The model of the spruce budworm population is approached with a simple description and extensions are considered throughout the paper. It begins with defining and categorizing slow variables and fast variables. The budworm will be a fast variable since it reproduces at a significantly faster rate than a tree. The purpose is to hold the slow variables fixed because we will see little change from them compared to the fast variables over a period of time. However, later in the paper, the dynamic of slow variables will be examined because certain parameters, in particular Kb, depend on the slow variables, which are the tree dynamics. A logistic model is used for B (budworm density),
dB/dt = rbB(1-B/Kb).
At first, it is assumed that Kb is independent of the amount of foliage. It could be argued that the foliage provided by the trees effect the total spruce budworm population that could be sustained, however this assumption is corrected later. Predators are then included in the current model by subtracting a function from the above. This function will be a saturation curve, since birds, the primary predator, only eats until its hunger is satiated. But also, if the worm population is low, the birds will find another food source. Thus the predator function is defined to be ß B2/(α2+B2). Here another assumption is made, ß does not depend on any slow variables, but this is corrected later. The parameters, rb, kb, ß, and α are scaled in order to reduce the number of parameters within the equation. We express the model in terms of R and Q with scaled variable µ.
Basic calculus is required to analyze the above. Since we are interested in the equilibrium of the budworm population, we set dB/dt = 0. The interpretation is the population is n...
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...riod of forest regeneration. However if an outside but common variable, such as disease, kill the trees at a much faster rate, E will be forced to 0 and no regeneration can take place. One could consider another part to the dS/dt or dE/dT equations to represent outside forces that may induce death or growth of trees but this also requires a higher level of biology and mathematics as the equation will become more complex. This particular extension could enlighten the importance of maintaining tree health and why tree diseases should be monitored. I would suggest assuming a saturation curve for the extra term. It will spread more quickly as more trees become infected until the whole forest has been infected, i.e. saturation occurs. This model is a great introduction into population dynamics, single species and extensions of a model that impact the conclusions.
The independent variable was moisture. The dependent variable was the bug’s behavior on which soil the sowbug spent the most time in. The controlled variables were temperature, type of soil, and light intensity.
Moore, M. R., & Vankat, J. L. (1986). Responses of the herb layer to the gap dynamics of a mature beech-maple forest. American Midland Naturalist, 336-347.
4. A) The functions for the problem would look like p=800*0.95*t and 0=50*1.15*t. P represents the pine
This implies that the prey population does not return to some particular equilibrium after deviation. The predation limiting hypothesis involves a density independent mechanism. The mechanism might apply to one prey - one predator systems (Boutin 1992). This hypothesis predicts that losses of prey due to predation will be large enough to halt prey population
The titmouse is a small songbird that searches acrobatically for insects among foliage and branches. The tufted titmouse, also known by their scientific name of baeolophus bicolor, is a widespread species from North America. Because the species is so widespread, it can be assumed that the species is not limited by the biotic and abiotic factors that other species are limited by. The titmouse eats only insects in the summer, including caterpillars, beetles, ants, wasps, stink bugs, and treehoppers; they also eat seeds, nut, and berries. However, every population, or a group of individuals of a single species living in the same general areas, is limited by a carrying capacity, or the maximum population size that a particular environment can sustain. At one point, the biotic or abiotic factors will limit the dispersion and dispersal of the
In creating the Paine killer Spider, the Eco Beaker simulator proved to be a easy and useful way of a conducting the experiment. By randomly selecting parameters for the spiders' eyesight, speed, and reproduction the Spider Division was we able to come up with numbers that would stabilize the ecosystem and allow for the genetically produced spider and aphids to live together harmoniously. In a matter of hours the Spider Division was able to come up with a set of parameters for the Paine Killer Spider that would allow for perfect biological control. While there could be numerous different combinations that could work for the different parameters, the Spider division found that the Paine Killer Spiders' parameters should be set at; 1 meter for sight; 1.
Many old-growth forests across the landscape of northern Lower Peninsula of Michigan contain a mixture of tree species rather than a monoculture. Many researchers have put forward ideas to explain the competition and co-existence of tree species in such communities. A theory explaining competition and co-existence between two species is gap regeneration. Gap regeneration is when a gap is created upon death of a plant individual and a new individual, sometimes of the same species as died and sometimes not dependent on environmental heterogeneity, takes its place (Kenneth Lertzman). Canopy gaps during gap regeneration can be explained by either reciprocal replacement or habitat preference . In a reciprocal replacement, seedlings of one species would be found predominately under large trees ...
2. The metabolic rate for the cricket and (Blaptica dubia) cockroach will be the same when physical stress and ...
The rate equation is in terms of concentration over time and the reaction rate compares the increase/decrease
Perry, D. A. (1998). The Scientific Basis of Forestry, Annual Review of Ecology and System Thematic 29:435-466, Retrieved July 9, 2005 from: http://www.panda.org/about_wwf/what_we_do/policy/policy_and_events/index.cfm
A different scenario takes place when an alien species is transported to a new area. Although direct competition with similar species is still a problem, the new kid in the block may have no natural pests and diseases. Thus, large stands of monocultures can occur. It is generally accepted that one plant species will support 10 species of animals. If one species takes over 99% of a given habitat dozens if not hundreds of species are lost from that area and some populations are stressed enough that extinction is possible.
Environmental issues affect every life on this planet from the smallest parasite to the human race. There are many resources that humans and animal needs to survive; some of the most obvious resources come from the forests. Forests make up a large percentage of the globe. The forests have global implications not just on life but on the quality of it. Trees improve the quality of the air that species breath, determine rainfall and replenish the atmosphere. The wood from the forests are used everyday form many useful resources. Moreover, thinning the forests increases the amount of available light, nutrients and water for the remaining trees. Deforestation (forest thinning) is one of the most critical issues of environmental problems that are occurring today.
Electricity and electrical components are a major part of our lives today. Our lives pretty much come to a halt if there is a power outage or if our electrical devices stop working, sometimes we even start panicking because we are so dependent on these components that we cannot afford to lose them and their importance and use only increases as time passes. We all use these electrical devices and also electricity itself but most of us do not think about the math and physics that works behind all of these things.
Zobel BZ and Talbert JT. 1984. Applied Forest Tree Improvement. New York: Wiley and Sons.
“Thus sustainable development can only be pursued if population size and growth are in harmony with the changing productive potential of the ecosystem (p.