10 Fascinating Facts about Bess Beetles

10 Fascinating Facts about Bess Beetles The  amiable bess beetles  (family Passalidae)  make great classroom pets, and are fun to watch. Bess beetles are so much more than cute; theyre also some of the most sophisticated bugs on the planet. Dont believe it? Consider these 10 fascinating facts about bess beetles. 1. Bess beetles are important decomposers Passalids live in hardwood logs, munching away on the tough tree fibers and turning them into new soil. They prefer oak, hickory, and maple, but will set up shop in just about any hardwood log that has sufficiently decayed. If youre looking for bess beetles, turn over rotting logs on the forest floor. In the tropics, where bess beetles are more diverse, a single log may house as many as 10 different Passalid species. 2. Bess beetles live in family groups Within their log homes, both bess beetle parents reside with their offspring. With their powerful mandibles, they excavate rooms and passages to house their family. The bess beetle family guards its home against any and all intruders, including other unrelated bess beetles. In some species, a large, extended family of individuals lives together in a colony. This subsocial behavior is quite unusual among beetles. 3. Bess beetles talk Like many other insects – crickets, grasshoppers, and cicadas, for example – bess beetles use sounds to communicate with one another. Whats remarkable, however, is how sophisticated their language seems to be. One North American species, Odontotaenius disjunctis, produces 14 distinct sounds, presumably with different meanings. An adult bess beetle talks by rubbing a hardened part of its hindwings against spines on the dorsal surface of its abdomen, a behavior known as stridulation. Larvae can communicate, too, by rubbing their middle and hind legs against each other. Captive bess beetles will complain loudly when disturbed in any way, and squeak audibly when handled. 4. Bess beetles co-parent their young The vast majority of insect parents simply deposit their eggs and go. A few, like some stink bug mothers, will guard her eggs until they hatch. In fewer still, a parent might stick around long enough to keep her nymphs safe. But rare are the insect parents that remain together as a pair to raise their young to adulthood, and bess beetles are counted among them. Not only do the mother and father bess beetle work together to feed and protect their offspring, but the older larvae stick around to help with rearing their younger siblings. 5. Bess beetles eat poop Like termites and other insects that feed on wood, bess beetles need the help of microorganisms to break down the tough plant fibers. Without these digestive symbionts, they simply couldnt process the cellulose. But bess beetles arent born with these vital fungi and bacteria living in their guts. The solution? They eat their own poop, much like rabbits do, to keep a healthy number of microorganisms in their digestive tracts. Without enough frass in its diet, a bess beetle will die. 6. Bess beetles lay their eggs in nests of poop Baby bess beetles are at an even greater digestive disadvantage, because their mandibles arent strong enough to chew wood and they lack gut microorganisms. So mama and papa bess beetle start their babies out in a cradle made of masticated wood and frass. In fact, when a  bess beetle larva reaches its final instar and is ready to pupate, its parents and siblings work together to construct it a cocoon made of frass. Thats how important poop is to a Passalid. 7. Bess beetles have a lot of nicknames Members of the family Passalidae go by a long list of common names: bessbugs, bessiebugs, betsy beetles, bess beetles, horned passalus beetles, patent leather beetles, peg beetles, and horn beetles.   The many variations on bess seems to derive from the French word baiser, which means to kiss, and is likely a reference to the smooching sound they make when they stridulate. If youve seen one, you already know why some people call them patent leather beetles – theyre quite shiny and black, like patent leather shoes. 8. Bess beetles look menacing, but are surprisingly gentle The first time you see a bess beetle, you might be a bit intimidated. Theyre hefty insects, often well over 3 cm long, with the massive mandibles youd expect from a beetle that eats wood. But rest assured, they dont bite, and dont even grab hold of your fingers with their feet the way scarab beetles do. Because theyre so easygoing and big, they make good first pets for young insect lovers. If youre a teacher interested in keeping insects in your classroom, you wont find one easier to care for and handle than the bess beetle. 9. Most bess beetles live in the tropics The family Passalidae includes roughly 600 described species, and nearly all of them live in tropical habitats. Only four species are known from the U.S. and Canada, and of these, two species havent been seen for decades. Some bess beetle species are endemic, meaning they live only in a certain area, such as on an isolated mountain or a particular island. 10. To date, just a single bess beetle fossil has been found The only prehistoric Passalid known from the fossil record is Passalus indormitus, collected in Oregon. Passalus indormitus dates to the Oligocene epoch, and lived about 25 million years ago. There are no known bess beetles living in the Pacific Northwest today, interestingly. Passalus indormitus is most similar to Passalus punctiger, a living species that inhabits Mexico, Central America, and parts of South America. Sources: Bringing Nature Home: How You Can Sustain Wildlife with Native Plants, by Douglas W. TallamyAmerican Beetles: Polyphaga: Scarabaeoidea through Curculionoidea, Volume 2, edited by Ross H. Arnett, JR, Michael C. Thomas, Paul E. Skelley, J. Howard FrankInsect Behavior, by Robert W. Matthews, Janice R. MatthewsNinety-nine Gnats, Nits, and Nibblers, by May BerenbaumBess Beetles of Kentucky, University of Kentucky Entomology website. Accessed December 10, 2013.Borror and DeLongs Introduction to the Study of Insects, 7th edition, by Charles A. Triplehorn and Norman F. JohnsonEncyclopedia of Entomology, 2nd edition, edited by John L. Capinera.

