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The relationship between oak trees and squirrels is referred to as a conditional mutualism because it can shift from mutualistic (both parties' benefit) to
The relationship between oak trees and squirrels is referred to as a conditional mutualism because it can shift from mutualistic (both parties' benefit) to predatory depending on ecological conditions. Squirrels eat acorns (the oak's seeds), but they do not eat all of them immediately. They bury some acorns in the ground to store them for later. If a squirrel buries an acorn but never returns to eat it (and if nothing else discovers it and eats it), then that acorn will have a much better chance of surviving to establish a new seedling than it would if it had never been buried. As a result, if squirrels bury and abandon enough acorns, their overall effect on the number of seedlings will be positive, and the oak-squirrel interaction will be mutualistic. On the other hand, if fewer acorns are buried and abandoned, then the overall effect is negative. In this case, the squirrels function as pure seed predators. In the following questions, let C be the event that an acorn is collected by a squirrel, B be the event that the acorn is buried, and A be the event that it is abandoned. In addition, let S be the event that an acorn survives to become a seedling. In addition, let a prime (') indicate the complement of an event (e.g., C' is the event that an acorn is not collected). Finally, let two letters next to each other denote an intersection. For example, CB = (CB) is the event that an acorn is collected and buried. Suppose that in one year, squirrels collect 95% of the acorns produced by a particular population of oak trees. They immediately eat 18% of the acorns that they collect. The remainder are buried, but only 2.3% of the buried acorns are abandoned. The rest of the buried acorns are eventually dug up and eaten. Only 0.5% of acorns that are not collected by squirrels survive to become seedlings (the others become desiccated and die). In contrast, 20% of the acorns that are buried and then abandoned survive to become seedlings. Symbol Value Interpretation P(C) 0.95 probability an acorn will be collected by a squirrel P(C') P(B|C) P(A|CB) P(S|CBA) P(B'|C') P(A'|C'B') P(S|C'B'A') Probability the acorn will not be collected by a squirrel Conditional probability that the acorn will be buried given that it is collected by a squirrel Conditional probability that the acorn will be abandoned given collection and burial by a squirrel Conditional probability that the acorn will survive to germinate given that it was collected, buried, and abandoned Conditional probability that the acorn will not be buried given that it is not collected Conditional probability that the acorn will not be abandoned given that it is not collected and not buried Conditional probability of survival given that the acorn is not collected, buried, or abandoned The following table lists a set of probabilities, all of which were given in the problem or are readily determined by basic probability rules. Please give the value for each probability and briefly explain its biological interpretation, as shown in the first line.
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