# Evolution as Explanation:
The Origins of Neural Codes and their Efficiencies

Han Kim

###### Abstract

Neural codes appear efficient. Naturally, neuroscientists contend that an
efficient process is responsible for generating efficient codes. They argue
that natural selection is the efficient process that generates those codes.
Although natural selection is an adaptive process, evolution itself, is not.
Evolution consists of not only natural selection, but also neutral stochastic
forces that can generate biological inefficiencies. The explanatory power of
natural selection cannot be appealed to, without regards for the remaining
evolutionary forces. In this paper, we aim to reformulate the explanatory role
of evolutionary forces on neural coding, with special attention to neutral
forces. We propose a framework that argues for differing contributions of
adaptive and stochastic evolutionary forces, for different phenotypic
‘levels’, including those of neural codes. We assert that this framework is of
special interest to neuroscience, because the field has derived much progress
from an efficiency-based worldview. We advocate for a pluralistic neuroscience
capable of appealing to both adaptive and non-adaptive explanations.

##  1 Introduction

Neuroscience seeks pluralistic explanations [43, 68, 32, 21]. In doing so, the
field borrows from the ethos of multiple disciplines. From engineering-
oriented fields, neuroscientists have learned to treat neural systems as
reverse-engineering problems. Such approaches hypothesize overarching cost
functions or goals, for neural systems, and test those hypotheses against
neurobiological observations [42, 5]. Although an optimization-based worldview
can be useful, biological features do not possess inherent goals or purposes
[19, 44, 12, 35]. The tenets of evolutionary biology are consistent with this
agnosticism, and accordingly, are incommensurable with an optimization-based
worldview. For this reason, neuroscience’s attempts to incorporate both the
ethos of evolutionary-biological thinking and those of engineering disciplines
have not been straightforward. This paper examines the nature of this
pluralism in neuroscience. We argue that the current pluralism is ill-fitting,
and reduces the evolutionary process to nothing more than some teleological
rendition of natural selection. In response, we attempt to restructure the way
in which neuroscientists invoke both optimization-based and historical
process-based explanations, in the face of empirical results.

In the current pluralism, neuroscience appeals to only a single evolutionary
force—natural selection—to explain neurobiological phenomena. Namely,
neuroscientists interpret natural selection as the process that generates
proposed neurobiological efficiencies, such as neural codes [5, 6, 62]. In
appealing to natural selection alone, however, neuroscientists not only
curtail the full explanatory power of evolutionary-biological thinking, but at
best, recast evolution as a force limited to natural selection. In actuality,
evolution is not just natural selection, but consists also of neutral
stochastic forces. We argue that these neutral forces can, in some cases,
provide more useful explanations of neurobiological phenomena than
optimization frameworks.

On this note, we must mention, at the outset, an important corollary. This
paper maintains that adaptive goal-oriented explanations are extremely useful.
The hypothesizing of efficient codes yields much progress for neuroscience.
Indeed, an automated appeal to adaptive explanations can be a sufficient
heuristic, when thinking about the origins of neurobiological features. Like
all types of explanations, however, optimization-based explanations have
epistemological shortcomings. Namely, the optimization thesis is
unfalsifiable, because we can interpret all observable phenomena in
optimization terms. Either we have already derived a fitting cost function
that the observations appear to match, or if not, we can contend that there
still exists some appropriate function that has not yet occurred to us. Our
position is that when faced with the latter case, the more useful approach—or
at least an approach that merits serious consideration—is to interpret the
observed phenomenon as the result of a historical process agnostic to any
speculative goal or function. We contend that neutral evolutionary forces are
one such explanatory process. Importantly, we acknowledge that historical non-
adaptive explanations are also unfalsifiable. All empirical observations can
be interpreted as the result of some preceding events from its history. In
other words, this paper is not about denigrating one type of explanation, in
favour of another—both have merits. Rather, we are concerned with deriving
appropriate contexts for appealing to each explanatory class.

We begin the paper by examining the history of the efficient coding
hypothesis. We argue that the hypothesis tacitly comprises of two types of
conflated explanations: a goal-based explanation, typical of engineering
disciplines, and a historical process-based explanation, typical of
evolutionary biology. We contend that making this distinction explicit is
worthwhile. It reveals how neuroscientists currently view the explanatory
capabilities of evolution. We then articulate the explanatory usefulness of
non-adaptive evolutionary forces. We show that under certain
conditions—namely, when species possess small effective population
sizes—neutral stochastic forces dominate a species’ evolutionary trajectory.
We provide established examples from molecular biology and genomics that
convey the explanatory power of non-adaptive forces. We then survey the
contrasting efficiencies observed in neural coding. Given the overwhelming
evidence that viewing neural codes in terms of efficiency is fruitful, we ask
under which circumstances we should incorporate non-adaptive explanations. We
articulate one evolutionary biological framework that considers both adaptive
and non-adaptive explanations. We argue that the appeal to either adaptive or
non-adaptive explanations should depend on both the phenotypic ‘level’ that
one is interested in, as well as the species’ effective population size. In
doing so, this framework is consistent with both the efficient codes argued in
systems neuroscience, as well as the non-adaptiveness conveyed in genetic
codes. We note that this framework can be applied to the thinking about
phenotypic evolution across the general biologies. We contend, however, that
it is of special interest to neuroscience, because unlike other biological
disciplines, an efficiency-based worldview has provided neuroscience with
immense progress. We provide neurobiological examples consistent with the
proposed framework. We close in support of a pluralistic neuroscience that
accommodates for both adaptive and non-adaptive explanations.

