Why would Bison out-compete the elk and drive them to extinction yet k1/alpha is less than k2 and also k2/beta is also less than k1??? I thought this was to be an unstable co-existence, could someone explain please?
So am I correct in thinking that Lotka-Volterra interspecific competition modelling cannot be depicted by a sigmoid curve? I know that these equations are modifications of the logistic equation for intraspecific competition, so does that mean sigmoid curves do not describe interspecific competition at all? Thank you for explaining these equations so well!
I was so panicky because I had to read the chapter for class for tomorrow and take an online chapter quiz tonight and I didn't understand a word of this in the textbook. Thank you so so much! You've no idea how much you've helped me ! Also quick question the equation you had was dN1/dt=r1N1 [k1-(N1+aN2/k1).. i was wondering how this is different to where the k1 in the numerator is replaced by a 1. Because the equation I have in my textbook is dN1/dt=r1N1 [1-(N1+aN2/k1) . Just wondering what the difference is?thank you!
Hi Farah - Glad it helped! Those equations are mathematically identically, just simplified differently (however you do have one of your parentheses in the incorrect spot, so what those!). If you want to prove it to yourself, just plug in any values for those variables and you should come up with the same answer. Because these equations are derived from the logistic population growth model, it depends on whether you expressed that model as rN(1-K/N) or rN((K-N)/K). Note that those are also the exact same expression (see 5:30ish). Our textbook used the forms of the equation that I included in the video which is why I stuck with those. Regardless of which form you use, just be sure to watch your parentheses and +'s and -'s. I see so many students come up with the wrong answers because of simple math errors. Good luck!
For question 2, say initial population was given, how do would you know if the initial coexistence of the two species stable or unstable? or would it be stable because the two species will coexist anyway
Thank you for this video! I was wondering if you could explain the maths for working out the population sizes of the coexisting fish? I can't get my head around it! I've drawn the graph and can see the numbers are right, but I can't get them from the equations somehow!
Jack Bedford Hi Jack - To find the fish population sizes you need to find the intersection of the two lines. One way to do this is to solve for N1 and then N2 (or vice a versa). For example: N1=K1-αN2 N2=K2-βN1 N1=K1-α(K2-βN1) N1=1500-0.5(500-0.25N1) N1=1500-250+0.125N1 N1=1250+.125N1 0.875N1=1250 N1=1428 bluegill Now plug that into the N2 equation: N2=500-(0.25*1428) N2=143 small mouth bass (Sorry - it won't let me use subscripts in a comment!)
Jennifer Olson Hi Jennifer thanks for getting back to me so quickly! This makes sense, I even tried it before but I think I somehow left out the alpha when I subbed in the equation for N2! Thank you so much again!
@@managerkalamazooconservati8646 Its been 4 years but basically you subsitute -0.125N1 on both sides and since N1 is basically 1 its 1(=N1)-0,125(*N1) so 0.875 N1 is on the left side and then you divide both sides by 0.875 so N1 stands alone and we get the actual Population size by 1250/0.875. I doubt this made sense because im bad at explaining and bad at maths but what ever I tried to understand it myself.
Do we have enough data to simulate the entire world, with all the different species on earth? It would be great to help mankind to build a sustainable world, what do you think?
Hypothetically...but you'd probably need a very large supercomputer! We'd also be challenged by the fact that we haven't even discovered every species, let alone how they compete.
1. You can definitely do this! In fact, I had my students do this as an extra credit problem on their exam. You would need to create some more competition coefficients (effects on species 1 on 3, 2 on 3, 3 on 1, and 3 on 2) which would make the numerators within the parentheses larger. You'd also have to create dN3/dt equation, incorporating those first two competition coefficients , the carrying capacity of 3, and the intrinsic growth rate of 3. Making the graphs by hand, however, would be much more difficult because you would now have a third axis. 2. I think you would have to create a second equation for whichever species had an increase in carrying capacity as a result of the increase in resources. Hope that helps - interesting questions!
