Field of Science

Evolution, sex, and mixability

ResearchBlogging.org
Last Friday Christos Papadimitriou gave a seminar at UC Santa Barbara in the Computer Science department. The title of his talk was Computational Insights and the Theory of Evolution [announcement].

Abstract 
Covertly computational ideas have influenced the Theory of Evolution from the very start. This talk is about recent work on Evolution that was inspired and informed by computation. Considerations about the performance of genetic algorithms led to a novel theory of the role of sex in Evolution based on the concept of mixability, while the equations describing the evolution of a species can be reinterpreted as a repeated game between genes. The complexity of local optimality informs the mystery of variation, and a theorem on Boolean functions helps us understand better the emergence of complex adaptations.

Papadimitriou is a very accomplished computer scientist, a member of the National Academy of Sciences and has written several textbooks and has received many awards.

The work he presented at the seminar was on evolutionary theory. Of the 60 minutes he spoke, he spent the first 30 talking about the science of evolution before Darwin, about the work of Wallace and Darwin, Mendel's work, and then briefly about Fisher, Wright, and Haldane.

Following that he then spoke about Mixability. He met Adi Livnat at Berkeley in 2006, and together they ended up publishing a paper on Livnat's theory of mixability in PNAS in 2008: A mixability theory for the role of sex in evolution [1]. In short, mixability is a theory that states that in sexually reproducing organisms, fitness alone is not what is optimized, but fitness plus population entropy is. What this means is that in addition to fitness, variation (as measured by entropy) is also optimized given the rate of recombination. Recombination introduces genetic variance by mixing the genetic material of two parents (rather than making a clone), and since genetic variance is the fuel of evolution, this is the benefit of sex, so the story goes.

Following this 2008 paper, three more papers have appeared on the same subject by the same two authors (and various others, including Marc Feldman, by the way). Now, the first PNAS paper from 2008 was edited by Dan Hartl. This means that it had a independent editor who sent the paper out for review. (As we shall hear soon, it was sent to six reviewers.) The next three papers appeared in PNAS (2010), Journal of Theoretical Biology (2011), and PNAS (2014) [2-4]. Both of these PNAS papers were contributed by Papadimitriou. Because he is a member of the NAS, he is allowed to contribute four papers per year to PNAS, which means that he acts as the editor, and is thus the person choosing which reviewers to send the paper to for review [source]:
Papers listed as “Contributed” by NAS members (at least one of the authors is an NAS member) account for only 5% of submissions and less than a quarter of published papers. NAS members are only allowed up to four Contributed papers per year. Member-contributed papers must have at least two independent reviews and are evaluated by the Editorial Board.
So only two reviewers chosen by one of the authors, and the editor/author makes the final decision anyway. Hmm. Just saying*...

Anyhow, Papadimitriou's presentation ends, and I eagerly raise my hand to ask my question. Check out this recording of the exhange.
Papadimitriou: I will pray for answers, but please give me your questions.

Me: So, you said you met Adi Livnat in 2006...

Papadimitriou: Yes.

Me: In 2005 there's a paper also in PNAS by Guy Sella and Aaron Hirsch [5]. Are you familiar with this paper?

Papadimitriou: Yes, I am familiar.

Me: They introduced the concept of free fitness analogous to the free energy.

Papadimitriou: Yes.

Me: And that seems to me to be curiously identical to mixability.

Papadimitriou: Not really, no. I mean...

Me: The point is that they update both fitness and entropy at the same time, yes?

Papadimitriou: We have two conclusions that seem to... First of all they came up with [?], supposedly do that. We came to this conclusion 1) through simulations. So, we came up with the concept of mixability, in other words that the alleles that are favored are not the ones that have the best combinations, but the ones that have the best average performance. By analyzing fitness landscapes. Please, when we published our paper we got six reviews. Two of them, they could have been from that group [i.e., Sella and Hirsch]. One of them said that this is well known, and the other one said it is wrong. The point is that once you have to articulate the theory. Let's take Kimura's neutral theory. Of course you'll find hunters in the literature. The point is that theories are cheap. Coming up with a model that says "well we know physics, so let's apply the free energy principle to evolution". The point is that it's the force of argument informed by the theory that eventually becomes the cradle of science.

Me: But you don't even cite them, which is...

Papadimitriou: Yeah, we didn't know at the time. So the second part is where we explicitly say it's a derivation. It's a derivation from the equations of Fisher and Wright. In other words, its a proof. Not a postulation. You understand what I say?   

Me: I Understand what you're saying, but it also rests on the fact that - something that biologists all agree on, which is that variation in a population is a good thing. And it's important for evolution. Without it evolution basically does not work, and you're saying that you are getting that through sex, but you're also ignoring mutations, which you said in the beginning as well. Everybody knows that this is something that happens as well, and especially in the bacterial populations that you were talking about where you said in the beginning that they are all sexual with conjugation and so on. But largely they are not. They are getting a lot of their variation from mutations, and this is known from experimental evolution as well.

[Here the moderator asked us to take it offline.]

Papadimitriou: So, mutations are paramount. Mutations in eukaryotes are also... relevant mutations are relevant. It's like meteorites: its important to understand what happens in everyday evolution, which means the evolution in populations. I'd be delighted to chat with you after the question session.

I did not stick around to talk with him afterwards. I had other obligations, plus I had basically gotten the answers that I was looking for. My conclusion is, based on this presentation and on reading the papers, that the three components at play in mixability
  1. variation drives evolution
  2. sexual reproduction increases variation through recombination
  3. free fitness is what is (attempted) optimized by populations
were already known prior to 2006. Then, showing this mathematically and by simulations is cool. But claiming that you have invented something new is not. And researchers can say that they just didn't know about the previous work, and that may be true, but as I often say, knowing the literature is half the job. Failure to give credit where it's due is egregious, especially if the following papers also do not cite the right source. None of their papers cite Sella and Hirsch**, even though Papadimitriou is familiar with the paper, and even speculated that one of them could have been a reviewer on the first paper from 2006.

On his Berkeley homepage Papadimitriou writes this about the 2008 paper:
There had been no satisfactory explanation of the advantages of sex in evolution, and yet sex is almost ubiquitous among species despite its huge costs. Here we propose a novel explanation: Using standard models, we establish that, rather astonishingly, evolution of sexual species does not result in maximization of fitness, but in improvement of another important measure which we call mixability: The ability of a genetic variant to function adequately in the presence of a wide variety of genetic partners. 
So the claim to novelty remains, and that seemingly includes a rediscovery of epistasis (the genetic interaction between genes)!