##  2 Two types of explanations and the efficient coding hypothesis

Figure 1: Different disciplines tend to use different types of explanations to
explain observable phenomena. A) In engineering, functional explanations that
reference some efficient goal are used to explain some observed feature. In
evolutionary biology, historical processes, which are either adaptive or non-
adaptive, are used to explain some observed feature. B) In neuroscience, both
adaptive and historical process-based explanations are used. Currently,
however, we argue that adaptive processes are used to explain the existence of
some hypothesized cost function, which is used to explain some observed
feature. We argue that a more useful epistemological framework is to refer to
both adaptive and non-adaptive processes, as well as functional explanations,
to explain some observed feature. Vertical braces denote the bottom term being
a subset of the top term. Terms before arrows explain terms after the arrow.

Thinkers of the natural world contend that multiple types of explanations can
explain a given observation [2, 3, 43, 68, 21]. Although there exists a rich
history on the divvying of explanatory types, in this paper, we will
categorize explanations of the biological world in one of two classes (Figure
1A). The first is functional. Biological features are the way they are because
they help achieve some supposed cost function or goal. This type of
explanation is typical of engineering disciplines and can be immensely useful.
They are popular with systems neuroscientists. The second type of explanation
is historical. Biological features are the way they are because of preceding
events in their generative process. This type of explanation is traditional to
developmental biologists and evolutionary biologists, and can also be
immensely useful. It has also found its way into systems neuroscience.
Recognizing this explicit distinction between explanation types is necessary
for understanding how neuroscientists use evolution to explain phenomena.

An examination of the efficient coding hypothesis reveals how neuroscience
employs both function-based and historical process-based explanations. In
Barlow’s original articulation of the hypothesis, he asks “what are sensory
relays for?” [5] Since then, the hypothesis has successfully explained many
empirical observations, and has spread to other aspects of neural coding. It
can be found in relation to not only early sensory processing, but also for
more central neural processes [50, 54, 7], as well as motor efferents [23, 65,
47]. In all these cases, the spirit of the original hypothesis remains intact:
what is the neural code for? In other words, the hypothesis squarely concerns
itself with devising a function-based explanation, and in doing so, assumes an
implicit goal for the nervous system’s properties. We emphasize that there is
nothing wrong with this position. It yields much explanatory insight for many
neurobiological phenomena.

The logic behind the efficient coding hypothesis, however, is not limited to a
function-based explanation. It also tries to explain how an organism might end
up with an efficient code of sorts (Figure 1B). To do so, it first answers its
original question, “what are sensory relays for?” It claims they are for
representing the animal’s natural environment. It hypothesizes that the animal
likely does so ‘efficiently’—perhaps by using minimal neural impulses—such
that the animal best represents its natural environmental statistics, over
some non-ecological statistics.

Given that efficient codes exist to optimally represent the animal’s natural
environment, the efficient coding hypothesis then returns to ask how such a
code could arise. It seeks to link the natural environment to the qualities of
the organism. To do so, it very intuitively invokes the process of natural
selection. The efficient coding hypothesis argues that, over historical time,
the process of natural selection alters the structure of a species’ neural
computations such that it efficiently represents its native environment. In
other words, the hypothesis invokes a historical process to explain how an
organism ends up with an efficient code. It explains neurobiological
observations via a function-based explanation, and it employs a process-based
explanation to explain how exactly the code meets its function.

This logic, however, risks a nuanced but meaningful misconception. Natural
selection, although an adaptive process, is explicitly not goal-oriented. In
the words of evolutionary biologist, Ernst Mayr, natural selection and other
“[h]istorical processes … can not act purposefully” [43]. The efficient coding
hypothesis’ invoking of a non-goal-oriented process, in order to explain how
something achieves its supposed goal, risks recasting the natural selection
process in teleological terms. Indeed, we think that as a result of the coding
hypothesis’ articulation, many neuroscientists tacitly interpret natural
selection as a goal-oriented process. Although we reject the notion that
natural selection could be at all purpose-driven, we do not disagree with the
idea that natural selection contributed to the rise of purported efficient
codes in the peripheral nervous systems. Natural selection, as it was
originally conceived—as an undirected and iterative process that imposes
ecological constraints on a species—perhaps provides the best explanation for
many efficient neural codes. We simply wish to articulate the necessary
evolutionary biological caveat that has been amiss from the incarnations of
the efficient coding hypothesis: although natural selection might explain
efficient codes, natural selection is not an efficient process with respect to
some goal. Goals and adaptive processes are two different things.

