Equations
What is the r-k model equation?
R=r(N/K)
Name one of the paradoxes
Levins, Ginzburg, Competition
Who was most influential in making the r-K model mainstream?
Gause
What is the r-K (carrying capacity) formulation of the logistic equation?
Mallet argues that this common textbook formulation obscures the relationship between ecology and evolution.
The author argues that natural selection is essentially the exact same thing as this ecological process?
ecological competition
What is the r-alpha equation?
R=r-αN
What is Levin's paradox?
Double negative:
If rate is negative (r<0) and population is greater than carrying capacity (N>K), the equation goes to infinity instead of decreasing
Who linked carrying capacity to K?
E.P. Odum (1953)
Mallet argues that this common textbook formulation obscures the relationship between ecology and evolution.
r-K (carrying capacity) formulation of the logistic equation?
The r−K model was popularized because it allowed for this "double-pass" method of fitting curves to data—first finding K, then finding r
curve-fitting
What is the Nest Box model?
R=bo-do-bo(N/T)
What is the competition paradox?
In competitive models, the equilibrium is completely independent of growth rate (r)
Who came up with [r = population growth rate] and named it the Malthusian parameter?
Fisher (1930)
In the r-α formulation, equilibrium density K equals this ratio.
r divided by α (K = r/α)?
in this theory there was a trade-off between the two; however, data shows they are often positively correlated
growth rate (r) and carrying capacity (K)
What is Levins' paradox?
when a population’s growth rate (r) is negative and its size (N) is already above the carrying capacity (K)
What is an independent carrying capacity parameter?
reducing r should not affect K, revealing confusion caused by treating K as this.
What were synonymous processes (i.e., essentially the same phenomenon)?
Before World War II, ecological competition and natural selection were widely regarded as this.
According to the paper, using the correct math makes the formation of new species up to ten times more likely
Speciation
According to the author, a "unified Darwinian theory" must treat these three processes as a single, integrated demographic process
competition, natural selection, and speciation
This parameter, introduced in the r-α model, represents the intraspecific crowding coefficient.
What is α (alpha)?
What is K (carrying capacity)?
Under MacArthur’s formulation, fitness at equilibrium was said to be this instead of Fisher’s Malthusian parameter.
What is a single, unified Darwinian theory?
Before modern textbooks separated them, ecology and evolution were originally treated as this kind of unified theory.
What is density-regulated Lotka–Volterra/logistic dynamics?
According to the article, unifying demography, natural selection, and speciation requires modeling them using this shared mathematical framework.
This type of selection occurs when the total population density remains the same during the evolutionary process?
Soft Selection