As you can also see from this paragraph, the other part of the story is that mixability is touted as an explanation for the evolutionary origin of sex (i.e., recombination). To that I just want to say that if you postulate a model in which there are no mutations, then yes, recombination saves the day, as it is now the only source of variation. However, this is clearly unrealistic in the extreme, and evades the real question, namely how could sex evolve when clonal growth is so much more efficient and asexual populations (which do exist!) have been doing so well since the dawn of time?

Adit Livnat took everyone by storm (I think) by writing the following final paragraph in 2010:
If sex is tied to the nature of genes, then one may reconsider the question of the origin of sex. Although it is common to imagine evolution as an originally asexual process that became sexual at some point, it is possible that sex had existed in a primitive sense of mixing before the emergence of genes as we know them, and that the interaction of sex and natural selection played a role in the shaping of the genetic architecture [2].
In other words - and I also have this from him verbally at the 2014 Evolution conference - Livnat thinks that sexual reproduction came first, followed by asexual reproduction later in the history of life. Papadimitriou mentioned this in his talk as well, saying that there are basically next to no species that are asexual - even bacteria have sex - and those that lost the ability to have sex are evolutionary dead ends. If you think evolution without sex is impossible, I dare you to explain why Lenski's E. coli populations - which do not exchange  genetic material laterally (i.e., between individual cells) - have been successfully evolving and adapting since 1988 [source].

* I am not the only only one who thinks this track for submissions to PNAS has got to go, but do see this article [6] for another take.

** In researching this topic I also learned that the idea of free fitness originates with Iwasa (1988) [7].

Professor
Kyushu University
Department of Biology


References
[1] Livnat A, Papadimitriou C, Dushoff J, and Feldman MW (2008). A mixability theory for the role of sex in evolution. Proceedings of the National Academy of Sciences of the United States of America, 105 (50), 19803-8 PMID: 19073912

[2] Livnat A, Papadimitriou C, Pippenger N, and Feldman MW (2010). Sex, mixability, and modularity. Proceedings of the National Academy of Sciences of the United States of America, 107 (4), 1452-7 PMID: 20080594

[3] Livnat A, Papadimitriou C, and Feldman MW (2011). An analytical contrast between fitness maximization and selection for mixability. Journal of theoretical biology, 273 (1), 232-4 PMID: 21130776

[4] Chastain E, Livnat A, Papadimitriou C, and Vazirani U (2014). Algorithms, games, and evolution. Proceedings of the National Academy of Sciences of the United States of America, 111 (29), 10620-3 PMID: 24979793

[5] Sella G, and Hirsh AE (2005). The application of statistical physics to evolutionary biology. Proceedings of the National Academy of Sciences of the United States of America, 102 (27), 9541-6 PMID: 15980155

[6] Rand DG, and Pfeiffer T (2009). Systematic differences in impact across publication tracks at PNAS. PloS one, 4 (12) PMID: 19956649

[7] Iwasa, Y. (1988). Free fitness that always increases in evolution Journal of Theoretical Biology, 135 (3), 265-281 DOI: 10.1016/S0022-5193(88)80243-1

Do all species form the same way as songbirds?

ResearchBlogging.org
As niches are filled up by new species speciation slows down. Comes to a halt, even. This makes sense, as the niches are ways of life that organisms can have, if there are no other ways of life currently available, thing will stay the same. This is in line with a mode of speciation driven by niches, in accordance with the Ecological Species Concept by Van Valen (1976)* (which is a definition; species is the concept; it should be a criterion**). I'll even go so far as saying that most speciation events can be explained by this framework, though there are some known instances of speciation driven by weird genetic events that cause reproductive isolation, e.g., in European crows.

A recent study uses Himalayan songbirds to show that speciation rates decrease as niches are filled (Price et al., 2014).
Speciation generally involves a three-step process—range expansion, range fragmentation and the development of reproductive isolation between spatially separated populations1, 2. Speciation relies on cycling through these three steps and each may limit the rate at which new species form1, 3. We estimate phylogenetic relationships among all Himalayan songbirds to ask whether the development of reproductive isolation and ecological competition, both factors that limit range expansions4, set an ultimate limit on speciation. 
It's a nice paper - the link between niches and speciation is close to my heart (Østman et al., 2014). Grrlscientist has a nice write-up about it in The Guardian. However, I have to mention that I am taken aback by three things in the above quote from the first lines of the abstract:

1) Generalizing from songbirds to everything else: Speciation is not always about reproductive isolation, and it may certainly not generally work the way it does in Himalayan songbirds. Especially not in asexual organisms.

2) Allopatric speciation (with geographic isolation) may be prominent, but we don't know how much sympatric speciation (without geographic isolation) occurs, so we can't discount it (and theoretically it is easy).

3) Species evolve, they don't develop. So does that mean that reproductive isolation evolves rather than develops? Semantics, I realize, but I think it's important to get this right.

So, fixed:
Speciation in sexually reproducing organisms generally involves a three-step process—range expansion, range fragmentation and the evolution of reproductive isolation between spatially separated populations1, 2. Allopatric speciation relies on cycling through these three steps and each may limit the rate at which new species form1, 3. We estimate phylogenetic relationships among all Himalayan songbirds to ask whether the evolution of reproductive isolation and ecological competition, both factors that limit range expansions4, set an ultimate limit on speciation. 
That'll be $20.

* Best title ever: "Ecological Species, Multispecies, and Oaks." I never get tired of saying this.
** I will also not likely get tired of saying that: Pragmatic definitions in biology.

References

Price TD, Hooper DM, Buchanan CD, Johansson US, Tietze DT, Alström P, Olsson U, Ghosh-Harihar M, Ishtiaq F, Gupta SK, Martens J, Harr B, Singh P, and Mohan D (2014). Niche filling slows the diversification of Himalayan songbirds. Nature, 509 (7499), 222-5 PMID: 24776798.

Østman B, Lin R, and Adami C (2014). Trade-offs drive resource specialization and the gradual establishment of ecotypes. BMC evolutionary biology, 14 PMID: 24885598

A morphological interpretation of traits

Have a look at this short video. Do you think it works?



It is supposed to show that new species form when traits are subject to trade-offs. However, in the actual model, those traits govern resource use, but here they are illustrated as morphological traits: tails, wings, legs, whiskers, ears, and eyes. The traits vary over time, resulting in four different species.

Now that you have watched it, my question is whether the nature of the traits in the model is adequately conveyed? What do you think?

The data is from our new paper, Trade-offs drive resource specialization and the gradual establishment of ecotypes in BMC Evolutionary Biology.