We contend that the overlooking of this subtlety persists in the many
articulations and applications of the efficient coding hypothesis, and is the
culprit behind neuroscience’s limited means of appealing to evolution as an
explanation. In the worst of such cases, neuroscientists invoke natural
selection as an epistemological panacea. They use it to explain how a neural
system wound up meeting whatever cost function objective they are interested
in, even when the code itself does not appear to be particularly efficient.
For example, several decades after Barlow published the efficient coding
hypothesis, he revisits his formulation, and argues that he was wrong in over-
emphasizing the role of ‘compression’ in an efficient code, and contends that
redundancy in neural coding is a crucial function for efficient nervous
systems [6]. Although we agree with this reasonable amendment, we disagree
with Barlow’s continued, and if anything, more explicit appeal to natural
selection as something that explains a redundant neural code. The continued
allegiance to natural selection in Barlow’s revisit may be a vestige from the
fact that his original efficient coding hypothesis invoked an adaptive
evolutionary process, albeit under more sensible circumstances. Alternatively,
or perhaps additionally, Barlow and other neuroscientists are unaware of
alternative evolutionary forces that may better explain their phenomena. In
the next section, we introduce such alternative forces. We articulate how
evolution is more than just natural selection, and we describe how non-
adaptive neutral forces can sometimes explain phenomena more usefully than an
optimization-based framework.

##  3 Evolutionary biology usefully explains inefficient codes

Even in the face of biological features that we might intuitively interpret as
inefficient—such as redundancy in neural representations—we can still appeal
to goal-oriented explanations. For example, we can argue that the observed
redundancy aids the system in achieving the goal of robustness, perhaps from
noise or from external perturbations. More generally speaking, we can always
formulate a goal-oriented explanation about an observation because we can
claim that either the observed inefficiency is exactly the point of the
system, or because we can argue that we do not yet know the goal of the
system, but the system most certainly has a goal, and with further empirical
evidence, such a goal will become clear. We contend that adopting these
epistemological positions is limited. As an alternative, we introduce non-
adaptive evolutionary forces, which we contend are more useful than
efficiency-based frameworks for explaining inefficiencies. We begin by
introducing the explanatory power of non-adaptive forces in its native
context. The goal of this section is, in part, pedagogical. We aim to explain
key evolutionary biology concepts, without being mired by technical
derivations.

###  3.1 The effective population size defines drift

Evolution is not natural selection. Rather, it consists of four forces, of
which natural selection is just one. The other three—mutation111A novel change
in genetic sequence. In nature, is the result of a random process.,
recombination222The rearrangement of genetic material. In nature, is the
result of a random process., and genetic drift333The random sampling of
genetic material from the parental generation, to produce the offspring
generation. Results in differing genetic compositions between the parental and
offspring generations.—are non-adaptive and neutral because they are random
and do not depend on an animal’s fitness properties. Under what conditions,
then, will neutral forces provide the most explanatory power regarding a
biological feature’s origins? We begin with drift.

Sewall Wright, a forefather of population genetics, first sketched the concept
of the effective population size ($N_{e}$) to provide a way of calculating the
rate of evolutionary change caused by the random sampling of allele444One of
two or more versions of a gene. They arise by mutation. frequencies—that is,
genetic drift [71]. An intuition for $N_{e}$, and how it differs from the
‘regular’ population size of breeding individuals ($N$), is essential for
understanding neutral forces. $N_{e}$ is best understood in a highly idealized
but important type of random sampling called the Wright-Fisher population [71,
14, 15]. The Wright-Fisher population assumes a randomly mating population
that consists of a number of diploid555A cell or organism with two complete
sets of genetic information. If the cell or organism has only one complete set
of genetic information, it is haploid. hermpahroditic individuals. In the
Wright-Fisher population, these individuals are the total number of breeding
individuals, $N$. They reproduce with discrete generations, and each
generation is counted at the time of breeding. The individuals of each new
generation are the result of random sampling, with replacement, from the
gametes of the parents, and the parents die immediately after reproduction. If
we accept all the idealized assumptions of the Wright-Fisher population, then
the rate at which drift, or random sampling, results in a differing genetic
composition in the offspring is $\frac{1}{2N}$. The coefficient ‘2’ comes from
the fact that the Wright-Fisher population assumes that the parents are
diploid, so each individual actually has two inheritable genetic sets. If the
members of the Wright-Fisher population were haploid or triploid, then the
rate of change from drift across the discrete generations would be
$\frac{1}{N}$ or $\frac{1}{3N}$, respectively. In other words, the goal of the
Fisher-Wright population is to identify a feasible set of biological
assumptions that result in the most simplified expression for genetic drift.
This theoretical concept provides us with an intuition for drift, and as we
will see, for $N_{e}$.

