened
3/17/16 11:54:15.466 AM Microsoft Excel[8906]: Stream 0x84afa5e0 is sending an event before being opened
3/17/16 11:55:31.678 AM WindowServer[193]: disable_update_timeout: UI updates were forcibly disabled by application "CrashPlan menu bar" for over 1.00 seconds. Server has re-enabled them.
3/17/16 11:55:32.489 AM WindowServer[193]: common_reenable_update: UI updates were finally reenabled by application "CrashPlan menu bar" after 1.81 seconds [0.55fps] (server forcibly re-enabled them after 1.00 seconds [1.00fps])
3/17/16 11:55:37.623 AM WindowServer[193]: disable_update_timeout: UI updates were forcibly disabled by application "CrashPlan menu bar" for over 1.00 seconds. Server has re-enabled them.
3/17/16 11:55:38.598 AM WindowServer[193]: common_reenable_update: UI updates were finally reenabled by application "CrashPlan menu bar" after 1.98 seconds [0.51fps] (server forcibly re-enabled them after 1.00 seconds [1.00fps])
3/17/16 11:55:59.860 AM Safari[9833]: tcp_connection_tls_session_error_callback_imp 33 __tcp_connection_tls_session_callback_write_block_invoke.434 error 22
3/17/16 11:59:05.761 AM Microsoft Lync[727]: Replacing namespace soap
3/17/16 11:59:52.770 AM Microsoft Excel[8906]: Stream 0x86b921d0 is sending an event before being opened
3/17/16 11:59:52.770 AM Microsoft Excel[8906]: Stream 0x86b921d0 is sending an event before being opened
3/17/16 12:00:07.000 PM kernel[0]: process prl_vm_app[8088] caught causing excessive wakeups. Observed wakeups rate (per sec): 167; Maximum permitted wakeups rate (per sec): 150; Observation period: 300 seconds; Task lifetime number of wakeups: 1909121
3/17/16 12:00:07.734 PM com.apple.xpc.launchd[1]: (com.apple.ReportCrash.Root[10314]) Endpoint has been activated through legacy launch(3) APIs. Please switch to XPC or bootstrap_check_in(): com.apple.ReportCrash.DirectoryService
3/17/16 12:00:23.115 PM spindump[855]: Saved wakeups_resource.diag report for prl_vm_app version 11.1.3 (32521) to /Library/Logs/DiagnosticReports/prl_vm_app_2016-03-17-120023_Ians-Computer.wake ups_resource.diag
3/17/16 12:01:54.000 PM syslogd[46]: ASL Sender Statistics
3/17/16 12:04:56.007 PM Microsoft Excel[8906]: Stream 0x80d34d20 is sending an event before being opened
3/17/16 12:04:56.008 PM Microsoft Excel[8906]: Stream 0x80d34d20 is sending an event before being opened
3/17/16 12:06:49.610 PM com.apple.backupd[10194]: Finished scan
3/17/16 12:06:49.827 PM com.apple.backupd[10194]: Saved event cache at /Volumes/IanTimeMachine/Backups.backupdb/Ians-Computer/2016-03-17-115157.inProg ress/767A0214-6F2C-4A29-8F77-FCF0E9657633/.F1B66153-5854-3901-AE43-765B142B5CF8. eventdb
3/17/16 12:06:49.869 PM com.apple.backupd[10194]: Not using file event preflight for Macintosh HD
3/17/16 12:07:55.316 PM com.apple.backupd[10194]: Will copy (165.7 GB) from Macintosh HD
3/17/16 12:07:55.396 PM com.apple.backupd[10194]: Found 4350 files (165.7 GB) needing backup
3/17/16 12:07:56.118 PM com.apple.backupd[10194]: 190.01 GB required (including padding), 160.84 GB available
3/17/16 12:07:56.205 PM com.apple.backupd[10194]: Error: Error Domain=NSOSStatusErrorDomain Code=-36 "ioErr: I/O error (bummers)" deleting backup: /Volumes/IanTimeMachine/Backups.backupdb/Ians-Computer/2016-03-13-214423
3/17/16 12:07:56.236 PM com.apple.backupd[10194]: Error: Error Domain=NSOSStatusErrorDomain Code=-36 "ioErr: I/O error (bummers)" deleting backup: /Volumes/IanTimeMachine/Backups.backupdb/Ians-Computer/2016-03-14-044139
3/17/16 12:07:56.292 PM com.apple.backupd[10194]: Error: Error Domain=NSOSStatusErrorDomain Code=-36 "ioErr: I/O error (bummers)" deleting backup: /Volumes/IanTimeMachine/Backups.backupdb/Ians-Computer/2016-03-14-161406
