Step 1Peel and slice the jicama into one-eighth-inch thick slices. Cut the slices into 1- by 3-inch strips or use a small decorative cookie cutter to cut out shapes. Cover the slices with a damp towel to keep fresh.
Step 2Cut the avocados in half and remove the pits. Scoop the pulp into a medium bowl and mash with a fork. Add the tomato, red pepper, jalapeno, salt and 2 teaspoons lime juice.
Step 3Gently break the crab into small pieces, setting aside a few larger pieces to cut up for garnish. Stir about 1 cup crabmeat into the salad.
Step 4Spoon 1 tablespoon of the salad on each jicama slice and arrange the topped slices on a platter.
Step 5Drizzle the remaining 2 teaspoons lime juice over the canapes. Cut the remaining crabmeat into slivers and place a sliver on top of each canape. Secure one cilantro leaf under each piece of crab. Sprinkle a pinch of cayenne over the top of each and serve.