Most biological populations, however, do not reproduce in a fashion similar to
the sampling from a bag of marbles. For example, many species have two sexes,
select mates non-randomly, and will not produce the progeny of the next
generation all at once. For these more complex situations, we invoke the
concept of the effective population size, $N_{e}$. The effective population
size has, within it, all the relevant biological complications that
distinguish this population from a Wright-Fisher population, such that we can
simply substitute $N$ for $N_{e}$, for most problems we wish. For example, in
a diploid non-Wright-Fisher population, we might say that the rate of change
in genetic composition due to drift is $\frac{1}{2N_{e}}$ instead of
$\frac{1}{2N}$. In other words, we defer. The consideration for any biological
complications when working with a given population genetic expression
originally meant for a Wright-Fisher population is offloaded from that
particular expression and its use of $N$, to its substitution for $N_{e}$.
Many theoretical and computational methods, such as coalescent theory, exist
for inferring $N_{e}$ for a population [9], but they are outside the scope of
this paper. The reader needs know only that the effective population size, and
more specifically, $\frac{1}{N_{e}}$, approximates the neutral force that is
drift666Some authors distinguish between various types of effective population
sizes, such as $N_{e}$, $N_{l}$, and $N_{g}$, which all take into account
different factors such as timescales, genome linkage effects, and the ploidy
of a species [35, 36]. For our purposes, we will not be making such
distinctions, because they do not matter for our arguments with the reader. We
will use exclusively $N_{e}$ when referring to the effective population size..

###  3.2 The selection coefficient expresses the strength of natural selection

In order to understand when neutral forces outweigh adaptive forces in
evolution, we need to introduce the selection coefficient, $s$. Doing so
requires an understanding of fitness. In the broadest sense, fitness involves
the ability of organisms or populations to survive and reproduce in their
environment[51]. The concept of fitness is important for natural selection and
the selection coefficient, because natural selection requires differing levels
of fitness across members of a population, and that some of those fitness
differences be inheritable—that is, that they have a genetic basis. For this
reason, we will express our understanding of fitness in more specific genetic
terms.

Evolutionary biologists distinguish between two types of fitness metrics[51].
One is the absolute fitness, $W$. It refers to a genotype’s expected total
fitness, and encapsulates the complexities that come with integrating all
imaginable biological properties, such as viability, mating success, and
fecundity. $W$ must be greater than or equal to zero. The other type of
fitness, which is more commonly used in evolutionary biology, is relative
fitness, or $w$. The relative fitness of a genotype is simply its absolute
fitness, but normalized in some way. Its most common normalization is dividing
the absolute fitness of a genotype by the absolute fitness of the fittest
genotype. In doing so, $w$ is often bound between 0 and 1, where 1 is the
fitness of the fittest genotype. From the definition of $w$, we can easily
understand the selection coefficient, $s$. It is simply a genotype’s $w$,
relative to the fittest genotype’s $w$. That is, $s=1-w$, where $w$ is the
relative fitness of some genotype. So if some genotype is incredibly fit and
has $w=1$, then for that genotype, $s=0$, and selection against that genotype
is non-existent. Conversely, if some genotype is extremely deleterious and has
$w=0$, then for that genotype, $s=1$, and selection against that genotype is
total. The genotype will contribute nothing to the subsequent generation. From
these examples, we can see how the value of $s$ expresses the strength of
natural selection. Like many terms in evolutionary biological theory—such as
$N_{e}$—several methods exist for empirically estimating $s$[51], but they are
outside the scope of this paper.

###  3.3 Random forces can dominate evolution

From our above definitions of drift and natural selection, we can formulate an
expression for evolution that considers the contributions of both non-adaptive
and adaptive forces. Given that we can articulate the strength of drift as
$\frac{1}{N_{e}}$, and the strength of natural selection as $s$, we can define
their relative contributions as
$\frac{\text{selection}}{\text{drift}}=\frac{s}{\frac{1}{N_{e}}}=N_{e}s$.

To appreciate the $N_{e}s$ ratio, we must consider a classic case of a diploid
population species, such as Drosophila melanogaster or Mus musculus. In such a
species, a given gene might have two possible alleles, A and a, where allele A
might have a slight selective advantage, s, over a. Given that one allele is
advantageous over the other, a worthwhile question that directly relates to
our original intents, is to ask under which scenario the advantageous version
of the gene, A, will become predominant, or fixate, in the population. In
other words, given the selective advantage that A has over a, will natural
selection always ensure the fixation of A? The answer to this question is no.
Let’s say that the mutation rate of a $\rightarrow$ A is $m$ times greater
than the mutation rate of A $\rightarrow$ a. If so, then standard population
genetics theory[29, 59, 35, 39, 37] argues that the probability of fixing a
mutation to A is $e^{2N_{e}s}$ times more likely than fixing a mutation to a.
That is, the ratio of probabilities of being A versus a is $me^{2N_{e}s}$.
This relationship is particularly interesting, because when
$\frac{1}{N_{e}}\gg|s|$, the probability of fixing A over a in the population
approaches exactly the ratio of mutation rates, $m$. That is, when
$\frac{1}{N_{e}}\gg|s|$, or said another way, when the effective population
size, $N_{e}$, is extremely small, then the likelihood of fixation for some
advantageous allele is a function of mutation pressures alone. Under small
$N_{e}$, random forces dominate the course of a population’s evolution. We can
plot this relationship, and observe the effects of altering the $N_{e}s$ ratio
(Figure 2A). Small $N_{e}s$ ratios result in evolutionary trajectories that
are nothing more than the product of mutation rates, a neutral stochastic
force.

