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Population Growth and Life Tables

by: Jesse McDonald

Population Growth and Life Tables Biology 286

Marketplace > Purdue University > Biology > Biology 286 > Population Growth and Life Tables
Jesse McDonald

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Summarizes population growth and effects
Introduction to Ecology and Evolution
Dr. Josh Springer
Class Notes
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This 5 page Class Notes was uploaded by Jesse McDonald on Saturday February 13, 2016. The Class Notes belongs to Biology 286 at Purdue University taught by Dr. Josh Springer in Spring 2016. Since its upload, it has received 32 views. For similar materials see Introduction to Ecology and Evolution in Biology at Purdue University.


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Date Created: 02/13/16
Population Growth     Population Growth:  ● Individuals are added to a population through births and immigration.  ● Individuals leave the population through death and emigration.  ● An open population has immigration and emigration.  ● A closed population does not have or has a very low level of immigration and emigration  that doesn’t influence growth. = isolated    Individuals Move within the Population:  ● Dispersal is the movement of individuals.  ● Generally implies the movement of individuals away from one another.  ● Movement of individuals between subpopulations is an important part of metapopulation  dynamics:  ○ It maintains gene flow between the subpopulations.   ● Migration could be daily or seasonal.    Population Distribution and Density Change in Both Time and Space:  ● Dispersal can affect the spatial distribution of individuals within a population.   ● Species introduced into an area where they did not previously live can expand into new  areas.  ○ These introductions may be intentional or unintentional.  ● Invasive species­ organisms successfully introduced to places they have never  occurred, freed from the constraints presented by their predators, parasites, and  competitors in their native ranges. Many species have become established and spread.   ○ Sometimes the introduced species are harmless, but more often than not, they  have negative effects on native species and ecosystems.   ○ Unintentional introductions often happen through the importation of agricultural  and forest products.   ○ Humans have intentionally introduced nonnative plants for ornamental and  agricultural purposes:  ■ Many examples in North America:  ● Purple loosestrife ­ introduced from Europe, it has spread into the  wetlands, eliminating many native plants.  ● Australian paperbark tree ­ introduced as an ornamental plant in  Florida, it has displaced many native species.  ● Kudzu ­ an ornamental vine that has spread throughout the  southern United States, outcompeting many other plants.  ○ Aquatic environments have also been affected:  ■ More than 139 nonnative aquatic species have invaded the Great Lakes  through shipping.  ■ The San Francisco Bay Area has 96 nonnative invertebrate species.  ■ Introduction of exotic fish are responsible for 68% of recent fish  extinctions in North America.     Population Growth Reflects the Difference between Rates of Death and Birth:   ● We can create simple mathematical model to describe how a population changes with  time:  ○ Example:Hydra​in an aquarium  ■ Closed population  ■ Most reproduction is asexual by budding  ■ Assume all reproduce asexually and all have one offspring at a time  ○ The population will not be diverse.   ● N = number of individuals in a population  ● t= time  ● N(t)= number of individuals in the population at a given time.   ● Assume the initial population size is 100 at time zero  ○ N(0) = 100  ● Budding will produce n​Hydra =  births  ● Some ​Hydra will die  ● B = number of new​ydra​produced each day  ● D = number of​ydra that die each day  ● To calculate the new population size, add the births and subtract the deaths.   ○ N(0) + B ­ =N(1)  ○ If you wanted to calculate the population for day two, you cannot use the same  population numbers.   ● Obviously the actual number of births and deaths depend on population size.   ○ An estimate that is independent of population size can be expressed as a rate,  rather than an absolute number.  ○ To determine the per capita birt​ ate, b ■ b =B/N(1)  ○ To determine the per capita birt​ ate, d ■ d = D/(1)  ● If we assume thab and  are constant, they can be used to predict the growth of a  population.   ● Therefore, the population on a given day can be represented by the equation:     N(t+1) = (t + b(t ­ d(t)    This represents a geometric population growth pattern               Life Tables     Life Tables:  ● A ife tabl​is an age­specific account of mortality  ● Ecologist use life tables to examine systematic patterns of mortality and survivorship  within populations.  ● Life tables can follo​ohort, a group of individuals in a population born in the same  period of time.  ○ Insurance companies use these types of data on us also!   ● Age­specific mortalitd_x ­ is the difference between the number of individuals alive for  any age class and the next older age class:  ○ d = n_0 ­ n_1   ● Age­specific mortality ra q_x­ is determined by the number of individuals dying  during a given time interval (d_x), divided by the number alive at the beginning of that  interval.   ● A mortality curve plots mortality rates (q_x) against age  ● For example, the gray squirrel: there are two distinct parts in the life history:  ○ A juvenile phase when mortality is high  ○ A post juvenile phase when mortality rate decreases with age to a point, then  increases again.      Dynamic Life Tables:  ● A cohort, odynamic​, life table shows the fate of a single group of individuals born at a  give time from birth to death.  ○ A dynamic composite life table is constructed from individuals born over several  time periods, not one.  ● A time­specific (static) lifis constructed by sampling a population in  way that  obtains a distribution of individuals.  ● The assumptions for a time­specific life table:  ○ Each age class sampled in proportion to its numbers in the population.  ○ Age­specific birthrates are constant over time.  ○ Age­specific mortality rates are constant over time.   ● Life­tables for long­lived vertebrates almost always have overlapping generations.  ● Some animals, especially insects, live only one breeding seasons so generations do not  overlap.   ● Three general types of curves:  ○ Type I ­ strongly convex ­ survival rate is high throughout the lifespan, with most  mortality at the older ages.  ○ Type II ­ straight ­ survival rates do not vary much with age.  ○ Type III ­ concave ­ mortality is very high early in life.      *The gray squirrel example would follow the Type II curve.   ● Age­specific mortality rates and age­specific birth­rates can be combined to project  future changes in the population.  ● In most life tables, we follow the females.  ○ The females form the reproductive units of the populations.   ● A population projection tableprojects the growth of a population using information  from a life table and fecundity table.  ● S_x is age­specific survival:  ○ S_x = 1 ­ q_x   ● Survivorship and fecundity are determined in the same way for each successive year.    Age­Distribution:  ● The proportion of individuals in each age class for any one year can be calculated from a  population projection table.   ○ Divide the number in each age class (x) by the total population size for that year,  N(t).  ● The finite multiplication r​ lambda = N(t+1) / N(t)   ○ Initially lambda varies from one year to the next, but once a stable age  distribution is reached, lambda is constant.     Finite Multiplication Rate:  ● if lambda = 1.0  ○ the population size is constant  ● if lambda > 1.0   ○ the population size is growing  ● if lambda < 1.0  ○ the population size is declining    Stochastic Processes Can Influence Population Dynamics:  ● Environmental stochasticity is the random variation in the environment that can influence  birthrates and death rates in a population. This variation can be a result of:  ○ Annual variations in climate:  ■ Temperature and precipitation  ○ Natural disasters:  ■ Fire, flood, drought, etc.        


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