by johnnydeep » Mon Feb 01, 2021 8:54 pm
neufer wrote: ↑Mon Feb 01, 2021 6:54 pm
orin stepanek wrote: ↑Mon Feb 01, 2021 5:25 pm
johnnydeep wrote: ↑Mon Feb 01, 2021 4:26 pm
My questions are in which direction were the two hares/rabbits going - to the trees or from them? And how close in time were their paths?
EDIT: actually I can now see that one path was from one of the trees and one path was toward the other one. And I guess it could even have been the same rabbit/hare!
Big feet probably a Jackrabbit--Hare went to trees on right & came back from trees on Left! Or it could be different ones!
https://en.wikipedia.org/wiki/Lotka%E2%80%93Volterra_equations wrote:
<<The Lotka–Volterra equations, also known as the predator–prey equations, are a pair of first-order nonlinear differential equations, frequently used to describe the dynamics of biological systems in which two species interact, one as a predator and the other as prey. The populations change through time according to the pair of equations:
where:
- x is the number of prey (for example, rabbits);
y is the number of some predator (for example, foxes);
t represents time;
α, β, γ, δ are positive real parameters describing the interaction of the two species.
The Lotka–Volterra system of equations is an example of a Kolmogorov model, which is a more general framework that can model the dynamics of ecological systems with predator–prey interactions, competition, disease, and mutualism. The Lotka–Volterra models have been used to explain the dynamics of natural populations of predators and prey, such as the lynx and snowshoe hare data of the Hudson's Bay Company and the moose and wolf populations in Isle Royale National Park.>>
Thanks, neufer. I also found this pic from
https://www.wildernessawareness.org/art ... -and-sign/, which shows the direction of travel:
[quote=neufer post_id=310460 time=1612205669 user_id=124483]
[float=left][img3="Snowshoe hare tracks."]https://i.pinimg.com/originals/d6/af/a1/d6afa19e45323b6406a73e640676ce71.jpg[/img3][img3="Snowshoe hare tracks across the Sun & their lynx to an 11yr cycle."]https://upload.wikimedia.org/wikipedia/commons/thumb/e/e1/Sunspot-bfly.gif/990px-Sunspot-bfly.gif[/img3][img3=Numbers of snowshoe hare (yellow, background) and Canada lynx (black line, foreground) furs sold to the Hudson's Bay Company. Lynx eat snowshoe hares.]https://upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Milliers_fourrures_vendues_en_environ_90_ans_odum_1953_en.jpg/660px-Milliers_fourrures_vendues_en_environ_90_ans_odum_1953_en.jpg[/img3][/float][quote="orin stepanek" post_id=310458 time=1612200331 user_id=100812]
[quote=johnnydeep post_id=310453 time=1612196794 user_id=132061]
My questions are in which direction were the two hares/rabbits going - to the trees or from them? And how close in time were their paths?
EDIT: actually I can now see that one path was from one of the trees and one path was toward the other one. And I guess it could even have been the same rabbit/hare![/quote]
Big feet probably a Jackrabbit--Hare went to trees on right & came back from trees on Left! Or it could be different ones! :wink: [/quote][quote=https://en.wikipedia.org/wiki/Lotka%E2%80%93Volterra_equations]
<<The Lotka–Volterra equations, also known as the predator–prey equations, are a pair of first-order nonlinear differential equations, frequently used to describe the dynamics of biological systems in which two species interact, one as a predator and the other as prey. The populations change through time according to the pair of equations:
[img3=""]https://wikimedia.org/api/rest_v1/media/math/render/svg/eba353633616971f427b13e175bfbdb1b99bcff0[/img3]
where:
[list][b] x is the number of prey (for example, rabbits);
y is the number of some predator (for example, foxes);
t represents time;
α, β, γ, δ are positive real parameters describing the interaction of the two species.[/b][/list]
The Lotka–Volterra system of equations is an example of a Kolmogorov model, which is a more general framework that can model the dynamics of ecological systems with predator–prey interactions, competition, disease, and mutualism. The Lotka–Volterra models have been used to explain the dynamics of natural populations of predators and prey, such as the lynx and snowshoe hare data of the Hudson's Bay Company and the moose and wolf populations in Isle Royale National Park.>>[/quote]
[/quote]
Thanks, neufer. I also found this pic from https://www.wildernessawareness.org/articles/rabbit-tracks-and-sign/, which shows the direction of travel:
[img2]https://static.wildernessawareness.org/wp-media/uploads/2020/03/zw-bound-variations-drawing-web.jpg[/img2]