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Definitions |
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R0 = Σ lxFx
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Net reproductive rate equation. Multiply the survivorship by the fecundity for each age, then sum across all ages.
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R/C
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The proportion of marked (recaptured) individuals in the sample at time 2, which should equal the proportion marked at time 1.
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M/N
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The proportion of individuals in the population that were marked at time 1.
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dN1/dt = r1N1[(K1 - N1 - αN2)/K1] and dN2/dt = r2N2[(K2 - N2 - βN1)/K2]
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Lotka-Volterra competition equations. Add terms representing interspecific competition.
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Nt = λ^t*N0
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Discrete predictive exponential growth equation.
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f
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Efficiency of turning prey into offspring.
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Ex
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Life expectancy for individuals reaching age x.
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∆N/∆t = B - D
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Continuously breeding population growth equation. Nt+1 - Nt = B - D. dN/dt = b*N - d*N = (b - d)N. Let r = b - d.
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Nx/N0
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Calculation to find Ix.
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D
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Number of deaths during time period.
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N = (M*C)/R
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Mark-recapture method equation. M/N = R/C. Solve for N.
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Nx+1/Nx
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Calculation to find Sx.
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r = b - d
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Instantaneous growth rate/intrinsic growth/per capita.
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N1 = K1 - αN2 and N2 = K2 - βN1
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Equilibrium solution equations. Set the Lotka-Volterra equations equal to zero to find the population size (N1 or N2) at which the species is in equilibrium (not increasing or decreasing).
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dN/dt = rN
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Continuous current/conceptual exponential growth equation.
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R0
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Net reproductive rate—the average number of offspring produced by individuals in a population throughout their lifetime. For animals, usually only consider females. Measures growth (>1) or decline (<1) in a population from one generation to the next. Similar to λ.
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I
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Number of immigrants during time period.
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Fx
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Fecundity—the average number of offspring produced by individuals of age x.
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R
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The number recaptured at time 2.
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Nt+1
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Population size at next time period.
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a
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Capture efficiency of predators.
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Nt
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Population size at current time period.
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M
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The number captured and marked at time 1.
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B
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Number of births during time period.
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dP/dt = faNP - dP
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Lotka-Volterra predator model.
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Nx
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The number of individuals surviving to age x.
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Nt+1 = Nt + B - D
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Closed population growth model equation. Used when comparing two different populations.
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N (mark-recapture method)
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The total number of individuals in the population.
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d
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Death rate for predators.
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r
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Prey population growth rate.
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Nt+1 = Nt + rdNt = (1 + rd)Nt
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Discrete breeding population growth equation. Let λ = 1 + rd.
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dN/dt = rN[1 - (N/K)]
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Logistic population growth equation.
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λ
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The finite rate of increase or decrease in a population.
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Sx
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Age-specific survival rate—the probability that an individual of age x will survive to age x + 1. Calculated as Nx+1/Nx.
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dN/dt = rN - aNP
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Lotka-Volterra prey model equation.
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N (Lotka-Volterra predator-prey model)
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Number of prey.
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λ = (Nt + 1)/Nt
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Discrete current/conceptual exponential growth equation.
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Nt+1 = Nt + B - D + I - E
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Open population growth model equation.
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E
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Number of emigrants during time period.
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C
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The total number captured at time 2.
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Nt = e^rt*N0
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Continuous predictive exponential growth equation.
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Ix
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Survivorship—the proportion of individuals that survive from birth (age 0) to age x. Calculated as Nx/N0.
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α and β
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Competition coefficients. α indicates the effect of an individual of species 2 on an individual of species 1. If a competitor of species 2 decreases the survival, growth, and reproduction of species 1 by the same amount as another individual of species 1 would, then α = 1. Intraspecific and interspecific competition have the same effect in this case. If a competitor of species 2 decreases the survival, growth, and reproduction of species 1 twice as much as another individual of species 1 would, then α = 2. Interspecific competition is then stronger than intraspecific competition. The interpretation of β is identical. If both α and β are greater than 1, the two species would not coexist.
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P
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Number of predators.
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