Tuesday, October 15, 2019

Range expansion shifts clonal interference patterns in evolving populations

While Nikhil was trying to sort out a simulation of Michael Baym's beautiful megaplate experiment, we started wondering about the comparison of effective population size and agents in his (Nikhil’s) individual based model. The struggle was that to 'realistically' simulate this in a CA model would require order 10^10 agents, something that is not feasible. We were looking at something more like order 10^4... so what did that mean? Each CA element was something like 10^6 bugs? If that was the case -- what does 'mutation' mean in terms of our CA model?


Figure 1B from Baym's science paper (link above). The real size is on the order of feet...  that is a LOT of bugs.

What it would mean is that instantly, all 10^6 or so bugs would change their genotype... well, this was clearly crazy wrong :)

So, we started thinking about how populations spread in space (Fisher-like waves), and we found the wonderful body of work from the Gore, Hallatschek and Korolev labs thinking about mutational surfing (essentially at the wave tip there is a changed effective population size so the balance between drift and selection can change)


Image


Formulating a model of (stochastic) mutation dynamics in a Fisher-like wave like those before us yielded known results. For a range of parameters, fixation of mutants can be promoted near the wave front - often called "mutations surfing on a wave".

Image

So far, all this is known. Let's also recall from standard (well mixed) popgen (think Kimura) that depending on the relationship between the average time to establishment of a mutant, and the time to fixation, we can have qualitatively different evolutionary dynamics (e.g. strong selection weak mutation (SSWM) when the time to establishment is far larger than time to fixation; and weak selection strong mutation (WSSM) or strong selection strong mutation (SSSM) when the opposite is true, of if they are comparable). This is where we started to wonder...




we think a lot about strong selection (like in the form of experimental evolution in antibiotics or associated mathematical models of similar systems) and often make the assumption that our dynamics are in the SSWM regime -- but this need not always be the case (in fact, it likely isn't).

So, to really get at this, Nikhil defined a 'clonal interference index' as the log of the ratio of the fixation and establishment time, and calculated this all along the wavefront. What popped out is a pretty fun result: depending where are you on the wave front, you experience qualitatively different evolutionary dynamics.




This is our first real effort working in the range expansion space -- so we are very eager for any feedback (in particular if we've missed key references or if this is already a solved problem!).

Please check out the full preprint on bioRxiv for more details, and drop us a line if you have comments/questions.



29 comments:

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      A MIRACLE TESTIMONY FOR WHAT Dr SAY0 HAS DONE FOR ME!!  
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      Hi Friends i am so glad to writing this article today to tell the world how Dr Sayo cured my HSV VIRUS,i have been detected with HSV-1 AND HSV-2 since five years ago, ever since then my life has been in complete bizarre and agony,i have used so many drugs that was prescribed to me by several doctors,but it didn't cure my HSV VIRUS neither did it reduce the pain,until a certain i was checking for solution in the internet,then miraculously came across Dr Sayo the powerful herbalist that cure numerous individuals HSV-1 AND HSV-2 INFECTION,then i contacted his email: sayoherbalhealer@gmail.com i explained everything to him and prepared a cure that cure my HSV-1 AND HSV-2 disease totally after receiving his herbal medicine, so my friends viewers why wait and be suffer when there is someone like Dr Sayo that can cure any disease HIV/ CANCER/ HEPATITIS B VIRUS, you can contact his via email: (sayoherbalhealer@gmail.com) check his FB page:  https://www.facebook.com/Sayo-Herbal-Healer-100145798345000/ OR visit his websites website; http://sayoherbalhealer.website2.me/  check blog: https://sayoherbalhealer.blogspot.com/  



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  5. I have read so much on Herpes Simplex virus. I hear of reaching clearance, I hear of no cure, I hear of recurrent lesions, poor immune system, poor diet, etc. I just do not know what to believe. I have visited many web pages that seem to sell you their version of removing or enforcing the immune system. Then I hear all the info on therapeutic vaccines as well as prophylactic vaccines and wonder how can that even help me. And I feel so worthless, Glad i came across Doctor Razor article on how to heal HSV forever. Endless Gratitude to doctor Razor for helping me get rid of my Herpes Virus. Reach him on his clinic email drrazorherbalhome@gmail.com
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  7. Its a miracle that I am alive today. I encounter HERPES SIMPLEX VIRUS (HSV1&2) for good four (4) years, six (6) months and Ten (10) days with my calculations, before I met Doctor Razor. I am from New York City ,NY USA,I was affected with herpes simplex virus.  Herpes is a viral infection cause by the Herpes simplex virus, marked by painful, watery blister in the skin or mucus membrane or on the genitals. This was what I suffered for over 4 years. I have visited so many hospitals in Houston for treatment but no improvement. I met Doctor Razor on the internet while I was searching for herpes cure,I read some testimonies about his work. I decided to give  his herbal medication a trial, which have now become a testimony in my life. i am so grateful to God almighty for sending doctor Razor my way when i thought all hope was lost. You too can get cured of herpes Simplex virus, if i could overcome it. Reach out to doctor razor via his clinic email : drrazorherbalhome@gmail.com. Whatsapp his cell phone ON +2349065420442