Moments - Definition of Statistics Terms

Moments - Definition of Statistics Terms Moments in mathematical statistics involve a basic calculation.  These calculations can be used to find a probability distributions mean, variance, and skewness. Suppose that we have a set of data with a total of n discrete points. One important calculation, which is actually several numbers, is called the sth moment. The sth moment of the data set with values x1, x2, x3, ... , xn is given by the formula: (x1s x2s x3s ... xns)/n Using this formula requires us to be careful with our order of operations. We need to do the exponents first, add, then divide this sum by n the total number of data values. A Note on the Term Moment The term moment has been taken from physics. In physics, the moment of a system of point masses is calculated with a formula identical to that above, and this formula is used in finding the center of mass of the points. In statistics, the values are no longer masses, but as we will see, moments in statistics still measure something relative to the center of the values.​ First Moment For the first moment, we set s 1. The formula for the first moment is thus: (x1x2 x3 ... xn)/n This is identical to the formula for the sample mean. The first moment of the values 1, 3, 6, 10 is (1 3 6 10) / 4 20/4 5. Second Moment For the second moment we set s 2. The formula for the second moment is: (x12 x22 x32 ... xn2)/n The second moment of the values 1, 3, 6, 10 is (12 32 62 102) / 4 (1 9 36 100)/4 146/4 36.5. Third Moment For the third moment we set s 3. The formula for the third moment is: (x13 x23 x33 ... xn3)/n The third moment of the values 1, 3, 6, 10 is (13 33 63 103) / 4 (1 27 216 1000)/4 1244/4 311. Higher moments can be calculated in a similar way. Just replace s in the above formula with the number denoting the desired moment. Moments About the Mean A related idea is that of the sth moment about the mean. In this calculation we perform the following steps: First, calculate the mean of the values.Next, subtract this mean from each value.Then raise each of these differences to the sth power.Now add the numbers from step #3 together.Finally, divide this sum by the number of values we started with. The formula for the sth moment about the mean m of the values values x1, x2, x3, ..., xn is given by: ms ((x1 - m)s (x2 - m)s (x3 - m)s ... (xn - m)s)/n First Moment About the Mean The first moment about the mean is always equal to zero, no matter what the data set is that we are working with. This can be seen in the following: m1 ((x1 - m) (x2 - m) (x3 - m) ... (xn - m))/n ((x1 x2 x3 ... xn) - nm)/n m - m 0. Second Moment About the Mean The second moment about the mean is obtained from the above formula by settings 2: m2 ((x1 - m)2 (x2 - m)2 (x3 - m)2 ... (xn - m)2)/n This formula is equivalent to that for the sample variance. For example, consider the set 1, 3, 6, 10. We have already calculated the mean of this set to be 5. Subtract this from each of the data values to obtain differences of: 1 – 5 -43 – 5 -26 – 5 110 – 5 5 We square each of these values and add them together: (-4)2 (-2)2 12 52 16 4 1 25 46. Finally divide this number by the number of data points: 46/4 11.5 Applications of Moments As mentioned above, the first moment is the mean and the second moment about the mean is the sample variance. Karl Pearson introduced the use of the third moment about the mean in calculating skewness and the fourth moment about the mean in the calculation of kurtosis.