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- https://bio.libretexts.org/Workbench/General_Ecology_Ecology/Chapter_15%3A_Competition/15.2%3A_Intraspecific_(Single_Species)_CompetitionHere x is the size of the population at a given time, r is the inherent per-capita growth rate, and K is the carrying capacity. However, as the population reaches its maximum (the carrying capacity), ...Here x is the size of the population at a given time, r is the inherent per-capita growth rate, and K is the carrying capacity. However, as the population reaches its maximum (the carrying capacity), intraspecific competition becomes fiercer and the per capita growth rate slows until the population reaches a stable size. At the carrying capacity, the rate of change of population density is zero because the population is as large as possible based on the resources available.
- https://bio.libretexts.org/Courses/Gettysburg_College/01%3A_Ecology_for_All/10%3A_Population_modeling/10.04%3A_Overview_of_Population_Growth_ModelsAlthough life histories describe the way many characteristics of a population (such as their age structure) change over time in a general way, population ecologists make use of a variety of methods to...Although life histories describe the way many characteristics of a population (such as their age structure) change over time in a general way, population ecologists make use of a variety of methods to model population dynamics mathematically. These more precise models can then be used to accurately describe changes occurring in a population and better predict future changes.
- https://bio.libretexts.org/Workbench/General_Ecology_Ecology/Chapter_10%3A_Population_modeling/10.3%3A_Overview_of_Population_Growth_ModelsAlthough life histories describe the way many characteristics of a population (such as their age structure) change over time in a general way, population ecologists make use of a variety of methods to...Although life histories describe the way many characteristics of a population (such as their age structure) change over time in a general way, population ecologists make use of a variety of methods to model population dynamics mathematically. These more precise models can then be used to accurately describe changes occurring in a population and better predict future changes.
- https://bio.libretexts.org/Courses/Gettysburg_College/01%3A_Ecology_for_All/15%3A_Competition/15.05%3A_Quantifying_Competition_Using_the_Lotka-Volterra_ModelNote the subscripts on the competition coefficients: α 12 expresses the effect of one member of Population 2 on the growth rate of Population 1; α 21 expresses the effect of one member of Population 1...Note the subscripts on the competition coefficients: α 12 expresses the effect of one member of Population 2 on the growth rate of Population 1; α 21 expresses the effect of one member of Population 1 on the growth rate of Population 2. If we solve for these intercepts, we wind up with the following two coordinates for Population 1: [0, K 1 /a 12 ] (setting x, or the size of Population 1, to 0) and [K 1 , 0] (setting y, or the population size of Population 2, to 0).
- https://bio.libretexts.org/Courses/Gettysburg_College/01%3A_Ecology_for_All/15%3A_Competition/15.02%3A_Intraspecific_(Single_Species)_CompetitionHowever, as the population reaches its maximum (the carrying capacity), intraspecific competition becomes fiercer and the per capita growth rate slows until the population reaches a stable size. At th...However, as the population reaches its maximum (the carrying capacity), intraspecific competition becomes fiercer and the per capita growth rate slows until the population reaches a stable size. At the carrying capacity, the rate of change of population density is zero because the population is as large as possible based on the resources available.
- https://bio.libretexts.org/Workbench/General_Ecology_Ecology/Chapter_15%3A_Competition/15.5%3A_Quantifying_Competition_Using_the_Lotka-Volterra_ModelNote the subscripts on the competition coefficients: α 12 expresses the effect of one member of Population 2 on the growth rate of Population 1; α 21 expresses the effect of one member of Population 1...Note the subscripts on the competition coefficients: α 12 expresses the effect of one member of Population 2 on the growth rate of Population 1; α 21 expresses the effect of one member of Population 1 on the growth rate of Population 2. If we solve for these intercepts, we wind up with the following two coordinates for Population 1: [0, K 1 /a 12 ] (setting x, or the size of Population 1, to 0) and [K 1 , 0] (setting y, or the population size of Population 2, to 0).
- https://bio.libretexts.org/Workbench/General_Ecology_Ecology/Chapter_10%3A_Population_modeling/10.3%3A_Overview_of_Population_Growth_Models/10.3.1%3A_Geometric_and_Exponential_Growth/10.3.1.1%3A_Logistic_population_growthWhen resources are limited populations only grow for a limited amount of time before reaching the maximum size the environment can support, which ecologists call the carrying capacity. This results i...When resources are limited populations only grow for a limited amount of time before reaching the maximum size the environment can support, which ecologists call the carrying capacity. This results in a classic "S"-shaped graph of population size over time, known as a logistic growth curve.
- https://bio.libretexts.org/Courses/Gettysburg_College/01%3A_Ecology_for_All/10%3A_Population_modeling/10.05%3A_Geometric_and_Exponential_Growth/10.5.01%3A_Logistic_population_growthWhen resources are limited populations only grow for a limited amount of time before reaching the maximum size the environment can support, which ecologists call the carrying capacity. This results i...When resources are limited populations only grow for a limited amount of time before reaching the maximum size the environment can support, which ecologists call the carrying capacity. This results in a classic "S"-shaped graph of population size over time, known as a logistic growth curve.