Press:
Evolutionary compromises drive diversity (MSU Today)
Compromise is key to evolving new creatures (Futurity)
A Winged Cat Helps Explain The Principle Of Evolutionary Trade-Offs (io9)
Evolutionary compromises drive diversity (Fox 47 News)

Death of the fittest

This is imho an excessively beautiful figure! I keep staring at it getting thrills, and bliss pours over me as I explore its intricacies. This is evolution.

Click to enlarge.

(You should enjoy this figure while listening to one or several of these:)


What are we looking at? Fitness over time of all individuals in a population of size 100. The blue line is average population fitness. The red line is the lineage that leads to the most fit individual after 100,000 updates.

And the real treasure? All the black lines which are all the other lineages that died out. Only the individuals who descend from the ancestor on the red line are alive near the end (technically, the most recent common ancestor (MRCA) is close to but obviously not quite at the end of the simulation).

We see two interesting facts:
  • Offspring that have deleterious mutations (that decrease fitness) survive for quite a long time, and those individuals even have offspring of their own some times. In fact, we can see that there are even deleterious mutations on the line of descent (the red line goes down on five occasions).
  • Offspring that have beneficial mutations (that increase fitness) don't always survive. In fact, most of them eventually die and those beneficial mutations are lost. Evolution does not imply survival of the fittest.
Deleterious mutations do not prohibit evolution; deleterious mutations hitchhike on the back of beneficial mutations and go to fixation that way (there is no epistasis in this model).

The simulation
I made this simulation in Matlab. Constant population size of 100. Mutation rate of 0.01. Effect of mutations is drawn at random from a uniform distribution of selection coefficients between -0.05 and 0.05. One individual reproduces per computational update (Moran process), and chance of reproducing is proportional to fitness.

73rd Carnival of Evolution: World Cup Edition

Welcome to the 2014 Carnival of Evolution World Cup of evolution blog posts.

We have an exciting post ahead of us today where we will find the winner of the inaugural CoE World Cup. Entered posts will be scored based on several parameters, and matches will be determined probabilistically.

The scoring system works like this:

+1 for mentioning "evolution" or "evolve"
+1 for posts about biological evolution
-1 for saying "develop" or "development" when meaning "evolve" or "evolution"
-1 for being very short
-2 for being very long
0 to +5 points based on the interest of the referee (the CoE host)
+2 for posts about peer-reviewed articles
+4 for posts whose authors clearly present opinions of their own
+1 per picture (up to three) included in the post
+1 for attracting any comments
+1 extra for each original picture (max 3)
+3 for showing videos
+25 for reports on rabbit fossils from the Cambrian
-5 for any hint of panadaptationism
-2 for each logical fallacy
-4 for any mention of aquatic ape theory
-7 for agreeing with Lynn Margulis that everything is endosymbiosis
-3 if talking about the work of others without citation
-5 to -1 for any wrong statements about evolution

19 posts entered into the CoE World Cup, so three posts needs to be eliminated for the round of 16. These were the three lowest scoring posts:

On guenon monkeys using facial recognition to prevent inbreeding.
D-brief. Carl Engelking.
Score = 7

On spiders hiding from predators by looking like bird poop.
Ecologica. Sam Hardman
Score = 8

On Twitter data from the 2014 Evolution conference.

The molecular ecologist. Jeremy Yoder.
Score = 9

The remaining 16 posts were paired up at random and the winner of each match determined randomly, with the probability of winning given by the score. For example, two scores of 10 and 15 will give the posts 40% and 60% chances of winning, respectively.

The following list of the remaining 16 posts have three numbers each: their ID number, their score, and their randomly assigned spot in the round of 16.


This gives us the following schedule of games [spot: post ID (score)]:


Game 1 is between Was Fisher W(right)? (score = 16) and The intricate world of cone snail venoms (score = 12). This gives them chances of winning of 52.1% and 42.9%. The CoE World Cup Random Number Generator™selects.... Was Fisher W(right)? and eliminate

On conus snail venom and how they are administered.
Teaching biology. Marc Srour.


Game 2 is between Is evolution predictable? (score = 15, P = 42.9%) and Wright's Shifting Balance Process (score = 20, P = 57.1%). Two very strong posts. And the winner is Is evolution predictable? and we must say farewell to the top seeded

On, well, Wright's Shifting Balance Theory.
Evolution in Structured Populations. Charles Goodnight.


Game 3 is between The Function Wars: Part I (score = 13, P = 56.5%) and A bizarre blood-sucking Jurassic maggot (score = 10, P = 43.5%). The Function Wars: Part I beats 

On a fossil of an aquatic fly larva from the Chinese mid-Jurassic.
Why evolution is true. Matthew Cobb


Game 4 is between The simulations behind the fitness landscape visualizations (score = 13, P = 46.4%) and Our skulls didn't evolve to be punched (score = 15, P = 53.6%). A win for Our skulls didn't evolve to be punched and a loss to 

On the computational details behind the simulations.
Pleiotropy. Bjørn Østman


Game 5 is between Add it up: the genetic basis of ecological adaptation (score = 17, P = 56.7%) and Spontaneous mutations - friend of foe? (score = 13, P = 43.3). Again the weaker post Spontaneous mutations - friend of foe? beats the odds and sends out

On the genetic and genomic changes that underlie adaptation to divergent environments.
Eco-evolutionary dynamics. Katie Peichel.


Game 6 pits Visualizing coevolution in dynamic fitness landscapes (score = 14, P = 45.2%) against Of Population Structure and the Adaptive Landscapes (score = 17, P = 54.8%). Victorious is Of Population Structure and the Adaptive Landscapes and out is

On the biology of the models behind the video.
BEACON. Bjørn Østman.


Game 7 sees Historical Contingencies at the Birthday Party (score = 12, P = 54.5%) against On Nicholas Wade and the blurring of boundaries between science and fantasy (score = 10, P = 45.5%). A close match where Nicholas Wade and the blurring of boundaries between science and fantasy prevails and goodbye to

On the probability of convergent evolution.
Synthetic Daisies. Bradly Alicea.


Game 8 - the last of the round of 16 - is between The 1984 founder event debate: Its relation to Phase 1 of Wright’s Shifting Balance Process (score = 11, P = 42.3%) and Evolution 2014 (score = 15, P = 57.7%). Somewhat surprisingly The 1984 founder event debate: Its relation to Phase 1 of Wright’s Shifting Balance Process wins this one and sends out

On the distribution of topics at the 2014 Evolution conference.
A great tree. Lewis Spurgin.


And that concludes the round of 16. Some surprises along the way so far. The least likely post to win actually won in 3 out of 8 games, and we had to say goodbye to two of the overall favorites, Wright's Shifting Balance Process and Add it up: the genetic basis of ecological adaptation.

On to the quarter-finals...