###  3.4 Empirical support for predictions on biological coding inefficiency

Figure 2: Stochastic forces make non-negligible contributions to evolution. A)
As the effective population size increases, relative to the selection
coefficient, then the probability that an advantageous allele fixates will
approach the fixation probability driven by mutation rates alone. This figure
is a modified reproduction [35]. B) Organisms with nervous systems possess
smaller effective population sizes. Values of $N_{e}\mu$ for different species
are depicted, from which $N_{e}$ values can be estimated, because $\mu$
ranges, at most, by an order of magnitude across known phyla (see text in
Section 3.4 for details). In bold and in colour on the x-axis are popular
model organism species for neuroscience research. This figure is a modified
reproduction [38].

From the above pedagogy, one might ask what sorts of populations or species
possess small effective population sizes? Such species are likely more
susceptible to neutral forces than species with larger $N_{e}$ values. To
answer this question, we must introduce another parameter from evolutionary
biology: $N_{e}\mu$. This composite parameter is the effective population
size, $N_{e}$, scaled by the mutation rate, $\mu$. It determines the standing
equilibrium level of approximately neutral genetic variability in a population
[29, 38, 9]. Biologists can estimate this value empirically, by quantifying
the extent of synonymous mutations777Mutations in the genetic sequence that do
not result in the encoding of different amino acids. For example, both GCA and
GCG genetic triplets, or codons, encode for the alanine amino acid, even
though the sequences differ by a base pair. The GCA $\rightarrow$ GCG mutation
is synonymous or silent. in a species, because synonymous mutations are
neutral [38]. Given that across species, the mutation rate per base per cell
division, $\mu$, ranges from $5\times 10^{-11}\text{ to }5\times 10^{-10}$
[13], that is, by a single order of magnitude, we can factorize and interpret
$N_{e}\mu$ as $N_{e}$. Doing so results in estimates of $N_{e}$ for
prokaryotes that is at least $10^{8}$, for unicellular eukaryotes that is
$10^{7}$ to $10^{8}$, for invertebrates that is $10^{5}$ to $10^{6}$, and for
vertebrates that is $10^{4}$ to $10^{5}$ [38]. A plot of $N_{e}\mu$ estimates
for various species is shown in Figure 2B. In other words, the effective
population sizes of nervous system-possessing animals is far smaller than
those without. They are more susceptible to random genetic drift than their
neuron-less counterparts. Within nervous system-possessing animals, we see
that invertebrates are less privy to random drift than vertebrate animals888An
interesting observation for the invertebrate neuroscientist. Its consequences
are slightly outside the scope of this paper.. We also note that, in general,
estimates of $N_{e}$ are much smaller than estimates of the true number of
breeding individuals, $N$ [36, 11, 16]. In other words, most biological
populations do not merely differ from Wright-Fisher population dynamics, but
do so in a way that promotes the effects of drift.

We have provided both theoretical and empirical evidence for thinking that
non-adaptive evolutionary forces are at least worth acknowledging, when
thinking about nervous system evolution. In addition, however, observed
biological features can also make more sense under a view of evolution that
incorporates stochastic forces. There are several established examples in
relation to genetic coding. Prokaryotes possess the largest $N_{e}$ values,
and accordingly, their genome architectures are remarkably efficient. Nearly
all of their genomes are dedicated to coding proteins and they possess
virtually no non-coding sequences, such as introns and non-coding RNA [36,
46]. In addition, genes that function in common biological processes are found
adjacent to each other in the genome, such that the organism can readily
achieve co-expression of those related genes [53]. Prokaryotic genes can also
be polycistronic, meaning that a single mRNA transcript can encode multiple
proteins at a time [31].

In contrast, genetic coding in multicellular eukaryotes appear to be anything
but efficient. Eukaryotes are monocistronic, and so more energy and molecular
machinery must be expended to transcribe and translate a given coding unit
[31]. Moreover, the majority of multi-cellular eukaryotic genomes are non-
coding elements. Less than 2% of human genes are protein-coding, whereas 90%
to 100% of prokaryotic genomes encode for functional units [46]. The dynamics
of coding in multi-cellular organisms is also remarkably inefficient. Most of
the eukaryotic genome is transcribed, and yet only a small fraction of those
transcripts undergo maturation and subsequent translation into proteins [45].
Transcripts not processed for maturation and translation are digested and
decayed [48]. The large investment of energy in producing intermediary
products from nearly all of the genome, only to have most of those
intermediates degraded, illustrates a highly inefficient biological coding
process.

Evolutionary biology can explain these observations without necessarily
invoking efficiency and natural selection [35]. Seemingly inefficient
biological qualities are nothing more than the outcomes contributed by random
sampling processes. Populations with smaller $N_{e}$ are simply more prone to
such processes. In contrast, when faced with putative inefficiencies,
optimization-based frameworks such as those seen in engineering disciplines
are resigned to one of the two positions mentioned at the very beginning of
this section: either the observed inefficiencies are, for some reason, exactly
the point of the system, or that the analyst has wrongly identified the goal
of the system. We maintain that these two positions are epistemologically
limited. They do not explain the observed phenomena by appealing to some
scientific process, but rather, defer the explanation to some function that is
not yet understood or known. We reassert, however, that optimization-based
frameworks still have an essential place in biology and neuroscience. To
demonstrate this point, we provide a brief review of the overwhelming evidence
in favour of an optimization framework in neuroscience.