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  8. A MIRACLE TESTIMONY FOR WHAT Dr SAY0 HAS DONE FOR ME!!  
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  11. Irrespective of receiving daily oral or future injectable depot therapies, these require health care visits for medication and monitoring of safety and response. If patients are treated early enough, before a lot of immune system damage has occurred, life expectancy is close to normal, as long as they remain on successful treatment. However, when patients stop therapy, virus rebounds to high levels in most patients, sometimes associated with severe illness because i have gone through this and even an increased risk of death. The aim of “cure”is ongoing but i still do believe my government made millions of ARV drugs instead of finding a cure. for ongoing therapy and monitoring. ARV alone cannot cure HIV as among the cells that are infected are very long-living CD4 memory cells and possibly other cells that act as long-term reservoirs. HIV can hide in these cells without being detected by the body’s immune system. Therefore even when ART completely blocks subsequent rounds of infection of cells, reservoirs that have been infected before therapy initiation persist and from these reservoirs HIV rebounds if therapy is stopped. “Cure” could either mean an eradication cure, which means to completely rid the body of reservoir virus or a functional HIV cure, where HIV may remain in reservoir cells but rebound to high levels is prevented after therapy interruption.Dr Afrid Herbal Medicine makes me believes there is a hope for people suffering from,Parkinson's disease,Schizophrenia,Cancer,Scoliosis,Fibromyalgia,Fluoroquinolone Toxicity
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  14. Hi Friends i am so glad to writing this article today to tell the world how Dr Sayo cured my HSV VIRUS,i have been detected with HSV-1 AND HSV-2 since five years ago, ever since then my life has been in complete bizarre and agony,i have used so many drugs that was prescribed to me by several doctors,but it didn't cure my HSV VIRUS neither did it reduce the pain,until a certain i was checking for solution in the internet,then miraculously came across Dr Sayo the powerful herbalist that cure numerous individuals HSV-1 AND HSV-2 INFECTION,then i contacted his email: sayoherbalhealer@gmail.com i explained everything to him and prepared a cure that cure my HSV-1 AND HSV-2 disease totally after receiving his herbal medicine, so my friends viewers why wait and be suffer when there is someone like Dr Sayo that can cure any disease HIV/ CANCER/ HEPATITIS B VIRUS, you can contact his via email: (sayoherbalhealer@gmail.com) check his FB page:  https://www.facebook.com/Sayo-Herbal-Healer-100145798345000/ OR visit his websites website; http://sayoherbalhealer.website2.me/  check blog: https://sayoherbalhealer.blogspot.com/  




















    Hi Friends i am so glad to writing this article today to tell the world how Dr Sayo cured my HSV VIRUS,i have been detected with HSV-1 AND HSV-2 since five years ago, ever since then my life has been in complete bizarre and agony,i have used so many drugs that was prescribed to me by several doctors,but it didn't cure my HSV VIRUS neither did it reduce the pain,until a certain i was checking for solution in the internet,then miraculously came across Dr Sayo the powerful herbalist that cure numerous individuals HSV-1 AND HSV-2 INFECTION,then i contacted his email: sayoherbalhealer@gmail.com i explained everything to him and prepared a cure that cure my HSV-1 AND HSV-2 disease totally after receiving his herbal medicine, so my friends viewers why wait and be suffer when there is someone like Dr Sayo that can cure any disease HIV/ CANCER/ HEPATITIS B VIRUS, you can contact his via email: (sayoherbalhealer@gmail.com) check his FB page:  https://www.facebook.com/Sayo-Herbal-Healer-100145798345000/ OR visit his websites website; http://sayoherbalhealer.website2.me/  check blog: https://sayoherbalhealer.blogspot.com/  