The first quarter-final has Was Fisher W(right)? (score = 16, P = 51.6%) versus Is evolution predictable? (score = 15, P = 48.4%). A tough game, but The CoE World Cup Random Number Generator™doesn't hesitate and chooses Was Fisher W(right)? sends out

On the probability to leave descendants based on trees contracted from nucleotide sequences.
Neherlab. Richard Neher.


The second quarter-final is between The Function Wars: Part I (score = 13, P = 46.4%) and Our skulls didn't evolve to be punched (score = 15, P = 53.6%). And the outcome is that The Function Wars: Part I wins and the loser is

On whether humans skulls evolved in response to taking a lot of punches.
Laelaps. Brian Switek.


The third quarter-final is a battle between the surprise post Spontaneous mutations - friend of foe? (score = 13, P = 43.3%) and Of Population Structure and the Adaptive Landscapes (score = 17, P =56.7%). Can the surprise post do it again? Noooo! Of Population Structure and the Adaptive Landscapes wins and there is no more

On measuring mutation rate and mutational effects in yeast.
The molecular ecologist. Ryosuke Kit.


The fourth and last quarter-final has the underdog Nicholas Wade and the blurring of boundaries between science and fantasy (score = 10, P = 47.6%) against The 1984 founder event debate: Its relation to Phase 1 of Wright’s Shifting Balance Process (score = 11, P = 52.4%). By The CoE World Cup Random Number Generator™the winner is Nicholas Wade and the blurring of boundaries between science and fantasy and going home is

On the role of genetic drift in Wright's Shifting Balance Theory.
Evolution in Structured Populations. Charles Goodnight.


That concludes the quarter-finals. We'll take a short break before we begin the semi-finals.

And we're back.



The first semi-final is an exiting match between Was Fisher W(right)? (score = 16, P = 55.2%) and The Function Wars: Part I (score = 13, P = 44.8%). Who will go to the 2014 CoE World Cup final? Aaaand... it's The Function Wars: Part I!!!! The post has done it again. This means goodbye to

On genetic drift and epistasis.
Evolution in Structured Populations. Charles Goodnight.


We now turn to the second semi-final that stands between the favorite Of Population Structure and the Adaptive Landscapes (score = 17, P = 63.0%) and the underdog Nicholas Wade and the blurring of boundaries between science and fantasy (score = 10, P = 37.0%) It's amazing it has made it this far. Let's see how they do today: Of Population Structure and the Adaptive Landscapes wins as expected and sends home

On what science can and cannot comment on.
it is NOT junk. Michael Eisen.


We are thus left with just two posts for the final match that will decide who wins the 2014 Carnival of Evolution World Cup.



It is The Function Wars: Part I (score = 13, P = 43.3%) versus Of Population Structure and the Adaptive Landscapes (score = 17, P = 56.7%). Both posts have played really well so far, surviving some really close calls. Both posts have a lot to offer on evolution, though one is severely disadvantaged by its excessive length. Can The Function Wars: Part I overcome this obstacle today, or will Of Population Structure and the Adaptive Landscapes prevail as most people expect?

The game is on, and it is over before we know it as the CoE World Cup Random Number Generator™ takes a mere 0.000349 seconds to decide that... The Function Wars: Part I is the winner of the 2014 CoE World Cup!!!! What a glorious and surprising victory! The readers go wild!!! In second place we thus have

On fitness landscapes.
Evolution in Structured Populations. Charles Goodnight.

And the winner of the 2014 Carnival of Evolution World Cup is 

On ENCODE and the definitions of function.
Sandwalk. Larry Moran.

Congratulations to the post from Sandwalk and to writer Larry Moran!!!


That concludes the inaugural Carnival of Evolution World Cup 2014.

Come back next month for more blogging about evolution. We still don't have a host, so if you're interested please contact the administrator by email, Facebook, or Twitter. You can submit posts via all three of those as well.

Vertebrate sexual systems

ResearchBlogging.org Awesome figure of the sexual systems used by 2,145 vertebrates species (705 fish, 173 amphibian, 593 non-avian reptilian, 195 avian, 479 mammalian).

Similar figures for plants and invertebrates.


Tree structure is derived from taxonomy, where each tip represents all species in a single genus. 
Diploid chromosome number is indicated by the height of the innermost ring.
The XY/ZW ring is colored blue for XY and red for ZW taxa.
ESD = environmental sex determination.
The ‘Other’ ring includes parthenogenesis, gynogenesis, and hybridogenesis.
Complex SCS indicates species with complex sex chromosome karyotypes (e.g., X1X2Y).

  • All mammals are XY.
  • All birds are ZW.
  • Half-ish of all fish and no other vertebrates are hermaphrodites.
  • Only some fish and some reptiles are environmentally sex determined.

Reference
Ashman, T., Bachtrog, D., Blackmon, H., Goldberg, E., Hahn, M., Kirkpatrick, M., Kitano, J., Mank, J., Mayrose, I., Ming, R., Otto, S., Peichel, C., Pennell, M., Perrin, N., Ross, L., Valenzuela, N., and Vamosi, J. (2014). Tree of Sex: A database of sexual systems Scientific Data, 1 DOI: 10.1038/sdata.2014.15

Video: Visualizing coevolution in dynamic fitness landscapes



The fitness landscape is the framework for thinking about evolutionary processes the same way the phylogenetic tree is how we think about evolutionary history. It can guide our thinking and even enable us to predict outcomes of evolution.

Fitness landscapes are usually depicted and thought of as static, i.e., not changing in time or space, but in reality they change in response to environmental changes. Populations have different fitness in different environments, so changes in both time and space can influence the fitness landscape. For example, releasing chicken on the moon will drastically change their chances to reproduce.

Many papers have been published about fitness landscapes, but with very few exceptions they investigate static fitness landscapes. Exceptions are landscapes that change between two or three different environmental conditions, such as microbes in salty or acidic conditions.

A consistent criticism of studies that look at evolutionary dynamics – the study of evolving populations – is that the fitness landscape is static, and that this is not realistic. But no one knows to what extent natural fitness landscapes change over time. Both the frequency and magnitude of such changes are completely unknown. On the time-scale of significant evolutionary change, do real fitness landscapes experience changes that make any serious difference to how populations evolve? Do they change qualitatively, with peaks coming in and out of existence? Or are the changes merely quantitative, keeping the rank order of fitnesses the same? The former is a possible solution to the problem of how populations can cross valleys between peaks in the fitness landscape: if a population is stuck on a local peak, just wait until the environment changes and leaves an uphill path to new genotypes and phenotypes. But it could very well be that in most cases most of the time populations are stuck in an approximately static landscape. We really don’t know.