I'm taking an accelerated course and my professor blew through this. Thanks for the in-depth explanation. Take care.
this just SAVED my grade thank you
Thank you soooo much! This was really useful! Especially the Lotka-Volterra part when you were explaining chipmunk and squirrel competition :)
i was so lost on isoclines until i watched this, you just saved my ecology mark bless you
I am writing a test tomorrow on this, and you just explained it adequately for me to do better. Thanks
How'd your test go?
I can get an A just by watching your videos.. Thank you so much for making my life easier!
I love u
Seriously u r the angel in my life u made my concept so clear
I have never ever seen such a good explanation
This was super helpful, clear and easy to follow! Thank you!!
Jennifer you are a great teacher!
Wow! Thank you so much such an interesting and easily put lecture! Truly inspiring.
14:00 saved me! This video is so helpful, thank you!
"Overall chipmunk effect" in "squirrel equivalents", for some reason I love those terms! 😆
Thank you for your help, I have an exam later today and you made it very clear and easy to understand. :)
You have a gift for teaching. Thank you!
thanks, but i still dont quiet get it. But it would be good to know the steps for the examples outcome, and to know if the answers wwe get is true
Why would Bison out-compete the elk and drive them to extinction yet k1/alpha is less than k2 and also k2/beta is also less than k1??? I thought this was to be an unstable co-existence, could someone explain please?
So am I correct in thinking that Lotka-Volterra interspecific competition modelling cannot be depicted by a sigmoid curve? I know that these equations are modifications of the logistic equation for intraspecific competition, so does that mean sigmoid curves do not describe interspecific competition at all? Thank you for explaining these equations so well!
thank you! you explained it way better than my professor
Great video and explanation! You are awesome!
Awesome video and good explanation thanks for this video.
can you explain How can we find out unstable or stable coexist using this equations?
17:04, 7:54 9:50 , 10:40
This is super helpful! Thanks!
this video really helped but id love to know if i did the problems right can u post the answers?
Answers will be reposted here soon (6/6/17)
Thanks a lot for the the in-depth explanation. Through the video i wondered if a > B, species 2 will aways
competitively exclude species 1?
I was so panicky because I had to read the chapter for class for tomorrow and take an online chapter quiz tonight and I didn't understand a word of this in the textbook. Thank you so so much! You've no idea how much you've helped me ! Also quick question the equation you had was dN1/dt=r1N1 [k1-(N1+aN2/k1).. i was wondering how this is different to where the k1 in the numerator is replaced by a 1. Because the equation I have in my textbook is dN1/dt=r1N1 [1-(N1+aN2/k1) . Just wondering what the difference is?thank you!
Hi Farah - Glad it helped! Those equations are mathematically identically, just simplified differently (however you do have one of your parentheses in the incorrect spot, so what those!). If you want to prove it to yourself, just plug in any values for those variables and you should come up with the same answer. Because these equations are derived from the logistic population growth model, it depends on whether you expressed that model as rN(1-K/N) or rN((K-N)/K). Note that those are also the exact same expression (see 5:30ish). Our textbook used the forms of the equation that I included in the video which is why I stuck with those. Regardless of which form you use, just be sure to watch your parentheses and +'s and -'s. I see so many students come up with the wrong answers because of simple math errors. Good luck!
Thank you so much again! (and for spotting my math error!)
Can you post the answers
For question 2, say initial population was given, how do would you know if the initial coexistence of the two species stable or unstable? or would it be stable because the two species will coexist anyway
Thanks Jennifer for your very interesting and informative presentation.
Bayangaramaana concept ka 🤟
How did u find the last part of Q2 ?? The remaining numbers ??
How do we compute for the intrinsic growth rate?
What are the answers?
Cate Taverna in the description :)
This video was a life saver- thank you!!!!
