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Theory of Convergent Evolution Analyzed


The knifefish, rather than having several fins like a trout, has one long “ribbon fin” that undulates along the length of its body. Studies of its motion reveal that it uses the optimal wavelength to get the most forward thrust, stability, and maneuverability out of its investment of energy. But the knifefish is not alone: the same optimal design can be found in cuttlefish (cephalopods), rays (cartilaginous fish), certain flatworms, and other bony fish that are evolutionarily unrelated. In fact — if evolution by natural selection is assumed to be the cause — this design emerged independently at least eight times. To the Darwinian, it’s another remarkable case of “convergent evolution.”

A paper in PLOS Biology investigates this phenomenon and tries to explain it. The five authors, primarily from Northwestern University, used a robotic knifefish to nail down the physical factors related to optimal swimming design: the length of the fin’s undulation and the mean amplitude. Dividing the one by the other yields what they call the Optimal Specific Wavelength (OSW). Then they measured the OSW on 22 live swimmers, such as cuttlefish and rays, to see how they rated. They found that the values “converge to a narrow range” around 20, even though the animals belong to eight separate groups whose presumed ancestors did not possess this kind of propulsion. Robin Meadows says in a companion piece likewise in PLOS Biology:

Many OSW swimmers have no known ancestor that swam with median/paired fins, and the 22 species in this analysis belong to eight clades (groups of organisms stemming from a common ancestor). This suggests that the OSW evolved independently at least eight times. [Emphasis added.]

Casey Luskin has argued that Darwinians appeal to convergence in order to have it both ways: basically, “biological similarity implies common ancestry, except when it doesn’t.” The authors of this new paper do not respond to that charge specifically, but they go further than most Darwinians by not just asserting convergence occurred, but by offering evolutionary mechanisms that might produce it. They begin with broad philosophical questions:

How would life look if it evolved again on Earth, or for that matter, on any other habitable planet? The question of the role of chance versus necessity in evolution is a foundational issue in biology. Gould gave us the metaphor of the “tape of life” for the evolution of life and argued that if it were somehow rewound and started again, life would have taken a very different course. Conway Morris has argued that, on the contrary, the laws of physics limit the number of good solutions that are within reach of evolution, and that therefore we should expect life to take a similar course upon rewinding. Examples of convergent evolution, such as wings on insects, birds, and mammals, are considered supporting evidence for this hypothesis. But our understanding of convergent evolution, as reflecting the dominance of natural selection plus variation over factors such as developmental constraints, pleiotropy, phylogenetic inertia, genetic drift, and other stochastic processes, is held back by a lack of quantitative arguments. Such arguments would expose the links from physical principles to the biological phenomena and help us understand where evolution is likely to converge to the same result or diverge to a wide variety of solutions.

Here, we present just such arguments for a phenomenon that unifies a vast diversity of swimming organisms, from invertebrates, like cuttlefish, to vertebrates, like cartilaginous and bony fish. Unlike the case of the convergently evolved wing, a morphological feature, here the evolved feature is a pattern of movement that occurs across a morphologically diverse set of moving appendages on aquatic animals.

We see at once that the implications go far beyond the knifefish’s OSW. Evolutionary theory itself is at stake: Is it truly contingent, or somehow directed? Their argument hinges on the ability of the environment (e.g., the properties of water) to direct natural selection so that it rewards, with higher fitness, the animals that hit the optimum. If the OSW is on a peak of the fitness landscape, natural selection will drive an animal up the peak, no matter its ancestry, because it will outcompete the others. That’s how separately evolving animals will end up (converge) on the same fitness peak.

What is the mechanism for macroevolutionary repeatability? In the language of the calculus of variations, these examples of convergent evolution — if correctly identified as such — imply that there is a gradient in the fitness landscape toward some optimum with respect to trait in question, and this gradient is large enough to overcome competing factors such as developmental constraints, pleiotropy, phylogenetic inertia, genetic drift, cases where optimality in one trait results in suboptimality in another trait … and approximations of the trait which provide local but not global optimality. With a sufficiently steep gradient in fitness in place and evolutionary dynamics capable of achieving near-optimal solutions, it is only a matter of time before the mechanism of selection with variation can arrive at the optimum. As the derivative of the trait with respect to fitness is stabilizing, departures from the optimum would be self-correcting over evolutionary time.

In fulfillment of the promise of quantifying their argument, they measure the loss in force for wavelengths that deviate significantly from the OSW. “The effect of any decline in propulsive force — even less than one percent — from what it is at the OSW is amplified over the vast number of undulations an animal may make in its life,” they argue. What animal would want to compete with less than the best?

Unfortunately, undulating fins are not the best. Tuna are the fastest swimmers in the ocean, but they rely on their caudal fins to thrust their bodies forward. So we have a conundrum; “The question is therefore why the slower forms of swimming exhibited by median/paired fin animals would emerge and thrive despite the prevalence of body/caudal fin swimming in ancestral species.” Why would evolution switch from the Ferrari to the Volkswagen?

