To estimate the daphnia population in a 10-gallon tank, a method involves using a small clear container, like a 10ml test tube, to sample the water. By covering the container and submerging it to count the daphnia, multiple samples (10-15) should be taken from various locations in the tank to ensure randomness. The counts from these samples are then averaged to find the mean. For example, if the mean count is 8.2 daphnia per sample, the total population can be estimated by multiplying this mean by the total volume of the tank in liters (approximately 39.3 liters). This results in an estimated daphnia population of about 32,226 in the tank.