POPULATION GROWTH AND REGULATION 1. Populations vary in size over time due to a number of factors some natural, some created. Births, deaths, and environmental conditions are examples of natural factors that can affect a population. Sometimes the allotted space is just not big enough or there are not enough resources to support a larger population, and the species growth levels off resulting in a logistic growth. Logistic model combines two ecological processes: reproduction and competition. Both processes depend on population numbers or density.

logistic growth curve can be described by the logistic growth equation: ?N = rN ? K N ?t K Where: ?N the change in number of individuals ?t the change in time r the rate of increase in number of individuals b natality; the average per capita birth rate d mortality; the average per capita death rate N the number of individuals K carrying capacity Here the population can just plateau or we could begin to see a decline. The biological assumption in this equation is that each individual added to the population makes things slightly worse for the others because it competes for available resources. Population growth stops when N = K because then (K N) = 0, so (K N) N = 0, and ?N / ?t=0. As (K N) approaches 0, the population is near carrying capacity and the growth rate of the population slows down considerably. The growth rate of the population can be determined by calculating the slope of the curve at the point in interest. In our example, starting population size is 20.

### The Essay on Modeling Population Growth

... this term decreases the population (n.p.). This is the logistic model of growth. In the model using exponential growth (the logistic growth) the individuals are not limited ... birth rate is the constant of proportionality and depends on several factors: The proportion of animal population that will mate The number of ...

Carrying capacity (K) 500. Natality is 2, mortality 0,25. With assumption that only females can produce, and they numbered a half of population, (b m) N0 =0,75. Let us compile a chart to illustrate calculation: t rN dN K-N/K N 0 20 1 15,00 14,40 0,96 34,40 2 25,80 24,02 0,93 58,42 3 43,82 38,70 0,88 97,12 4 72,84 58,69 0,81 155,82 5 116,86 80,44 0,69 236,26 6 177,20 93,47 0,53 329,73 7 247,30 84,22 0,34 413,94 8 310,46 53,43 0,17 467,38 9 350,53 22,87 0,07 490,25 10 367,69 7,17 0,02 497,42 11 373,06 1,93 0,01 499,34 12 374,51 0,49 0,00 499,84 13 374,88 0,12 0,00 499,96 14 374,97 0,03 0,00 499,99 15 374,99 0,01 0,00 500,00 16 375,00 0,00 0,00 500,00 17 375,00 0,00 0,00 500,00 18 375,00 0,00 0,00 500,00 19 375,00 0,00 0,00 500,00 20 375,00 0,00 0,00 500,00 21 375,00 0,00 0,00 500,00 22 375,00 0,00 0,00 500,00 23 375,00 0,00 0,00 500,00 24 375,00 0,00 0,00 500,00 25 375,00 0,00 0,00 500,00 The logistic growth equation produces a sigmoidal curve. Population growth slow at first, then accelerates, and finally slows as population size approaches K. 2.

Let us consider factors that limit population density of plants. The most common density-dependent factors are: Food and water supplies A given supply of food and water might be enough for a small plant population density. However, that same supply might not be enough for a high-density population, and competition among the individuals of the population would develop. Light Light is a very common resource needed by plants. A plant density increases those plants that don’t get enough light will not grow strong enough and might even die. Space This is an obvious limiting factor, especially if we think of plants in a forest. Predators Higher densities of a prey plant population attract more predators (locust) and as the number of prey increases, so does the number of predators. On the other hand, if the number of prey decreases, so does the number of predators. Diseases Diseases can certainly have an impact on vegetation and thus affect growth rate.

### The Essay on Student Exploration: Rabbit Population By Season

Vocabulary: carrying capacity, density-dependent limiting factor, density-independent limiting factor, limiting factor, population, population density Prior Knowledge Questions (Do these BEFORE using the Gizmo.) 1. Suppose you had a pet rabbit. What would the rabbit need to stay alive and healthy? Pet rabbits need food, fresh water, a clean living space, and shelter from the elements in order to ...

Since many plant diseases are contagious, they are therefore dependent on density. Parasitism Parasitism is a relationship where one organism the parasite (mistletoe for example), feeds on the tissues or body fluids of another organism the host (tree).

In this type of relationship the parasite benefits and the host is harmed, sometimes to the point of killing the host. Like diseases, since parasites spread easier in a high-density host, their impact depends on the density. There are also limiting factors that don’t depend on the population density. These density-independent factors are abiotic factors such as weather, storms, fires or floods. Any of these factors can have a severe impact on plant population sizes regardless of density..