Ecoknowledge

Ecoknowledge

Some thoughts on ecology, evolution and economics

A Tale of Tails

By far, the most recurring theme in this blog is an exploration of the lopsided nature of evolutionary success – what I have called Haldane’s Rule.  Is this a function of the process of speciation or is it something more mundane – something that we would expect in any branching process?  I have come to the realization that the expectation that species groups should be approximately equal is all wrong.  It is unlikely to happen in a rarely occurring branching process that accumulates over time.

Let’s begin with a coin toss.

coin tossFor any succession of coin tosses, the expected outcome is that half of them will be “heads”. So, for 10 tosses you get a probability curve like this with a maximum value at 5 “heads”.

equal odds

one tenthIf the coin is weighted or you are dealing with some other random outcome with less than equal odds, the peak migrates to one end or the other of the distribution and trails behind it a long tail.  Whenever the expected outcome is equal to one or fewer tosses then all you get is the tail.

For the evolutionary lineages we have been looking at, for example the perching birds. the expected number of branching events is one or less.  This does not rule out the long tail of possible outcomes with many – even hundreds – of branching events.  What you will not find as these lopsided odds get compounded over the eons is an evenly divided group of different kinds of organisms.  You must expect some groups to be much larger than others, even if the tendancy to have many branching events is not handed down through the lineages.  This is entirely because speciation is a rare event and need not be explained by any bias in how species are formed.

As an illustration, I simulated two evolutionary lineages, each of them a taxonomic Class with 5 Orders.  One lineage branched into Families, Genera and Species with a binomial distribution without tails and one lineage branched with the same average frequency but with a long tail.  The results looked like this:

Distribution Orders/Class Families/Order Species/Family Total # of species
Tail 5 11.8 77 4551
No tail 5 5.8 74 2167

The tailed distribution of a rarely occurring event produces the lopsided results that we have been witnessing in the birds, flowering plants and insects. The no tail distribution never produces a lack of branching events – an outcome that is common in all lineages. With a sufficiently long tail, the idea of an incredibly species rich group like the Arthropods – and eventually the beetles is not so very strange.  Indeed, perhaps J.B.S.Haldane should have anticipated God’s fondness for beetles.

22 Responses to A Tale of Tails

  1. I saw that your stephenmccanny.com website may be missing out on approximately 1K visitors daily. Our AI powered traffic system is tailored to increase your site’s visibility: https://ln.run/_s3yp
    We’re offering a free trial that includes 4,000 targeted visitors to show the potential benefits. After the trial, we can supply up to a quarter million targeted visitors per month. This solution could greatly enhance your website’s reach and traffic.

    Permalink
  2. I see that your stephenmccanny.com website could be missing out on approximately a thousand visitors daily. Our AI powered traffic system is tailored to increase your site’s visibility: https://cutt.ly/8eDg5TMA
    We’re offering a free trial that includes four thousand targeted visitors to show the potential benefits. After the trial, we can supply up to 250K targeted visitors per month. This solution could greatly enhance your website’s reach and engagement.

    Permalink
  3. This study was supported by grants from The Swedish Research Council Medicine the Health Research Council in South East Sweden FORSS and ALF grants from the Östergötland County Council viagra priligy ceftin desvenlafaxine succinate er tablet Deutsche Bank sued Indian property firm Unitech last year for the repayment of a loan made in 2007 bya consortium of lenders and also for repayment of 11 millionowed for a related interest rate swap

    Permalink
  4. Medicines that have an adverse physical effect on the blood vessels in the penis those that act on the brain or interfere with the transmission of nerve messages can all cause erectile dysfunction best site to buy priligy In the treatment of benign nodules and nontoxic multinodular goiter TSH is generally suppressed to a higher target e

    Permalink
  5. Thus it may be important to talk to the family about the process of detoxification and dispel their fears and concerns as well as the patient s priligy 30mg tablets

    Permalink
  6. 293 or OS HR 1 priligy online pharmacy What they re really trying to do is to focus on education because everybody realizes as you ve said already education is the thing for providers for patients for authorities to understand that we re not trying to you know make everybody high on cannabis

    Permalink
  7. My Dr told me to start as soon as there is bleeding priligy at walgreens Hi I m sorry to hear about the negative

    Permalink
  8. Opioid is secreted into human milk; in women with normal opioid metabolism normal CYP2D6 activity the amount of opioid secreted into human milk is low and dose dependent; some women are ultra rapid metabolizers of opioid; these women achieve higher than expected serum levels of opioid s active metabolite opioid leading to higher than expected levels of opioid in breast milk and potentially dangerously high serum opioid levels in their breastfed infants that can potentially lead to serious adverse reactions including death in nursing infants Priligy cialis biotech ciprofloxacin tablets In order to provide our users with a better overall experience we ask for more information from Facebook when using it to login so that we can learn more about our audience and provide you with the best possible experience

    Permalink
  9. is reported can you buy priligy online

    Permalink
  10. buy priligy cheap There is increased swelling and such inside the nose in pregnancy which contributes to it

    Permalink
  11. Medicare doesn t cover it can you buy cheap cytotec pill In the ARC ERО± is the dominant ER and levels of ERОІ are negligible 80

    Permalink
  12. C reactive protein decreases expression of thrombomodulin and endothelial protein C receptor in human endothelial cells cost cheap cytotec without a prescription Tamoxifen has been the standard of care for estrogen receptor О± ERО± positive breast cancer in premenopausal and postmenopausal women for over 15 years 1

    Permalink
  13. It is characterized by a burning sensation in the chest where to get generic cytotec

    Permalink
  14. 26 27 Chemotherapy propecias Based on body surface area the high dose is 2

    Permalink
  15. IUI in a stimulated cycle versus IUI in a natural cycle buy augmentin for pets

    Permalink
  16. Hey aare using WordPress ffor your site platform? I’m
    neww to the blog worfld but I’m tryikng too gett started annd set
    up my own. Do yoou requiire any copding expertise tto make your oown blog?

    Anyy help would bee greatly appreciated!

    Permalink
  17. Ahaa, its pleasant iscussion about this article herfe at tthis
    weeb site, I have rerad alll that, sso at this tiome me aalso
    commednting att tjis place.

    Permalink
  18. Howdy! I could have sworn I’ve visited thiis bllog beforfe
    but aftwr browsijg through may oof thhe artiicles I realized
    it’s neww to me. Anyways, I’m certtainly pledased I found it andd I’ll bbe bookmarking it and checking bak regularly!

    Permalink
  19. We’re a gaggle of volunteers and starting a new sheme iin oour community.
    Your web sitte provvided uss with valuable informationn too work on. Yoou hafe done
    ann impressivve job andd our entirre communiyy might be grateful too you.

    Permalink
  20. It’s very effortless tto find ouut any topic oon weeb as compared tto books, as I
    found this poat at thjs wweb site.

    Permalink
  21. Hi, I ddo think this iis a great web site. I stumbleddupon it 😉 I am oing tto revksit yet again sunce I
    book-marked it. Money and freedom iis thhe greatest wayy tto change, may youu bee rich annd conntinue
    tto help others.

    Permalink
  22. I know this web page gives quality depending articles aand extra
    data, is therre aany other web ssite which presents these
    kinhds of things in quality?

    Permalink

Leave a Reply

Your email address will not be published. Required fields are marked *

You may use these HTML tags and attributes:
<a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <cite> <code> <del datetime=""> <em> <i> <q cite=""> <s> <strike> <strong>