54 Fluctuations in Population Densities Exponential growth can be represented mathematically: N/ t...
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![Page 1: 54 Fluctuations in Population Densities Exponential growth can be represented mathematically: N/ t = (b – d)N N = the change in number of individuals.](https://reader035.fdocuments.in/reader035/viewer/2022062713/56649f4a5503460f94c6c74c/html5/thumbnails/1.jpg)
54 Fluctuations in Population Densities
• Exponential growth can be represented mathematically:
N/t = (b – d)N
• N = the change in number of individuals
• t = the change in time
• b = the average per capita birth rate (includes immigrations)
• d = the average per capita death rate (includes emigrations)
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54 Fluctuations in Population Densities
• The difference between per capita birth rate (b) and per capita death rate (d) is the net reproductive rate (r).
• When conditions are optimal, r is at its highest value (rmax), called the intrinsic rate of increase.
• rmax is characteristic for a species.
• The equation for population growth can be written
/t = rmaxN
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54 Fluctuations in Population Densities
• Real populations do not grow exponentially for long because of environmental limitations.
• Environmental limitations include food, nest sites, shelter, disease, and predation.
• The carrying capacity of an environment (K) is the maximum number of individuals of a species it can support.
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Figure 54.7 Logistic Population Growth
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54 Fluctuations in Population Densities
• The mathematical representation of this type of growth (logistic growth) is:
N/t = r[(K – N)/K]N
• The equation for logistic growth indicates that the population’s growth slows as it approaches its carrying capacity (K).
• Population growth stops when N = K.
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54 Fluctuations in Population Densities
• Per capita birth and death rates usually fluctuate in response to population density; that is, they are density-dependent.
Competition for resources Easier for disease to spread.
• Factors that affect birth and death rates in a population independent of its density are said to be density-independent.
• For example, a severely cold winter may kill large numbers of a population regardless of its density.
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Figure 54.9 Population Sizes May Be Stable or Highly Variable
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54 Population Fluctuations
• Densities of populations that depend on limited resources fluctuate more than those that use a greater variety of resources.
• Why does this make sense?
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54 Population Fluctuations
• Predator–prey interactions generate fluctuations because predator population growth lags behind growth in prey and the two populations oscillate.
Lynx-Hare activity.
• Experiments with Canada lynx and snowshoe hares revealed that the oscillating cycle of their populations was driven by both predation and food supply for the hares.
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Figure 54.11 Hare and Lynx Populations Cycle in Nature (Part 1)
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54 Managing Populations
• A general principle of population dynamics is that the total number of births and the growth rates of individuals tend to be highest when a population is well below its carrying capacity.
• If we wish to maximize the number of individuals that can be harvested from a population, that population should be managed so that its population is far below its carrying capacity.
• Hunting seasons are established with this objective in mind.
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54 Managing Populations
• Populations with high reproductive capacities can sustain their growth despite a high rate of harvest.
• Fish are an example of a population with high reproductive capacity.
High number of eggs produced by each.
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54 Managing Populations
• The whaling industry engaged in excessive harvests that almost caused the extinction of blue whales.
• Management of whale populations is difficult because they reproduce at a low rate.
• Since whales are distributed worldwide, their management is dependent on cooperative action by all whaling nations (which is difficult to achieve).
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54 Managing Populations
• To reduce the size of populations of undesirable species, removal of resources is more effective than large-scale killing.
• By removing resources, the species will have a reduced carrying capacity and therefore lower numbers.
• Killing large numbers of the species would simply reduce them to a population size that grows more rapidly to reach its carrying capacity.
• Conversely, if a rare species is to be preserved, the most important step usually is to provide it with suitable habitat.
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54 Managing Populations
• Humans have introduced many species to new habitats outside their native ranges.
Rabbits in Austrailia Opuntia cactus in Austrailia.
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Figure 54.19 Biological Control of a Pest
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54 Managing Populations
• For many thousands of years, Earth’s carrying capacity for humans was set at a low level by food and water supplies and by disease.
• What caused the increase? Medicine Agriculture Others
• Earth’s carrying capacity is currently limited by: “Waste” removal Willingness to destroy other species.
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Figure 54.20 Human Population Growth