d.py

R = 500000 # Region area, in sq. ft
C = 120 # Camera FOV, in degrees
D = 25.3 # Distance from camera to limit, in ft
A = C * D # Area surveyed by camera, to D, in sq. ft

animal = 'cat' # term to use when spitting out the result

V = 3 # Approx. area taken up by a single specimen, in sq. ft
# In this case, a cat. I'm being a bit lenient about size, because
# I know they would rarely be close enough to each other to
# occupy the same space. In the end, this addition to the formula
# doesn't seem to have a very large impact at all. Possibly should
# be removed.

# In this example, my camera of 120 degrees field of view
# surveyed an area to a distance of 25.3 feet (the fence
# in my backyard). I am interested in an estimation of
# 500,000 square feet around me, roughly a 3 block raidus.

sd = [13, 13, 15, 3, 14] # list of sightings, each in feet
aR = R - (V * len(sd)) # region area minus total area taken up by sepcimens, in sq. ft
n = len(sd) # number of sightings, total
maxd = sorted(sd)[-1] # max sighting distance

mapped_distances = {}
covered = 0
unknown = 0

for distance in sd:
    unknown += maxd - distance
    covered += distance
    if distance in mapped_distances:
        mapped_distances[distance] = mapped_distances.get(distance) + 1
    else:
        mapped_distances[distance] = 1

ratio = covered / unknown
percentage_of_sightings = ratio
estimated_population_size = (n / percentage_of_sightings) / (A / aR)
specimen_per_sqft = estimated_population_size / aR

# print results
print(f'\n approximately ~{round(estimated_population_size)} {animal}s in the area\n')