##  4 Efficient codes and nervous systems

Given the relatively small effective population sizes seen in nervous system-
possessing animals, we might expect abundant inefficiencies across neural
codes. This hypothesis, however, appears to be exceptionally false.
Optimization frameworks can clearly provide much explanatory power, especially
in neuroscience. In this section, we provide the reader with diverse examples
from across the nervous system that support the epistemological benefits of
assuming purposes in natural systems.

###  4.1 Sensory systems

In feline, human, and grasshopper auditory systems[40, 63], sensory systems
appear to use a sparse spike code to represent the acoustic structure of a
given stimulus. Kernel functions for an optimal sparse representation learned
from auditory stimuli closely approximate the physiological reverse-
correlation filters [63]. Importantly, these efficient codes only succeed in
using a sparse representation when the auditory stimulus is derived from
natural scene statistics. In other words, efficient neural codes appear to at
least be correlated with the germane particulars of the animal’s natural
environment. One reasonable interpretation to the exquisite match between an
animal’s native environment and the neural code that processes that
environment is that the nervous system is somehow tuned or optimized for the
environment. A simple process-based and folk-biological explanation of these
findings might be that selective forces encompass ethological cues, and
animals that fail to efficiently respond to those cues exhibit survival-
inappropriate behaviours, and are selected against. Indeed, efficient codes
tend to match not only the ethological sensory space, but are especially tuned
for those stimuli that are behaviourally relevant[40, 41].

We observe theoretical and experimental evidence for efficient neural codes in
modalities apart from audition. For example, a survey of ommatidia diameter
and eye height from 27 Hymenoptera species suggest that their facets have
evolved to maximize visual sampling, while minimizing the blur from
diffraction [4]. This conclusion derives from a fundamental physics principle
showing that the optimal resolving power of a lens with diameter $d$ is
equivalent to $\sqrt{a\lambda}$, where $a$ is the angle subtended by two point
sources that can still be detected as double, and $\lambda$ is the wavelength
of incoming light. The surveyed insects indeed possess a linear and
proportional relationship between $\sqrt{a}$ and $d$ [4]. In terms of neural
coding, the retinal ganglion cells of both salamanders and macaques
decorrelate spatial features of visual inputs, as a means of achieving sparse
spiking in the retina and optimizing visual coding efficiency [54].

###  4.2 Motor systems

We also find efficiency at the opposite end of the periphery, although not
necessarily with respect to neural coding. Instead, most examples of efficient
motor control are seen in terms of the amount of energy expended in muscles,
to achieve a particular task. Given that the amount of muscle energy required
for a behaviour vastly exceeds those needed for neural spiking [52, 60], one
can argue that the relevant cost function at the motor periphery should relate
to the joules of muscle work expended, rather than some sparse spike code.
Classic work on horse gaits show that freely moving horses self-optimize their
movement speeds. Under naturalistic conditions, they largely operate in
locomotor regimes that require minimal amounts of consumed oxygen for moving
some unit distance. These results hold across multiple gait types, such as
walks, trots, and gallops [23]. Similar results of self-optimization with
respect to gross energy expenditure have also been reported in human ergometer
studies [65].

Despite the foremost relevance of muscle expenditure over neural spiking for
motoric efficiency, some recent evidence suggests that the encoding of
naturalistic behaviours may also have some efficient basis. Simultaneous
microdrive recordings and 3D posture tracking of the head, neck, and back of
freely moving rats reveals that proportionately fewer cells in the posterior
parietal and motor cortices fire when the animal partakes in common ‘default’
postures [47]. The encoding of naturalistic poses appears to use a minimal
number of cells to represent the repertoire of ethological motor ensembles.

###  4.3 Central systems

Further examples of efficiency have been argued in deeper processing regions,
albeit often with different, and arguably more ambiguous, objectives from the
sparse coding seen at the periphery [61]. Learning algorithms that maximize
sparseness, for example, succeed in recapitulating the spatially localized,
oriented, and bandpass features of mammalian visual cortical cells [50]. In
general, sparse codes in the visual cortex appear to be useful for learning
and processing incoming spike patterns [50], or for parsing large amounts of
signal from background noise [57], in the face of overcomplete
representations. Even though these kinds of objective functions differ from
those efficient representations seen in the periphery, where the goal is to
minimize the number of spikes needed for expressing some maximal description
of the environment, both scenarios still offer examples of efficient coding.

Operating on the assumption that nervous systems have innate goals or
functions is undeniably useful for neuroscience. An appeal to natural
selection as the historical process that explains these findings is also not
problematic. In fact, it is likely the most appropriate and useful type of
process-based explanation for these observations. In light of the previous
section’s pedagogy, however, the reader may ask themselves two questions:
first, why do small $N_{e}$ species, such as those with nervous systems,
possess efficient neural codes, and second, whether there is a general place
or context under which an appeal to neutral evolutionary processes is most
appropriate. We directly address this question in the next section.

