tag:blogger.com,1999:blog-3077210.post5935355435258169123..comments2024-03-28T08:37:58.136+01:00Comments on Limited, Inc.: the mathematical theory of the struggle for lifeRoger Gathmannhttp://www.blogger.com/profile/11257400843748041639noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-3077210.post-16116701366730238972008-02-21T04:03:00.000+01:002008-02-21T04:03:00.000+01:00Wow, S.M. Good explanation. I was translating what...Wow, S.M. Good explanation. I was translating what I understood about the different relations of predator-prey to reflect the fact that they “vary periodically with time” In, Mathematical modeling for the Life Sciences, the author talks about steady states of the system given by the equation, which can change with the number of predators. This is really all I meant. Sorry I wasn’t more specific. I don’t think the model gives us any information about the species type – whether the predator is of a different species than the prey. It is true that the species difference would prevent any mixed states – for instance, Europeans and Amerindians could reproduce, so that messes up applying the model to humans without major modification. <BR/><BR/>But maybe this is why Queneau never finished his work!Roger Gathmannhttps://www.blogger.com/profile/11257400843748041639noreply@blogger.comtag:blogger.com,1999:blog-3077210.post-21313582694276058972008-02-21T03:44:00.000+01:002008-02-21T03:44:00.000+01:00Man is an animal which, if it lives among others o...Man is an animal which, if it lives among others of its kind, requires a master...But then the master is himself an animal, and needs a master.<BR/><BR/>(Kant channeling Kafka, from "history from a cosmopolitan point of view", sixth thesis.)<BR/><BR/>AmieAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-3077210.post-50894676458732112802008-02-21T03:15:00.000+01:002008-02-21T03:15:00.000+01:00Some nitpicks:—the Lotka-Volterra are periodic; ma...Some nitpicks:<BR/>—the Lotka-Volterra are periodic; maybe everyone uses oscillation as a synonym for periodicity these days, but I have to draw the line somewhere.<BR/>—Lotka-Volterra depends on four parameters. I have no idea what you might mean when you say the "oscillation (sic) takes on four states."<BR/>—Depending on the values of the parameters—which are the increase in the prey population <I>sans</I> predators, the decrease in prey population due to predators, the decrease in the predator population due to natural causes, and the increase in predator population due to consuming prey—the prey and predator populations can<BR/>(1) increase and shrink periodically, or<BR/>(2) go extinct, or<BR/>(3) remain constant.<BR/>(3) is a special case that only occurs when the prey population is equal to the predator population death rate divided by the predator population's increase from eating prey, and the predator population is equal to the growth rate of prey divided by the rate at which the predators eat 'em.<BR/><BR/>I don't know why I'm being so cranky. None of this changes your larger point....although since Lotka-Volterra has to do with two difference species, it's application to intraspecies killing seems dubious.<BR/><BR/>Sorry. I either need coffee or a stiff drink. Maybe a little of both? I really hated both diff eqs classes I took, and the thought that someone somewhere is enjoying thinking about them is driving me mad.Scissors MacGillicuttyhttps://www.blogger.com/profile/15547171778193032655noreply@blogger.com