And yet, for all the criticism of studies of static landscapes, not much research has been done on evolution in dynamic fitness landscapes.

One environmental factor that can change the fitness landscape of a population is a population of another species. If one species is in any way dependent on another, then there is a potential for the fitness landscape to depend on the other species.

In the video above we present three such cases of coevolution. (Details of the simulations.)

Moth-orchid coevolution. The moth eats nectar from the bottom of the orchid spur. In order to do that, its proboscis needs to be at least as long the orchid’s spur. In this model, the moth therefore gains some fitness if this is true. The more orchids it can feed on, up to a limit, the more fitness it gains. The orchids have a different agenda. They need to get someone to transport pollen from plant to plant so they can be fertilized. The moths can do this for them: when a moth sucks nectar, it touches the male flower parts and some pollen is deposited on the moth, which it carries to the next orchid, where some pollen is deposited on the female flower parts. However, if the moth’s proboscis is longer than the spur, then the moth can suck nectar without coming into touch with pollen. As a result, orchids gain some fitness if their spurs are longer than some or all of the moth’s proboscises. The orchids therefore affect the fitness landscape of the moths, and the moths affect the fitness landscape of the orchids, driving both of them to have longer and longer proboscises/spurs. We visualize this in a two-dimensional phenotype-fitness landscape, where one axis is the proboscis length in the moth landscape (spur length in the orchid landscape), and the other axis is some arbitrary neutral trait that does not affect fitness.

Rock-paper-scissors. The second dynamic fitness landscape is the familiar rock-paper-scissors system. The phenotypes consist of two arbitrary traits, and the three populations are evolving in sympatry, meaning there is no spatial component in the model. Each of the three populations dominate over one of the other two and is inferior to the third. In this model that means that if an organism has the same phenotype as the some members of the population it dominates, then it gains some fitness. The more individual members it has the same phenotype as, the more fitness it gains (density-dependence). Consequently, if this organism has the same phenotype as a member of the population that it is inferior to, then it loses fitness. This system makes the fitness landscape of each population very dynamic, with peaks and valleys appearing and disappearing over time.
Q: Are there any real systems that work like this?

Host-parasite coevolution. The third dynamic fitness landscape is a system with two populations, where the host loses fitness when it shares a phenotype with parasites, and the parasites gain fitness when their phenotypes are the same. The host organism therefore benefits from being different from the parasite, and the parasite benefits from being similar. This results in a situation where the host population evolves away from the parasite phenotype, and the parasite’s population evolves towards the host phenotype. However, it often happens that the parasite population causes the host population to split into two or more subpopulations centered around dissimilar phenotypes. The parasite population will then evolve to climb only one of those peaks, as is always the case when a population of competing organisms is facing two or more peaks. Climbing that peak will cause the host organisms that make up that peak to die out. As a result, the peak disappears, and the parasite population now finds itself dislocated from the surviving host population. Both the host and the parasite populations now have uniform fitness, and they consequently undergo neutral evolution and drifts about in phenotype space. In order to prevent this situation, we have given the parasite population a per-trait mutation rate that is twice as high as the host population. This makes it much less likely that the hosts can escape, because the parasites can now explore a larger area of phenotype space than the host. They move faster around the fitness landscape.

The last model results in two populations that continue to evolve indefinitely. Given enough time they will explore the whole fitness landscape, obtaining all the possible phenotypes. This is arguably open-ended evolution, in that evolution keeps going and populations do not encounter a stopping point. A definition of open-ended evolution requires that the population never reaches a stable phenotype, which in this case it does not. OEE can also be defined to require that new adaptive traits keep appearing, in which case this coevolving system does not qualify. New traits values keep appearing, but after a while they will not be novel, as they will have been attained and then lost in the past.

Some conclusionary words
While these movies are based on actual simulations of a model with two traits, we haven’t really done any science to speak of. Nothing has been measured and no hypotheses have been tested. However, the visualizations could be used as a tool for hypothesis testing and discovery. We can think of videos just as a modern version of the Cartesian coordinate system that enables us to visualize a temporal component (or another spatial component). When populations are seen evolving right in front of your eyes, we can sometimes observe effects that weren’t apparent by any other means.

More about fitness landscapes
Using fitness landscapes to visualize evolution in action
Evolution 101: Fitness Landscapes
Smooth and rugged fitness landscapes
Crossing valleys in fitness landscapes
BEACON Researchers at Work: Holey Fitness Landscapes

Mike Riddle: Does Evolution Have a . . . Chance?

It's all very well to have a degree in mathematics and try and calculate the probability for proteins forming, but if you don't know - or choose to ignore - the current models of how new proteins are made, and instead use your own naîve model involving everything at random, then no wonder you get a very small probability.

But I'm getting ahead of myself. I just read (don't know why, really) an article by Mike Riddle, President of the Creation Training Initiative:


Does Evolution Have a . . . Chance?


Here's the whole things with my comments in red.