##  5 An account of phenotypic evolution

Figure 3: Higher phenotype traits in organisms with large effective population
sizes are most susceptible to adaptive evolutionary change. In contrast, lower
phenotype traits in organisms with smaller effective population sizes are most
likely the result of a drift-dominant evolutionary process. Each rectangle
above represents a phenotypic ‘layer’, and each layer consists of a fraction
of changes from adaptive forces (in pink), and a complementary fraction of
changes from neutral forces (in blue). The fraction of adaptive change
increases as the level of phenotype is higher. The fraction of adaptive change
increases across all phenotype levels as the effective population size
increases.

Nervous system-possessing animals have, relatively speaking, the smallest
$N_{e}$ values. These values do not, however, suggest that those species are
impervious to natural selection. The previous section’s survey of efficient
neural codes argues, if anything, that natural selection is well at work for
nervous system-possessing animals. Indeed, we remind the reader that a given
$N_{e}$ value should only be considered small relative to some selection
coefficient, $s$, for that species, and that quantifying $s$ for the heritable
basis of a species’ neural coding scheme is, like for many complex traits,
incredibly challenging and unknown. Rather, the purpose of highlighting the
small $N_{e}$ values of nervous system-possessing animals is to argue that
some species are less, but not totally, immune to stochastic evolutionary
processes. As we saw in Section 3.4, unicellular eukaryotes, despite having
one of the highest $N_{e}$ values, still exhibit inefficiencies in their
genetic coding schemes not seen in their higher $N_{e}$ counterparts, such as
the retention of genomic non-coding elements. For this reason, we think it is
not unreasonable to expect the occasional inefficiency from species with the
lowest $N_{e}$ values, like those with nervous systems. In this section, we
outline a framework that will provide us with intuitions for when we might
expect a biological trait to be the function of a stochastic historical
process. We realize that this framework may be broadly applicable for
biological observations outside of the neural sciences, but we think its
impact might be particularly useful for neuroscience, because of the immense
success that an efficiency-based worldview has had for the field.

###  5.1 Phenotypes can be stratified into a hierarchy

Under what contexts might a non-adaptive historical process, as opposed to an
adaptive one, better explain a neurobiological observation? For example, why
do so many neural codes—in particular, ones at the periphery—lend themselves
so easily to an efficiency-based worldview? Shouldn’t the small $N_{e}$ values
of nervous system-possessing animals lead us to expect inefficiencies across
the nervous system?

We argue that small $N_{e}$ values should not result in our thinking that non-
adaptive forces exert themselves uniformly across all levels and traits of the
species in question. That is, if a species’ $N_{e}$ is small, the contribution
of drift will be quite different, depending on whether we are trying to
explain something like neural firing patterns, or gene expression. In some
ways, this view is quite distinct from existing accounts of evolution. Most
evolutionary frameworks express themselves exclusively in genetic terms. For
example, in the allele fixation case from Section 3.3, the prevalence of a
biological trait in a population is described in terms of its underlying
genetics—that is, in terms of allele A’s fixation. In reality, however, one or
two genes rarely encode for a phenotype, and theorizing about gene fixation
dynamics is not identical to theorizing about the fixation dynamics of
phenotypes that those genes contribute to. Although genetic material is the
unit of inheritance and ultimately encodes for all biological processes, an
account of evolution that is about the root cause is not the same as an
account of evolution that is about the encoded products of the genetics. The
central dogma of molecular biology [10] explains how genetic material encodes
for protein products, but it does not explain how those proteins encode for
organismal function. Theories about genetic information are not equivalent to
theories about phenotypes ultimately derived from genetic information, and
explanations about genes do not, by mere substitution, extend to their
products. Even Motoo Kimura, the founder of neutral evolutionary theory,
speculated that the relevance of neutral theory is likely minimal, with
respect to the evolution of phenotypes [29, 30, 72].

We contend that an account of evolution that at least acknowledges the gap
between the evolution of genotypes and the evolution of phenotypes will best
inform intuitions about when to appeal to adaptive or non-adaptive
evolutionary explanations. More specifically, we propose the divvying of
phenotypes into constituent ‘layers’ [22, 44, 70, 72]. We posit that doing so
will explain seeming discrepancies such as the observed efficiencies in neural
coding in small $N_{e}$ species. The key advancement that a hierarchy of
‘layered’ phenotypes provides is that elements of a bottom layer can afford to
drift and be ‘inefficient’, provided that their effects do not impinge on the
integrity of the layer directly above. In other words, intermediary layers
‘buffer’ the effects that bottom layers have on the highest layers, such as
animal fitness. In this way, small $N_{e}$ species may possess many neutral
mutations and their genetics may be subject, relatively strongly, to drift,
but higher level physiologies such as their neural coding schemes, are still
subject to strong natural selection, and contribute towards some form of
efficient neural code. In contrast, a ‘layer-free’ conception of phenotypes
wherein genes directly encode for organismal attributes, results in an
unrealistic and onerous emphasis of the genetic level’s impact on species
fitness. Such a conception is not compatible with existing biological
evidence, because alleles that are slightly deleterious with respect to
biochemical and cell-biological levels can exist, without dramatically
compromising fitness [70].