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  15. I’m Blessing by name, i was diagnosed with Herpes virus for 3 years, i lived in pain with the knowledge that i wasn’t going to ever be well again i contacted so many herbal doctors on this issue and wasted a large sum of money but my condition never got better i was determined to get my life back so one day i saw Mr Brown post on how Dr Akuza saved him from the VIRUS with herbal medicine i contacted Dr Akuza. on his email address  (drakuzasolutioncenter@gmail.com)  we spoke on the issue i told him all that i went through and he told me not to worry that everything will be fine again so he prepared the medicine and send it to me through courier service and told me how to use it, after 14 days of usage I went to see the doctor for test, then the result was negative, am the happiest woman on earth now. This testimony is real. thanks to Dr Akuza. God bless you. you can also reach him on his whatsApp number +2348072437003.,

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  16. NATURAL HERBS  AND REMEDIES FOR CURING HIV, HERPES, HPV, HSV1&2, CANCER AND DIABETES I just experienced the wonders of Dr. Kham herbs. God will continue to bless you Dr. Kham more abundantly for the good work you are doing in people's life by curing them from different types of diseases. I will keep on testifying about your good work. I was diagnosed with herpes 6 months ago and my doctor told me that there is no cure. I did not believe him and I keep my faith up hoping that one day I will be cured from this horrible disease. One day I saw a post on the Herpes Virus Blog forum about a herbal doctor called Dr. Kham on how he cures people from diseases with his herbs and I quickly contacted Dr. Kham on his email explained my problem to him and he told me not to worry that he is going to cure me and truly he prepared the cure and sent it to me through UPS and gave me instructions on how to take it. After two weeks of taking the herbal Medication, I went to my doctor for a checkup and my results showed Negative and my doctor told me that there is no trace of herpes in my body and the virus is completely gone from my body. Everybody at the clinic rejoices with me and they all ask for Dr. Kham contact. You can contact Dr. Kham on his email: dr.khamcaregiver@gmail.com or add whats-app +2348159922297  and you can get in touch with him on his website: https://drkhamherbalhealingcenter.wordpress.com/   or https://drkhamcaregiver.wixsite.com/drkhamcaregiverherba , He also have herbs medicine to cured the following diseases: [eczema], [urethra wart], [chronic problems], [Herpes], [Cancer], [Als], [Hepatitis], [Diabetes], [HPV], [Infertility/PCOS Infections] , [ulcer  ETC......

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  17. Am Laura Mildred by name, i was diagnosed with Herpes 4 years ago i lived in pain with the knowledge that i wasn't going to ever be well again i contacted so many herbal doctors on this issue and wasted a large sum of money but my condition never got better i was determined to get my life back so one day i saw Mr. Morrison Hansen post on how Dr. Emu saved him from Herpes with herbal medicine i contacted Dr. Emu on his Email: Emutemple@gmail.com we spoke on the issue i told him all that i went through and he told me not to worry that everything will be fine again so he prepared the medicine and send it to me and told me how to use it, after 14 days of usage I went to see the doctor for test,then the result was negative, am the happiest woman on earth now thanks to Dr. Emu God bless you. Email him at: Emutemple@gmail.com Whats-app or Call him: +2347012841542 

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  19. hello everyone here i want to tell the whole world about Dr AKIOYA herbal mixture cream ...Dr AKIOYA penis enlargement herbal cream in Africa.This is the only Male Penis Enlargement Cream has been used by men around the world like USA,CANADA,AUSTRALIA,BELGIUM,SWEDEN,GERMANY,UK,SINGAPORE,MALAYSIA AND SO MANY MORE supplement that has been PROVEN to-enlarge your penis – safely, quickly, and importantly – PERMANENTLY.Full Dr AKIOYA Penis Enlargement Cream when used will Increase in penis length by 1-5 inches Increase in penis width by 20%helps in preventing Premature Ejaculation.Achieved longer, rock hard erections All gains in penis length and width are 100% permanent Full AKIOYA Penis Enlargement Cream is also:100% Herbal, 100% Safest with no side effect and its of two types I have the one for enlargement and for reduction and your advised to use it by message 100% Satisfaction and Money Back Guarantee. DR. AKIOYA , About my products i have herbal cream and oil 100% Permanent Guaranteed resulting it on your body where you feel you want to reduce or enlarge which will help you to be strong and you get the desirable size you want-within 3-5 days and when you get your desirable size you are advised to stop using it and the results you gain will remain permanent We also do deliveries all over AFRICA, and worldwide so i would like to know first when do you need the product.for more information call or whatsapp Dr.AKIOYA +2348105257464 email drakioya17spellhome@gmail.com or visit his website http://drakioyaherbalcenter.home.blog
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  20. just wanna say a big thank you patrice cythia for introducing me to Dr Akioya the great HERBALIST that helped me prepare home remedies that cured my herpes simplex virus (HSV1&2) I was infected with herpes for the past two years and i was not happy all day so i was desperate to get a cure so that i can live normal and get healthy. One day i was less busy so i decided to make latest research on herpes cure and i found a site were everyone was talking about Dr Akioya and has ability to cure Herpes, HIV, HPV, Cancer, ALS, COPD, Anthrax, genital wart, cold sore, Arthritis skin tag and all manners of diseases and virus. So i discussed with cythia and she explained to me that its very easy working with Dr Akioya so i contacted Dr Akioya via email dr.akioya17spellhome@gmail.com and he helped me just as he has helped others now I am now cured from herpes am very happy now. and i can also assure you that he can also help you. so if you need the service of DR Akioya kindly contact him drakioya17spellhome@gmail.com. or whatsapp +2348105257464.He can also cure so many sickness

