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14.2-Measuring and Modelling Population Change Carrying capacity: maximum number of organisms that can be sustained by available resources over a given period of time Population dynamics: changes in population characteristics determined by natality, mortality, immigration and emigration Fecundity: the potential for a species to produce offspring in one lifetime Births, deaths, immigration and emigration can be used to calculate changes in population size Population size= [(births + immigration)-(deaths + emigration)]/initial population size x100 Open population: a population in which change in number and density is determined by births, deaths, immigration and emigration Closed population: a population in which change in size and density is determined by natality and mortality alone Biotic potential: the maximum rate a population can increase under ideal conditions Geometric growth: a pattern of population growth where organisms reproduce at fixed intervals at a constant rate Can be determined by comparing the population size in one year to the population size at the same time the previous year λ= N(t+1)/N(t) Exponential growth: a pattern of population growth where organisms reproduce continuously at a constant rate dN/dt= rN per capita growth rate (r) o difference between the per capita birth rates and the per capita death rates population size (N) Logistic growth: a model of population growth describing growth that levels off as the size of the population approaches its carrying capacity dN/dt= rmaxN[(K-N)/K] dN/dt population growth at a given time rmax maximum per capita growth rate N population at a given time K carrying capacity of the environment The curve formed by the logistic growth pattern on a graph has three distinct phases: Lag phase: the initial stage in which population growth rates are slow as a result of small population size Log phase: the stage in which population growth rates are very rapid Environmental resistance: any factor which limits a population’s ability to realize its biotic potential when it nears or exceeds the environment’s carrying capacity Stationary phase: the phase in which population growth rates decrease as the population size reaches the carrying capacity and stabilizes Dynamic equilibrium: the condition of a population in which the birth rate equals the death rate and there is no net change in population size Practice Problems: 1a) 32,000 – 29,000= 3,000 3,000 + 50,000= 53,000 53,000/50,000= 1.06 The geometric growth rate is 1.06. 1b) N(2)= 53,000 x 1.00 = 56,180 N(10)= 50,000 x (1.06)10 = 89,542 The population size after two years will be 56,180 and 89,542 after 10 years. 2a) 980 x 0.345= 338 The initial instantaneous growth rate of the population is 338 per day. 2b) 0.69/0.345= 2 The doubling time for the population is 2 days. 2c) 11 doubling times (22 days) will have to pass in order for the population to exceed 2,000,000. 3) r max 1.00 1.00 1.00 1.00 1.00 1.00 Population size N 20 200 500 900 990 1,000 ((K-N)/K) 980/1,000 800/1,000 500/1,000 100/1,000 10/1,000 0 Population growth rate 19.6 160 250 90 9.9 0 4) The maximum growth rate influences the relationship between population size and the environment’s carrying capacity because it leads to an increase in population growth rate. Section Questions: 1) population: 34, births/migration: 57+20+4, deaths/emigration: 28+9+11+8 81-56=25 25+34=59 59/34= 1.74 The population growth rate is 1.74. 2) population: 90, births: 342, deaths: 43, emigration: 0, migration: ? 4.29x90=386 342-43=299 386-299=87 87 mice migrated into the field. 3) population: 42, births: 263, deaths: 26+8+12=46 42+263-46=259/42 = 6.2 The population growth rate of the frogs in the ravine from April to August is 6.2. 4a) Exponential growth is occurring. 4b) N(8)= 2x(4.5)8 = 336,302 The number of individuals in the population after eight years is about 336,302. 5a) Exponential growth is occurring. 5b) Factors that would have to be in place for the population to its biotic potential could include enough food supply and a large area of living space. 5c) Types of environmental resistance that might restrict the cats from reaching their biotic potential could include a decrease in food supply and an increase in predation. 7a) population: 198, births: 34, deaths: 86, migrated:12 34+12-86= -40/198 = -0.2 The growth rate of the population is -0.2. 7b) It may be a concern considering almost half of the population of frogs died in the first year. 7c) I do not think that tracking the population growth rate of one population of frogs over one year in this marsh is an adequate to make a conclusion about the environment because of the short time span that they were studied. Many factors could have contributed during the year that may have not been applied in previous years. Other years need to be studied so that they can be compared. 8b) Exponential growth has occurred throughout the generations. 8c) The growth curve of the graph would differ if there were only three offspring instead of six because the graph would be increasing at a lower rate, however it would still be an exponential graph. 14.3-Factors Affecting Population Change Density-dependent factor: a factor that influences population regulation, having a greater impact as population density increases or decreases Intraspecific competition: an ecological interaction in which individuals of the same species of population compete for resources As population density increases, there is more competition so the growth rate slows Can have an effect on reproductive success Predation: an ecological interaction in which a predator catches and consumes prey Can result in density-dependent regulation of the preferred species of prey (faster prey may escape being killed by the predator) → Some density-dependent factors reduce population growth rates at low rather than high densities Allee effect: density-dependent phenomenon that occurs when a population cannot survive or fails to reproduce enough to offset mortality once the population density is too low If a population is too small, it may be difficult to find mates Some species need a large population density to display social interaction Threatened populations may have low reproductive success If a species has low reproductive rates, they need increased numbers to maintain the population Minimum viable population size: the smallest number of individuals needed for a population to continue for a given period of time Consists of enough individuals to ensure the population can cope with variations in death as well as environmental changes and disasters Varies among species Density-independent factors: factors that influence population regulation regardless of population density Human intervention, extreme weather changes Species may not breed in extreme temperatures Limiting factor: any essential resource that is in short supply or unavailable Determines how much the individual or population can grow → More drastic population growth or decline can result in adverse changes to the habitat or even to the population itself → When the population passes the carrying capacity, the number of deaths increase and the number of births decrease Section Questions: 1) Natality and immigration makes the population bigger because individuals are being added to the total population and mortality and emigration makes the population smaller because individuals are being removed from the population. 2) Density-dependent factors are factors that influence the population regulation which has an impact as population density increases or decreases. Density-independent factors are factors that influence the population regulation regardless of the population density. 3a) density-independent factor 3b) density-independent factor 3c) density-dependent factor 4) A density-independent factor is pollution and a density-dependent factor is disease. These factors could limit the growth of the population. 5a) This is a case of density-dependent regulation 5b) I think that when food supply is on the y-axis and population density is on the x-axis, the slope of the graph is negative because as there is more individuals of the population, there is less food per individual. 7 Food Supply 6 5 4 3 2 1 0