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University of Toronto Mississauga
Maria Arts

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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