##### BIO 325: Midterm 2 Equations
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#### Complete list of Terms and Definitions for BIO 325: Midterm 2 Equations

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