BIO 325: Midterm 2 Equations Flashcards

Terms Definitions
M
The number captured and marked at time 1.
N (mark-recapture method)
The total number of individuals in the population.
R
The number recaptured at time 2.
C
The total number captured at time 2.
M/N
The proportion of individuals in the population that were marked at time 1.
R/C
The proportion of marked (recaptured) individuals in the sample at time 2, which should equal the proportion marked at time 1.
N = (M*C)/R
Mark-recapture method equation. M/N = R/C. Solve for N.
Nt+1 = Nt + B - D + I - E
Open population growth model equation.
Nt+1 = Nt + B - D
Closed population growth model equation. Used when comparing two different populations.
Nt+1
Population size at next time period.
Nt
Population size at current time period.
B
Number of births during time period.
D
Number of deaths during time period.
I
Number of immigrants during time period.
E
Number of emigrants during time period.
dN/dt = rN[1 - (N/K)]
Logistic population growth equation.
Nx
The number of individuals surviving to age x.
Sx
Age-specific survival rate—the probability that an individual of age x will survive to age x + 1. Calculated as Nx+1/Nx.
Nx+1/Nx
Calculation to find Sx.
Ix
Survivorship—the proportion of individuals that survive from birth (age 0) to age x. Calculated as Nx/N0.
Nx/N0
Calculation to find Ix.
Fx
Fecundity—the average number of offspring produced by individuals of age x.
Ex
Life expectancy for individuals reaching age x.
R0 = Σ lxFx
Net reproductive rate equation. Multiply the survivorship by the fecundity for each age, then sum across all ages.
R0
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.
dN1/dt = r1N1[(K1 - N1 - αN2)/K1] and dN2/dt = r2N2[(K2 - N2 - βN1)/K2]
Lotka-Volterra competition equations. Add terms representing interspecific competition.
α and β
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.
N1 = K1 - αN2 and N2 = K2 - βN1
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).
dN/dt = rN - aNP
Lotka-Volterra prey model equation.
N (Lotka-Volterra predator-prey model)
Number of prey.
P
Number of predators.
r
Prey population growth rate.
a
Capture efficiency of predators.
dP/dt = faNP - dP
Lotka-Volterra predator model.
d
Death rate for predators.
f
Efficiency of turning prey into offspring.
dN/dt = rN
Continuous current/conceptual exponential growth equation.
Nt = e^rt*N0
Continuous predictive exponential growth equation.
∆N/∆t = B - D
Continuously breeding population growth equation. Nt+1 - Nt = B - D. dN/dt = b*N - d*N = (b - d)N. Let r = b - d.
r = b - d
Instantaneous growth rate/intrinsic growth/per capita.
λ
The finite rate of increase or decrease in a population.
Nt+1 = Nt + rdNt = (1 + rd)Nt
Discrete breeding population growth equation. Let λ = 1 + rd.
λ = (Nt + 1)/Nt
Discrete current/conceptual exponential growth equation.
Nt = λ^t*N0
Discrete predictive exponential growth equation.
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