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BIO205H5 (180)
Lecture

intraspecific comp all missing notes from the lecture are added

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School
University of Toronto Mississauga
Department
Biology
Course
BIO205H5
Professor
Maria Arts
Semester
Fall

Description
Intraspecific Population Regulation Outline Density independent growth Density dependent growth Logistic Model Intraspecific competition Types of intraspecific competition Intraspecific competition affects: - growth/development - reproduction -stress - social behavior 1. Density Independent Growth A) Discrete (geometric) growth –Populations that breed over discrete time  intervals (eg. one year period) –All births occur in spring; do a census one year  later after reproduction is complete t N(t) = N(0)   1. Density Independent Growth A) Discrete or geometric population growth t N(t) = N(0)   1 N(1) = N(0)   Eg., if number of females breeding in spring of 2009 = 41 And if number of females breeding in spring of 2010 = 49  = 49/41  = 1.2 1. Density Independent Growth B) Exponential or continuous population growth –If reproduction is continuous, then it is more  appropriate to look at the instantaneous rate of  increase = r –Independent of time periods: smooth curve N(t)/N(0) =   = e or  r = ln • Example: gray squirrel population: r = ln(1.2) = 0.18 1. Density Independent Growth What is r? b = instantaneous birth rate per individual d = instantaneous death rate per individual dN/dt = (b‐d)N = rN dN/dt = rN r = intrinsic rate of increase = rate at which a population grows under ideal conditions Population Growth Reflects the Difference between  Rates of Birth and Death “r” ‐ varies among species ‐ varies among populations ‐ dN/dt = (b‐d)N = rN ‐ Rate of change of a population over time, dN/dt,  is a function of population size N (in rN) Trend: as you go from small towards large animals, the intrinsic rate of  increase declines with increasing size Growth Rates Can Be Used to Predict Population  Sizes • We want an equation to predict population size N(t) under  conditions of exponential growth  N(t) = N(0)e rt    • N (t) = number at time t • N(0) = initial population size at t = 0 • e = base of natural logarithm = 2.72 • r = intrinsic rate of increase in young/time interval • t = number of time intervals (days, years) Calculating Exponential Growth Rate - Whooping cranes were near extinction due to overhunting and habitat destruction Characteristics of population : -small population size -protected from hunting -abundant resources Whooping crane N = 15 birds in 1941 Q1. If there are 425 birds alive in 2004, what is r? N(t) = N(0)ert 425 = 15e r(63) 425/15 = 28.33 = er(63) r = ln(28.33)/63 = 3.34/63 Endangered species: 15 whooping cranes remained in 1941 = 0.053 Calculating Exponential Growth Rate Q2. If the flock in a protected reserve consists of 189 birds, how long will it take the population to double in size? N(t) = N(0)ert 378 = 189e (0.053)t Whooping crane 2 = e(0.053)t ln 2 = 0.053t t = 0.693/0.053 = 13.1 years Endangered species: 15 whooping cranes remained in 1941 Calculating Exponential Growth Rate Q3. What is the discrete growth rate ()? rt N(t) = N(0)e N(t)/N(0) =  r = e Whooping crane  = e 0.053  1.05 Endangered species: 15 whooping cranes remained in 1941 Density Independent Growth • Birth and death rates are influenced by density‐ independent factors, regardless of the number of  individuals • abiotic factors 2. Density Dependent Growth r = (b‐d) K = carrying capacity (depends on habitat and species) dN/dt = rN(K – N) K dN/dt = rN(1 – N/K) N/K = environmental resistance The Logistic Model of Population Growth • The logistic model of  population growth dN/dt = rN(1 – N/K)  • When N is low relative to K,  the term (1 – N/K) is close to  1.0: population growth  follows exponential model  (rN) • As N approaches K, the term  (1 – N/K) approaches zero:  population growth slows  down and falls to 0 • Should N exceed K,  population growth becomes  negative and N declines back  toward K The Logistic Model of Population Growth When the population is small (N
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