Thank you for this video! I was wondering if you could explain the maths for working out the population sizes of the coexisting fish? I can't get my head around it! I've drawn the graph and can see the numbers are right, but I can't get them from the equations somehow!
Jack Bedford
Hi Jack - To find the fish population sizes you need to find the intersection of the two lines. One way to do this is to solve for N1 and then N2 (or vice a versa). For example:
N1=K1-αN2
N2=K2-βN1
N1=K1-α(K2-βN1)
N1=1500-0.5(500-0.25N1)
N1=1500-250+0.125N1
N1=1250+.125N1
0.875N1=1250
N1=1428 bluegill
Now plug that into the N2 equation:
N2=500-(0.25*1428)
N2=143 small mouth bass
(Sorry - it won't let me use subscripts in a comment!)
Jennifer Olson Hi Jennifer thanks for getting back to me so quickly! This makes sense, I even tried it before but I think I somehow left out the alpha when I subbed in the equation for N2! Thank you so much again!
how do you go from N1=1250+.125N1 to 0.875N1=1250 to
N1=1428 bluegill?
@@managerkalamazooconservati8646 Its been 4 years but basically you subsitute -0.125N1 on both sides and since N1 is basically 1 its 1(=N1)-0,125(*N1) so 0.875 N1 is on the left side and then you divide both sides by 0.875 so N1 stands alone and we get the actual Population size by 1250/0.875. I doubt this made sense because im bad at explaining and bad at maths but what ever I tried to understand it myself.
Seriously awesome video.
Hi there! Thanks for the lecture! I still wanna ask if the two populations stabilize when on the isocline?
thankyou so much explaining so well
Wonderful video, thank you!
How to get k1 over alpha and k2 over beta? Help me
Did you ever happen to post solutions to the exercises, particularly the second one?
If you expand the video description by clicking on "SHOW MORE" you will see the answers to the exercises.
Amazing video, good explanation thanks for this!
is there anyone that could help me with this problem pertaining to this video
Do we have enough data to simulate the entire world, with all the different species on earth? It would be great to help mankind to build a sustainable world, what do you think?
Hypothetically...but you'd probably need a very large supercomputer! We'd also be challenged by the fact that we haven't even discovered every species, let alone how they compete.
Thank you so much!! This is really helpful!!
This was so helpful for me, thank you!
HUGE help..thank you!
4:37 - 21:13
So a zero Growth Isocline is the same thing as a Nullcline, right?
That's correct - same thing
Thx, i was confused in alpha beta lol in my book Alpha12 and aplha 21🥴effect of species on each other my professor taught same like you alpha beta
1. What happens with 3 species?
2. What happens if the available resources grow in time? How can we model this?
Thank you very much for the video!
1. You can definitely do this! In fact, I had my students do this as an extra credit problem on their exam. You would need to create some more competition coefficients (effects on species 1 on 3, 2 on 3, 3 on 1, and 3 on 2) which would make the numerators within the parentheses larger. You'd also have to create dN3/dt equation, incorporating those first two competition coefficients , the carrying capacity of 3, and the intrinsic growth rate of 3. Making the graphs by hand, however, would be much more difficult because you would now have a third axis.
2. I think you would have to create a second equation for whichever species had an increase in carrying capacity as a result of the increase in resources.
Hope that helps - interesting questions!
Awesome video!
fantastic video thanks so much!
Flecks class, am I right
Thank you thank you thank you!
It's great! Thanks a lot! ♡
thank you so much for the video!!!!! this is really helpful~~
Thank God for that
so helpful, thank you!!
Ans was species 1 or 2 wins
Thank you
❤
Thank you :)
Cool!
thank you!!
goat
Try to show answers
Just click on "Show More" to see the full video description. The answers have been right there for years ;)
Anyone watch these for fun, like not for a class. I watch these for fun
Statics, statics, statics 😒
ah yes, linear programming
thank you!
You are most welcome! Glad to see students still find this video useful.