One has only to contemplate the magnitude of this task to concede that the spontaneous generation of a living organism is impossible. Yet we are here—as a result, I believe, of spontaneous generation.1
—George Wald, Nobel Laureate
In today’s culture, molecules-to-man evolution is being taught as a fact, even though it is known to “go against the odds.” But few realize the odds they are up against! And they are immense! 
The Bible teaches that God is the Creator of all things (Genesis 1Colossians 1:16John 1:1–3Revelation 4:11). While these passages rule out any possibility of Darwinian evolution, they do allow for variation within a created kind. But there is much opposition to what the Bible teaches. People holding to evolution would argue that random chance events, natural selection, and billions of years are sufficient to account for the universe and all life forms. The fact they they rule out evolution merely means that they are wrong. Evolution - including macroevolution - has been observed.
Do You Believe in “Magic”?
Most people recognize “magic” as an illusionary feat or trickery by sleight of hand. But how far are you willing to go to believe something can happen by “dumb luck” or chance? For example, if I were to role a die and have it come up six three times in a row, would you consider that lucky? How about if I rolled six ten times in a row? Now you might suspect that I am using some trickery or that the die is weighted. It is much more incredulous to believe chance as an explanations than the magic of creationism. (Also, [sic]).
How far are we willing to go to accept something as a chance occurrence or before we recognize that it was just an illusion? We can test this by measuring our credulity factor. Credulity is the willingness to believe something on little evidence.
Measuring Our Credulity Factor against Evolution
Evolutionists state that life originated by natural processes about 3.8 billion years ago. Is there any evidence for this happening? Freeman Dyson, theoretical physicist, mathematician, and member of the U.S. National Academy of Sciences states:
Concerning the origin of life itself, the watershed between chemistry and biology, the transition between lifeless chemical activity and organized biological metabolism, there is no direct evidence at all. The crucial transition from disorder to order left behind no observable traces.2
Since the origin of life has never been observed, this is a major hurdle! Yes, true. It is a darned annoying fact that we cannot directly observe anything that happened in the past. If only we could directly observe murderers in the act, then detective work would be much easier. We are left with the question, “Is the origin of life by naturalistic processes possible?” This can, in part, be tested by examining two areas:
  1. The success of scientists in creating life or the components of a living cell.
  2. The probability that such an event could occur.
We are not really "left with the question" of the origin of life (aka abiogenesis) if we are concerned with evolution. Suppose for a moment that God created life initially - this doesn't rule out evolution following that. Those two things are quite distinct, and even though natural selection plays an important role in abiogenesis, the scientists who work on abiogenesis are different that those who work on evolution, because they require very different areas of expertise. So, if we could never find a scientific solution to abiogenesis, that wouldn't mean that we cannot understand evolution as a natural process (which we do).
The Structural Unit of Living Organisms—The Cell
Protein
Cells are made up of thousands of components. One of these components is protein. Proteins are large molecules made up of a chain of amino acids. In order to get a protein useful for life, the correct amino acids must be linked together in the right order. There are of course many different ways to put together proteins that are useful for life. How easy is this and does it happen naturally? It turns out that this is not an easy process. No, not if your "process" is random chance with nothing else. There are large hurdles that evolutionary processes must overcome in order to build a biological protein.
Protein molecules contain very specific arrangements of amino acids. Even one missing or incorrect amino acid can lead to problems with the protein’s function. Yes, some amino acid changes will mess with protein function, but many changes are neutral and do not change protein function.
Making Mathematics Painless
Before applying mathematics and probability to the origin of life, we need to consider seven parameters that will affect the formation of a single protein.
Amino Acid
First, there are over 300 different types of amino acids. However, only 20 different amino acids are used in life. This means that in order to have life, the selection process for building proteins must be very discriminating. But it didn't necessarily have to be this discriminating in the beginning. 
Second, each type of amino acid molecule comes in two shapes commonly referred to as left-handed and right-handed forms. Only left-handed amino acids are used in biological proteins; however, the natural tendency is for left- and right-handed amino acid molecules to bond indiscriminately.
Third, the various left-handed amino acids must bond in the correct order or the protein will not function properly.3 Again, there is not one correct protein, but a lot of variation, and proteins that doesn't work for one thing can work for another.
Fourth, if there was a pond of chemicals (“primordial soup”), it would have been diluted with many of the wrong types of amino acids and other chemicals available for bonding, making the proper amino acids no longer usable. This means there would have been fewer of the required amino acids used to build a biological protein. But there could have been enough. Plus, the twenty that are currently used could have been a function of those being to most abundant ones. 
Fifth, amino acids require an energy source for bonding.4 Raw energy from the sun needs to be captured and converted into usable energy. Where did the energy converter come from? It would require energy to build this biological machine. However, before this energy converter can capture raw energy, it needs an energy source to build it—a catch-22 situation.5 See the video below. 

Sixth, proteins without the protection of the cell membrane would disintegrate in water (hydrolysis), disintegrate in an atmosphere containing oxygen, and disintegrate due to the ultraviolet rays of the sun if there was no oxygen present to form the protective ozone layer.6
Seventh, natural selection cannot be invoked at the pre-biotic level. The first living cell must be in place before natural selection can function. No, selection works on anything that replicates. Self-replicating molecules like ribozymes are used in laboratory experiments. They are affected by natural selection.
Considering all seven of these hurdles, how probable is it that a single protein could have evolved from a pool of chemicals? Probability outcomes are measured with a value ranging from zero through one. The less likely an event will happen, the smaller the value (closer to zero). The more likely an event will occur, the larger the value (closer to one). Wow, talk about dumbing it down! If you know nothing about the natural processes that are involved, then it does seem very unlikely. But do watch this video to learn one or two things about those processes:



Let’s practice this using a coin. What are the chances of getting a heads when we flip a penny? The answer is 50 percent, or one chance in two (written 1/2). What is the chance of getting two heads in a row? Since each toss is 1/2 we can multiply each occurrence to get the final probability. This would be 1/2 x 1/2 which would equal 1/4 (or one chance in four). Now let’s use some bigger numbers.
When we flip a coin we have two possible outcomes, heads or tails. In this problem, we want to calculate the probability of getting all heads every time we flip a coin. We can use this exercise to test our credulity factor. How many heads in a row are we willing to accept as a chance occurrence? At what point would we suspect an illusion or some form of magic (trickery)? We wouldn't expect magic. Ever. Only godbots do that. We would instead expect some other natural process being involved.
The objective of using probabilities is to demonstrate the probability or chance of getting a certain result. On average, how many times and how often will we need to flip the coin to achieve 100 heads in a row? Over 300 million times a second for over one quadrillion years! If you could only do one trial at a time, then that would take a long time. But if you can do many at the same time in parallel, then you could get one hundred heads very quickly. If we could run just a billion such trials in parallel, then it would only take a million years, which is not long on geological time-scales. (Also, that number is slightly wrong. Only a little over 40 million times per second is needed for a quadrillion (1015) years. - My math is better than yours so I win!!! ;P)
The chances of getting all heads 100 times in a row is similar to the chance of getting 100 left-handed amino acids to form a biological protein. Proteins range in size from about 50 to over 30,000 amino acids. To get a small protein of 100 left-handed amino acids from an equal mixture of left- and right-handed amino acids, the probability would then be 1030 or 1 followed by 30 zeros (1,000,000,000,000,000,000,000,000,000,000). But but but, this is assuming that the process is random (again, it isn't - see the video above). How believable (credulity factor) is it that this could happen by random chance? Also, consider that this has never been observed! We all agree that it hasn't been observed, but we all agree that things that haven't been observed have taken place, right? Like a fallen tree in the forest is assumed to have fallen, even though no one were there to observe it. Chance protein formation has always been accepted as a matter of faith by evolutionists. No, not chance formation. Again, again, see the video. You are ignoring the natural processes that can explain these things.
Number of desired heads in a rowProbabilityNumber of flipsCredulity factor (chance)
11/2 have2Yes / No
21/4 (1/22)4Yes / No
31/8 (1/23)8Yes / No
41/16 (1/24)16Yes / No
51/32 (1/25)32Yes / No
81/256 (1/28)256Yes / No
101/1024 (1/210)1024Yes / No
201/1,048,576 (1/220)1,048,576Yes / No
1001/1030(1/2100)1 followed by 30 zerosYes / No
Ten is pretty good! We can work with ten. Not that we thereby admit that Riddle's puerile model here is the correct one (cause it isn't), but suppose to have a bunch of string of ten heads in a row, then those could be assembled together three at a time to make strings of 30 heads in a row.

