After 5/11 events for the men and 5/10 events for the women, the following athletes are provisionally in a qualifying position from the World Surf League. Note: athletes from Hawaii are marked with (HAW) as they compete separately in Surfing. I am only including athletes that are qualified to compete on the tour in the selection battle (theoretically an athlete that isn't on tour could qualify for enough events to be selected, but this is unlikely).
Men
(HAW) John John Florence
Kolohe Andino
Filipe Toledo
Jordy Smith
Kanoa Igarashi
Italo Ferreira
Ryan Callinan
Julian Wilson
Michel Bourez
Jérémy Florès
As far as International qualification goes the biggest development is that Leonardo Fioravanti is injured, which means that Ricardo Christie is now the closest challenger to France's second quota. However he has not finished higher than 17th in any competition this season, which makes his chances very low. In practice the biggest threat to France is injury replacement Frederico Morais, who scored a third place in Rio. He is very far behind Florès, having only competed in two events this season, but he has at least showed the potential to get some big results.
American selection battle:
(HAW) John John Florence - 32,160 points
Kolohe Andino - 27,760 points
Kelly Slater - 17,735 points
Conner Coffin - 16,035 points
(HAW) Seth Moniz - 14,610 points
Griffin Colapinto - 7,575 points
(HAW) Sebastian Zietz - 6,510 points
(HAW) Ezekiel Lau - 6,510 points
The American selection battle has been completely shaken up by the news that world number one John John Florence is out for the year with a torn ACL. This means he will finish the year on 33,220 points (taking into account that injured competitors get last place points for every events and that only the best nine results count). This means that Kelly Slater or Connor Coffin will overhaul him if they can maintain good results. Slater, widely considered the GOAT of the sport, would be 48 in Tokyo.
Brazilian selection battle:
Filipe Toledo - 27,195 points
Italo Ferreira - 22,150 points
Gabriel Medina - 16,895 points
Michael Rogrigues - 13,395 points
Deivid Silva - 10,630 points
Wilian Cardoso - 10,630 points
Caio Ibelli - 10,340 points
Yago Dora - 9,565 points
Peterson Crisanto - 9,565 points
Jesse Mendes - 9,565 points
Jadson Andre - 5,585 points
Adriano de Souza - 2,390 points
Filipe Toledo takes a fairly commanding lead thanks to his win in Rio. Ferreira and Medina have maintained the same distance between each other since the last update.
Australian selection battle:
Julian Wilson - 16,810 points
Ryan Callinan - 16,810 points
Wade Carmichael - 14,405 points
Owen Wright - 12,620 points
Jack Freestone - 8,640 points
Adrian Buchan - 7,935 points
Mikey Wright - 6,510 points
Soli Bailey - 5,585 points
Wilson jumps from seventh to second in the Australian selection battle thanks to a third place in Margaret River and a fifth place in Rio. Carmichael falls out of Olympic qualification.
French selection battle:
Michel Bourez - 14,610 points
Jérémy Florès - 14,045 points
Joan Duru - 9,565 points
Bourez takes the lead over Florès while Duru isn't able to make up ground over the top two.
Women
Sally Fitzgibbons
Caroline Marks
Stephanie Gilmore
Courtney Conlogue
Tatiana Weston-Webb
Brisa Hennessy
Johanne Defay
Silvana Lima
Lima slightly increases the gap over Paige Hareb who has still not managed to reach a quarter-final this season
American selection battle (where the real action is on the women's side, the US has 7 of the top 12):
(HAW) Carissa Moore - 31,175 points
Courtney Conlogue - 26,845 points
Caroline Marks - 26,050 points
Lakey Peterson - 26,050 points
(HAW) Malia Manuel - 21,715 points
(HAW) Coco Ho - 15,185
Carissa Moore has established herself as the clear favourite with a third place in Margaret River and a second place in Rio. Lakey Peterson has introduced herself as a contender thanks to her win in Margaret River, in the process becoming the third American to win on tour this season. The American selection battle on the women's side remains the most interesting and high calibre of the lot.
Australian selection battle:
Sally Fitzgibbons - 32,580 points
Stephanie Gilmore - 30,320 points
Bronte Macaulay - 15,185 points
Nikki Van Dijk - 14,960 points
Kelly Andrew - 13.395 points
Macy Callaghan - 9,920 points
Tyler Wright - 5,225 points
Gilmore and Fitzgibbons continue to increase their lead over the rest of the field. At this point it is hard to imagine them failing to qualify baring injury.