If the sequence of numbers doesn't have a gap, how can pictures be missing unless they are from the very beginning or the very end? Recorded files don't just change names randomly if some are yanked out of the midst of them. Once they are recorded with a specific number they stay that way until manually changed by renaming them on a PC. If the photos were moved instead of copied, you'd see a gap in the number sequence, so that's not an option.

My question and comment, beneficial and not a caustic one by the way, is why you would vacation in a great place like Taiwan and put 2500 photos on a single 16GB card and then you even let it out of your possession into the hands of your sister-in-law. Red warning flags everywhere! Your whole trip could have been wiped from existence in one dipstick move by someone else, from losing the single card, from accidentally formatting it, from the card failing, or any number of other goof ups. At the very least you should have been backing up to a 32GB thumb drive every couple hundred shots to protect yourself - or using several $8.00 8GB memory cards to split the trip into daily or couple-day segments between backups. Even locally I never put more than one day's shots on a card before I start over with a fresh card.