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  21. just wanna say a big thank you patrice cythia for introducing me to Dr Akioya the great HERBALIST that helped me prepare home remedies that cured my herpes simplex virus (HSV1&2) I was infected with herpes for the past two years and i was not happy all day so i was desperate to get a cure so that i can live normal and get healthy. One day i was less busy so i decided to make latest research on herpes cure and i found a site were everyone was talking about Dr Akioya and has ability to cure Herpes, HIV, HPV, Cancer, ALS, COPD, Anthrax, genital wart, cold sore, Arthritis skin tag and all manners of diseases and virus. So i discussed with cythia and she explained to me that its very easy working with Dr Akioya so i contacted Dr Akioya via email dr.akioya17spellhome@gmail.com and he helped me just as he has helped others now I am now cured from herpes am very happy now. and i can also assure you that he can also help you. so if you need the service of DR Akioya kindly contact him drakioya17spellhome@gmail.com. or whatsapp +2348105257464.He can also cure so many sickness

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  22. I want to share this wonderful testimony to the Good people all over the world on how I was able to Enlarge my Penis by Dr. Aziba. I was living a shameful life from my young age, just last month as I was browsing on the internet about Penis size  and Enlargement Products, I saw a testimony of a Man called Tim James testifying of how he was able to get his penis Enlarged by Dr. Aziba and I decided to also Email Dr. Aziba for my small penis size and he quickly respond to me and gave me the normal instructions which i did and then he shipped the product to me here in the united state which i received in just 3 working days and today i am very happy because i started seeing positive changes in my penis size in just 7 days of use.  Dr Aziba herbal product is the best recommended for you and to whom ever suffering from this shame or having any other diseases as well should Contact this great herbal doctor via his Email : Priestazibasolutioncenter@gmail.com and WhatsApp Him on +2348100368288

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  23. I want to share this wonderful testimony to the Good people all over the world on how I was able to Enlarge my Penis by Dr. Aziba. I was living a shameful life from my young age, just last month as I was browsing on the internet about Penis size  and Enlargement Products, I saw a testimony of a Man called Tim James testifying of how he was able to get his penis Enlarged by Dr. Aziba and I decided to also Email Dr. Aziba for my small penis size and he quickly respond to me and gave me the normal instructions which i did and then he shipped the product to me here in the united state which i received in just 3 working days and today i am very happy because i started seeing positive changes in my penis size in just 7 days of use.  Dr Aziba herbal product is the best recommended for you and to whom ever suffering from this shame or having any other diseases as well should Contact this great herbal doctor via his Email : Priestazibasolutioncenter@gmail.com and WhatsApp Him on +2348100368288

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  24. i want to tell the whole world of great Herbalist herbal mixture CREAM. i was unhappy ever since my girlfriend back then in college mocked me of having a small penis and weak in bed ,ever since then i have been trying to improve my sex life but all effort failed ..but it got worse when i got married ,my wife was so angry with me and Threatened to leave me if i do not find a way out and i love my wife so much, so one faithful day i was reading some comments on a blog then i saw a comment of someone testifying of how Herbalist Dr helped him enlarge his penis and Fertilize his sperm count so i quickly contacted him by his email and he got back to me and i did as he said ..to my greatest surprise i got 10 inches within two weeks of using his herbal mixture cream and now its just 3 weeks i am having 10.5 inches i am so happy now..my wife told me am so much good in bed now all thanks to OGODO herbal mixture cream for saving my marriage and disgrace. NOTE: he also cure sicknesses and diseases like
    PENIS ENLARGEMENT ERECTILE DYSFUNCTION DIABETES type 1 and type 2 HERPES GENITAL WART
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