But wait, there is more! This number, 1030, only measures the possibility of getting all left-handed amino acids. It does not say anything about their order. In our example, we have a chain of 100 amino acids. Each position can be occupied by any 1 of 20 different amino acids common to living things, and these must be in a specific order to form a functional protein. What is the probability that the correct amino acid will be placed in position number 1 of the chain? It will be 1/20. What is the probability that the first two positions will be correct? This can be calculated by multiplying the two probabilities together (1/20 x 1/20 = 1/202). Therefore, the probability of getting all 100 amino acids in the correct position would be 1/20 multiplied by itself 100 times or 1/20100 (this equates to 1/10130). This is 1 followed by 130 zeros! Which is not how proteins are thought to have formed. See the video above. This is like me saying that the process by which the Bible is written is by randomly stringing letters together. There are 3,566,480 letters in the bible (Bing it yourself), so with 26 different letters that gives a chance of one in 263566480. This is 1 followed by more than 5 million zeros! Therefore the Bible could not have been written by random chance. - Point here being that that is of course not the process by which the Bible was written, just as proteins of length 100 are not assembled by chance.
Coin
Large numbers can be hard to visualize or even comprehend. To put this in picture format we can use a smaller number 1021 (1 followed by 21 zeros). If we were to take 1021 silver dollars and lay them on the face of the earth; they would cover the entire land surface to a depth of 120 feet.7
Are there upper limits for which we can logically expect an event will not occur by random chance? The mathematician Emile Borel proposed 1/1050 as a universal probability bound. This means that any specified event beyond this value would be improbable and could not be attributed to chance.8 Repeat after me: scientists do not attribute random chance to the formation or proteins.
As we can see, the probability of getting a single small protein (1/10130) far exceeds this limit. Even if the protein can interchange amino acids at various positions (such as in the case of the protein cytochrome a),9 the resulting probability still exceeds the limit of 1/1050. So far we have only looked at the probability of getting a single small protein by random chance. What are the chances of getting all the proteins necessary for life? By chance? Negligible. Relevance...? 
No matter how large the environment one considers, life cannot have had a random beginning . . . there are about two thousand enzymes, and the chance of obtaining them all in a random trial is only one part in (1020)2000 = 1040,000, an outrageously small probability that could not be faced even if the whole universe consisted of organic soup.10
Let our conclusion be that life did not have a random beginning (that is, completely random, as described here). 

This number is so large (1 followed by 40,000 zeros) that it staggers the imagination how life could have evolved by natural, random processes. Yet, people continue to hold onto their belief that life did evolve by random chance (high credulity factor). Yes, staggering, I tell you. If you only rely on random processes, which scientists do not. Watch the video above!
Time is in fact the hero of the plot. . . . What we regard as impossible on the basis of human experience is meaningless here. Given so much time, the “impossible” becomes possible, the possible probable, and the probable virtually certain. One has only to wait: time itself performs the miracles.11
Time
This statement attributes supernatural qualities to time! It also allows for anything to happen. This means we are no longer bound by the laws of science or any other natural limits. The statement thus becomes meaningless. You are the one not bound by the laws of science when you think the science says it is all random chance.
Tricks of the Trade
Since scientists have been unable to create life, they are forced to speculate through research and sometimes “sleight of hand” how it might have arrived on earth. Below are some of the tricks of the trade used to avoid the obvious—that God is the Creator of all things (Colossians 1:16). God or Allah or Odin or Zeus or Baal, or whatever. False dichotomy. Also, "speculate though research." *chortle* No, even if we understand natural processes that can create life, we can never know for sure how it actually happened, because all evidence of of has been erased. There are no fossils or anything else left from back then that we can take a direct look at. Too bad. But we can make very informed models by which we can understand abiogenesis. Sorry if this offends your religious sensibilities.

1. It happens naturally

“The formation of biological polymers from monomers is a function of the laws of chemistry and biochemistry, and these are decidedly not random.”12 This is a link to a great discussion on the probability of abiogenesis on TalkOrigins. It is also from 1998, and we have learned a lot since then. See, for example, the video above.

Explanation

This is an incorrect statement. I see nothing incorrect about it! Those laws are really not random!!! If it happens naturally, then why can’t scientists duplicate this in the lab? See video above. Amino acids do not spontaneously bond together to make proteins. First, it takes a source of energy to do this. The Sun or geothermal energy. Second, the natural tendency is to bond left- and right-handed amino acids, but life requires all left-handed amino acids. Third, they must be in the correct order or the protein will not function properly. Fourth, it requires the instructions of DNA to get the right amino acids. Where did DNA come from? Fifth, protein molecules tend to break down in the presence of oxygen or water. For answer to all of these, see the video above.

2. The deck of 52 cards

In a deck of 52 playing cards there are almost 1068 possible orderings of the cards. If we shuffle the deck we can conclude that the possible ordering of the cards having occurred in the order we got is 1 chance in 1068. This is certainly highly improbable, but we did come up with this exact order of cards. Therefore, no matter how low the probability, events can still occur and evolution is not mathematically impossible.

Explanation

In this example the math is correct but the interpretation is wrong. Your interpretation of your math is what's wrong here. If the arrangement had been specified beforehand, then the actual outcome would be surprising. By shuffling the cards, the probability is one that a sequence will occur. The fallacy is that the order is predicted after the fact. Your fallacy is that you assumed that there is just one correct protein, and is contains a hundred amino acids. That is false.

3. All the people

We are in a room of 100 people. What is the probability that all 100 people would be here in this room at this exact time? The probability is enormous, but yet we are all here.

Explanation

Two things are wrong with this reasoning. First, the people were not pre-specified. This is another example of an after-the-fact prediction. Second, each person made a decision to attend; therefore, this is not a chance gathering. This turns out to be a misunderstanding between a chance event and intelligent choice. Right! Just like proteins are not chance gatherings. There are natural non-random processes involved. I think you are getting it now.

4. Probability is not involved

Probability has nothing to do with evolution because evolution has no goal or objective.