3/17/16 12:07:56.381 PM com.apple.backupd[10194]: Error: Error Domain=NSOSStatusErrorDomain Code=-36 "ioErr: I/O error (bummers)" deleting backup: /Volumes/IanTimeMachine/Backups.backupdb/Ians-Computer/2016-03-15-005023
3/17/16 12:07:56.415 PM com.apple.backupd[10194]: Error: Error Domain=NSOSStatusErrorDomain Code=-36 "ioErr: I/O error (bummers)" deleting backup: /Volumes/IanTimeMachine/Backups.backupdb/Ians-Computer/2016-03-15-070127
3/17/16 12:07:56.435 PM com.apple.backupd[10194]: Error: Error Domain=NSOSStatusErrorDomain Code=-36 "ioErr: I/O error (bummers)" deleting backup: /Volumes/IanTimeMachine/Backups.backupdb/Ians-Computer/2016-03-15-183245
3/17/16 12:07:56.484 PM com.apple.backupd[10194]: Error: Error Domain=NSOSStatusErrorDomain Code=-36 "ioErr: I/O error (bummers)" deleting backup: /Volumes/IanTimeMachine/Backups.backupdb/Ians-Computer/2016-03-16-041012
3/17/16 12:07:56.521 PM com.apple.backupd[10194]: Deleted backup /Volumes/IanTimeMachine/Backups.backupdb/Ians-Computer/2016-03-17-115157.inProg ress/002BF473-24F2-4811-9573-DEE493081253 containing 37 KB; 160.84 GB now available, 190.01 GB required
3/17/16 12:07:56.650 PM com.apple.backupd[10194]: Error: Error Domain=NSOSStatusErrorDomain Code=-36 "ioErr: I/O error (bummers)" deleting backup: /Volumes/IanTimeMachine/Backups.backupdb/Ians-Computer/2016-03-17-115157.inProg ress/B2ABC79D-4E66-498E-BB2E-B3B7E8EAD8B3
3/17/16 12:07:56.654 PM com.apple.backupd[10194]: Error: Error Domain=NSOSStatusErrorDomain Code=-36 "ioErr: I/O error (bummers)" deleting backup: /Volumes/IanTimeMachine/Backups.backupdb/Ians-Computer/2016-03-13-214423
3/17/16 12:07:56.657 PM com.apple.backupd[10194]: Error: Error Domain=NSOSStatusErrorDomain Code=-36 "ioErr: I/O error (bummers)" deleting backup: /Volumes/IanTimeMachine/Backups.backupdb/Ians-Computer/2016-03-14-044139
3/17/16 12:07:56.661 PM com.apple.backupd[10194]: Error: Error Domain=NSOSStatusErrorDomain Code=-36 "ioErr: I/O error (bummers)" deleting backup: /Volumes/IanTimeMachine/Backups.backupdb/Ians-Computer/2016-03-14-161406
3/17/16 12:07:56.665 PM com.apple.backupd[10194]: Error: Error Domain=NSOSStatusErrorDomain Code=-36 "ioErr: I/O error (bummers)" deleting backup: /Volumes/IanTimeMachine/Backups.backupdb/Ians-Computer/2016-03-15-005023
3/17/16 12:07:56.669 PM com.apple.backupd[10194]: Error: Error Domain=NSOSStatusErrorDomain Code=-36 "ioErr: I/O error (bummers)" deleting backup: /Volumes/IanTimeMachine/Backups.backupdb/Ians-Computer/2016-03-15-070127
3/17/16 12:07:56.672 PM com.apple.backupd[10194]: Error: Error Domain=NSOSStatusErrorDomain Code=-36 "ioErr: I/O error (bummers)" deleting backup: /Volumes/IanTimeMachine/Backups.backupdb/Ians-Computer/2016-03-15-183245
3/17/16 12:07:56.679 PM com.apple.backupd[10194]: Error: Error Domain=NSOSStatusErrorDomain Code=-36 "ioErr: I/O error (bummers)" deleting backup: /Volumes/IanTimeMachine/Backups.backupdb/Ians-Computer/2016-03-16-041012
3/17/16 12:07:56.682 PM com.apple.backupd[10194]: Error: Error Domain=NSOSStatusErrorDomain Code=-36 "ioErr: I/O error (bummers)" deleting backup: /Volumes/IanTimeMachine/Backups.backupdb/Ians-Computer/2016-03-17-115157.inProg ress/B2ABC79D-4E66-498E-BB2E-B3B7E8EAD8B3
3/17/16 12:07:56.682 PM com.apple.backupd[10194]: Removed 1 expired backups so far, more space is needed - deleting oldest backups to make room
3/17/16 12:07:56.684 PM com.apple.backupd[10194]: Deleted 1 backups containing 37 KB total; 160.84 GB now available, 190.01 GB required
3/17/16 12:07:56.684 PM com.apple.backupd[10194]: Backup date range was shortened: oldest backup is now Mar 17, 2016
3/17/16 12:07:56.703 PM com.apple.backupd[10194]: Backup failed with error 7: Not enough available disk space on the target volume.