The authors are ready with auxiliary hypotheses:

A similar question has arisen in simulation studies that show that a light-sensitive patch of skin can evolve through several intermediate forms into an advanced camera-type lens eye in only a few hundred thousand years — why, then, are there so many existing animals with intermediate forms of eyes? Nilsson and Pelger’s answer is that camera-type lens eyes are only the best solution for certain animal — ecosystem combinations. Our answer is similar: body/caudal fin swimming makes little sense in isolation. It is only within particular ecological contexts that some types of animals are able to survive better with this type of swimming than with alternative approaches.

In particular, median/paired fin swimming appears to be a low speed, low cost of transport specialization. The lower amplitudes of fin movement that are possible in median/paired fin swimmers, compared to the very high amplitudes possible when the high power axial musculature is used in body/caudal fin swimmers, is therefore an advantage instead of a liability due to the lower energetic cost of transport of median/paired fin swimming. The fact that median/paired fin swimming is used at lower speeds should not be confused, however, with the concept of maximizing speed by swimming at the OSW. Even when swimming at lower speeds (or whatever speed for that matter, which is determined by frequency and amplitude), for a given set of parameters (amplitude of undulations, frequency, fin height, and fin shape), if an animal swims with elongated median/paired fins, then its speed can be maximized for that set of parameters by swimming at the OSW.

Our regular readers will jump at that lateral pass to Nilsson and Pelger. Their claim about the evolution of camera eyes was thoroughly trounced by David Berlinski almost a decade ago in these pages. It’s an example of how scientists can continue to trust flawed arguments for years — decades, sometimes — without considering (or even knowing about) the counter-arguments.

Aside from that, the authors make a point: You can’t just look at a fin in isolation. You need to consider the ecological niche of the animal. They point to members of the group Gymnotiformes, electric fish who use their ribbon fins in low-oxygen murky waters, that swim mostly at night where high speed is not advantageous.

Given these constraints, the elongated fins that are universally present within the more than 150 species comprising Gymnotiformes may be favored, but clearly a tremendous amount of work would need to be done to assess the relative importance of all of these factors in giving rise to this one group of median/paired fin swimmers.

While the existence of body/caudal fin swimmers and the existence of median/paired fin swimmers may or may not be subject to robust repeatability, what is clear is that if median/paired fin swimming with elongated fins and semirigid trunks emerges — as it has independently on multiple occasions according to Fig 1 — it is very probable that the specific trait of swimming at the OSW will also emerge.

This is a very different claim, much reduced from the original one. No longer are they asserting that the environment will force different swimmers up the same fitness peak, because clearly it didn’t for the tuna. Now we have the more modest claim that “if” a ribbon fin “emerges,” then natural selection will push it toward the OSW. But where is their scientific law of emergence? What about the ocean environment can cause that? And we see they just admitted that their hypothesis “may or may not be subject to robust repeatability.”

Another complication is that some of the undulating-fin fish can switch to high-speed caudal-fin swimming when needed, as when under attack from predators or when zooming in on prey. Why would natural selection provide both methods of propulsion? The fitness landscape just got more complicated; the animal has to climb multiple fitness peaks to survive. (We might point out, in passing, that according to evolutionists, electric organs are examples of convergence, too, having evolved six times independently according to a report last year from the University of Wisconsin posted at NewsWise.)

Notice, also, that while the ecological hypothesis seems to work for the Gymnotiformes, it doesn’t for the others. Rays and cuttlefish, for instance, use their undulating fins in the open sea or coastal shallows during the daytime. The authors have not shown that their auxiliary hypotheses rescue convergent evolution, nor have they identified any evolutionary mechanism to account for fast swimmers with caudal fins swimming right alongside slow swimmers with undulating fins in the exact same watery environment. Every proposal has exceptions; where is that quantitative argument, exactly?

Thus, we can only speculate that the 7.5% decline in force occurring over the observed variation in SW is not large enough to overcome the many causes of suboptimality listed above, whereas the 25% decline we find beyond this range is large enough to cause selection pressure toward the OSW. Additional research is needed to establish whether this hypothesis is true.

We thus circle back to Casey Luskin’s challenge: Common ancestry explains traits, except when it doesn’t.

For these reasons, we cannot take Robin Meadows’s praise of this paper seriously:

This elegant work reveals that a physical problem — how to get from here to there — can be optimized by a wondrous diversity of biological solutions. Moreover, these findings strengthen the case that mechanical optimization can drive evolution, contributing to the longstanding debate over the evolutionary roles of randomness versus physical constraints that limit the solutions that are feasible in living creatures. As the researchers point out, quantifying physical properties that underlie biological phenomena could help us recognize when an optimal mechanical solution is likely to drive convergent evolution.

Ockham is tapping his foot by the door.

Image: Cuttlefish, by David Sim from London, United Kingdom (Cuttlefish) [CC BY 2.0], via Wikimedia Commons.

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