Explanation

This statement disagrees with modern biology textbooks. Agreed. Probability does have something to do with it. I don't know where the quote in point 4 comes from (it isn't in the TalkOrigins article). It's just your probability calculations that have the wrong premises, namely ignoring lots of natural processes.
When there is more than one possible outcome and the outcome is not predetermined, probability can become a factor. In the case of evolution there is no pre-assigned chemical arrangement of amino acids to form a protein. Right again! (Yeah!) There are indeed not only one possible outcome, but many proteins that could work. Therefore, the formation of a biological protein is based on random chance. No, that really doesn't follow. I thought for a moment you were with us, but science lost you again. Scientists know today that it is only because of the instructions (information) in DNA that only left-handed amino acids are linked in the proper order. 
Cells link amino acids together into proteins, but only according to instructions encoded in DNA and carried in RNA.13
Both creationists and evolutionists agree that DNA is essential for linking the correct amino acids in a chain to form a protein. The unanswered question is, “Where and how did DNA acquire the enormous amount of information (instructions) to form a protein?” There is no known natural explanation that can adequately explain the origin of life, or even a single protein. Yes there is. See the vid... The evolutionists are then left to rely on the odds (chance) that such a tremendous, improbable event occurred. No, there are other processes. zomg! Molecular biologist Michel Denton puts the event in perspective:
Is it really credible that random processes could have constructed a reality, the smallest element of which—a functional protein or gene—is complex beyond our own creative capacities, a reality which is the very antithesis of chance, which excels in every sense anything produced by the intelligence of man?14
But wait, there is still more!
The Human Body, Time, and Evolution
It is estimated that the human body is made up of 60 trillion cells (60,000,000,000,000).15 How long would it take to just assemble this many cells, one at a time and in no particular order at the rate of: What the fuck does this have to do with anything?!? Who thinks that the human body is assembled one cell at a time? Also, this doesn't seem to have anything to do with evolution, but development - a process that we can and have observed directly.
One per second1.9 million years
One per minute114 million years
One per hour6.8 billion years
These ages assume no mistakes! However, the evolutionary mechanism is based upon random errors (mistakes) in the DNA. Also included in assembling all the 60 trillion cells is that they have to make the right organs which all have to interact. Relevance?
The human body contains more than 40 billion capillaries extending over 25,000 miles, a heart that pumps over 100,000 times a day, red blood cells that transport oxygen to tissues, white blood cells that rush to identify enemy agents in the body and mark them for destruction, eyes and ears that are more complex than any man-made machine, a brain that contains over 100 trillion interconnections, plus many other parts such as the nervous system, skeleton, liver, lungs, skin, stomach, and kidneys. Relevance?
The complexity and dimensions of the human body are staggering. The probability of assembling 60 trillion cells that form specific organs that all work together to form a single human being in the evolutionary time scale of 3.8 billion years is a giant leap of faith. However, an all-knowing, all-powerful Creator has told us in His Word that He is the designer. That's not how anybody thinks the human body develops!
The hearing ear and the seeing eye, The Lord has made them both (Proverbs 20:12).
Every human body is a testimony to a purposeful Creator. As Malcolm Muggeridge said:
One of the peculiar sins of the twentieth century which we’ve developed to a very high level is the sin of credulity. It has been said that when human beings stop believing in God they believe in nothing. The truth is much worse: they believe in anything.16
Nonsense! Both statements are false. I believe in many things, and God is not one of them. 

Conclusion
Probability arguments can present a strong argument for the existence of a Creator God. The probability arguments presented here - even if they were based on sound assumptions, which they aren't - argues nothing for the existence of a Creator God. Certainly not any particular God. Maybe FSM. However, even when such evidence is presented to an evolutionist there is no guarantee that he or she will be persuaded. No, immature arguments like these persuade no scientists. Creationists, maybe. The real issue is not about evidence If you admit that you think it has nothing to do with evidence, why are you going through all these exercises in the first place?; it is a heart issue. As Christians we are called to have ready answers and break down strongholds that act as stumbling blocks to the unbeliever. It is the Holy Spirit that changes lives.
But sanctify the Lord God in your hearts, and always be ready to give a defense to everyone who asks you a reason for the hope that is in you, with meekness and fear (1 Peter 3:15).
For the weapons of our warfare are not carnal but mighty in God for pulling down strongholds, casting down arguments and every high thing that exalts itself against the knowledge of God, bringing every thought into captivity to the obedience of Christ (2 Corinthians 10:4–5).
Your real creationist weapon is ignorance - something that you rely heavily on when calculating probabilities for protein formation by random chance alone.

Footnotes
  1. George Wald [biochemist and winner of Noble Prize in Physiology or Medicine, 1967], “The Origin of Life,”Scientific American 191 no. 48 (1954): 46.
  2. Freeman Dyson, Origins of Life (New York, NY: Cambridge University Press, 1999), p. 36.
  3. “The order of the amino acids in a protein determines its function and whether indeed it will have a function at all.” Lee Spetner, Not By Chance (New York, NY: Judaica Press, 1997), p. 31.
  4. “The important fact that amino acids do not combine spontaneously, but require an input of energy, is a special problem.” Charles Thaxton, Walter Bradley, and Roger Olsen, The Mystery of Life’s Origin (Dallas, TX: Lewis and Stanley, 1992), p. 55.
  5. “A source of energy alone is not sufficient, however, to explain the origin or maintenance of living systems. The additional crucial factor is a means of converting this energy into the necessary useful work to build and maintain complex living systems.” Thaxton, Bradley, and Olsen, The Mystery of Life’s Origin, p. 124.
  6. “What we have then is a sort of ‘catch 22’ situation. If we have oxygen we have no organic compounds, but if we don’t have oxygen we have none either.” Michael Denton, Evolution: A Theory in Crisis (Bethesda, MD: Adler and Adler, 1985), p. 262.
  7. Peter Stoner, Science Speaks (Wheaton, IL: Van Kampen Press, 1952), p. 75.
  8. Emile Borel, Probabilities and Life (New York, NY: Dover, 1962), p. 28.
  9. A transport protein involved in the transfer of energy (electrons) within cells.
  10. Sir Fred Hoyle and Chandra Wickramasinghe, Evolution from Space (London: Dent, 1981), p. 148, 24.
  11. George Wald, “The Origin of Life,” p.48.
  12. Ian Musgrave, “Lies, Damned Lies, Statistics, and Probability of Abiogenesis Calculations,” TalkOrigins, www.talkorigins.org/faqs/abioprob/abioprob.html.
  13. G.B. Johnson, Biology: Visualizing Life (Austin, TX: Holt, Rinehart, and Winston, 1998), p. 193.
  14. Denton, Evolution: A Theory in Crisis, p. 342.
  15. Boyce Rensberger, Life Itself (New York, NY: Oxford University Press, 1996), p. 11.
  16. Malcolm Muggeridge, “An Eighth Deadly Sin,” Woman’s Hour radio broadcast, March 23, 1966. Quoted in Malcolm Muggeridge and Christopher Ralling, Muggeridge Through the Microphone: B.B.C. Radio and Television(London: British Broadcasting Corporation, 1967).