Given that natural selection acts directly on phenotype, rather than genotype
[44], the hierarchical stratification of phenotype, with respect to the
genetic level, means that the relative contribution of natural selection on
animal evolution is, in fact, a function of two parameters (Figure 3). One is
the effective population size, $N_{e}$, as detailed above. The other is the
phenotypic level at which species variation is observed. Such variation can
range from the lowest level, genetic material, to the highest levels, such as
behaviour and physiology. Change occurring at a level to which selection is
blind will be neutral, provided that it does not affect the higher level [44,
70, 72]. By this definition, the probability of a given change being neutral
is greater, the lower the level of the change.

###  5.2 A hierarchical view on phenotypes can explain differing efficiencies
across species and phenotypes

Figure 4: Differing contributions of adaptive and non-adaptive evolutionary
forces can explain neurobiological phenomena. A) For a given species, like the
lobster, Homarus americanus, multiple biophysical parameter combinations can
realize the same higher level network phenotype. Lower phenotypic levels can
afford to drift more than higher level phenotypes. This figure is a modified
reproduction [55]. B) For a given phenotype level, like a circuit, or a
neuron, non-adaptive forces make stronger contributions to the evolution of
species with smaller effective population sizes. Vertebrates possess inverted
retina with blind spots and most vertebrate neurons are multipolar cells that
perform single computations. Invertebrates possess everted retina without
blind spots and most invertebrate neurons are unipolar and can perform
multiple computations. For the retina schematics, arrows refer to the
direction of information flow, and yellow refers to the photoreceptive cells.
The non-retinal figures are modified reproductions [24, 20].

The above conception of phenotypes alters when we might appeal to adaptive or
non-adaptive historical explanations, when thinking about the origins of
neural codes. Despite the relatively small $N_{e}$ of nervous system-
possessing animals, the efficiency of neural codes can be understood because
of their close proximity to the highest level of phenotype. The fact that most
efficient neural coding evidence relates to sensory processing—in particular,
peripheral sensory processing—as well as the control of naturalistic
behaviours, is likely not a coincidence. Neural codes instantiated in these
systems interact directly with the native environment, and by extension, with
selective forces. Indeed, in the case of the optimal facet angles of
Hymenoptera ommatidia [4], the efficient implementation is not necessarily
neural, but has in common the involvement of an apparatus that routinely
interacts with the environment. The relevant parameter that explains the
evolution of efficient neural codes is the proximity to phenotype, rather than
it being neural, per se. For this reason, the proposed framework also applies
more broadly to general phenotypic attributes, such as gross animal
morphology, and not just to nervous systems. That being said, we argue that a
balanced evolutionary framework that incorporates both adaptive and non-
adaptive processes is of special relevance to neuroscience, because of the
unusual success that an exclusively optimization-based worldview has had for
the field.

In this section, we interpret neurobiological results under the above
articulated framework. We attempt to demonstrate, via examples, that a
knowledge of both non-adaptive and adaptive evolutionary processes better
explains the possible origins of neurobiological observations, than an appeal
to adaptive processes alone.

####  5.2.1 Two levels of the lobster stomatogastric ganglion

A clear example of how neutral forces may be more dominant in lower biological
levels, but less so for higher phenotypes, can be seen in the lobster
stomatogastric ganglion. This ganglion consists of a small and defined network
of neurons that fire in a precisely ordered and periodic manner, so that the
foregut of the lobster can contract rhythmically, in a so called pyloric
rhythm, and enable the lobster’s digestion of food. The simulation of more
than 20 million biophysical models of the lobster’s pyloric rhythm reveals
that 20% of these models can multiply realize the same pyloric-like rhythms.
Importantly, these 4 million models, despite realizing the same network
activity, were non-similar. Each model comprised of disparate biophysical
parameter combinations [55].

For the neuroscientist limited to only the powers of natural selection,
explaining the origins of such a finding is not necessarily straightforward.
An appeal to adaptive processes alone struggles to explain the wanton
biophysical degeneracy found in this ganglion. A complete understanding of
evolutionary processes, however, provides some added explanatory value.
Similar to the bottom-most level of genetic material, biophysical circuit
parameters can afford to drift, provided they accomplish the same higher level
phenotype—in this case, the network dynamics—required for organismal function
and species fitness (Figure 4A). This example demonstrates the importance of
stratifying phenotypes in a neuroscientific context. Natural selection is
increasingly blind to bottom layer changes, which are effectively neutral, and
need not be selected for or against. Bottom level changes can afford to drift
because their ability to alter essential higher level phenotypes and viability
is limited, and the relatively small $N_{e}$ values of nervous system-
possessing lobsters predicts this drift. An appeal to adaptive historical
processes is a more palatable hypothesis when explaining the evolution of
higher, rather than lower, phenotypes.

####  5.2.2 Vertebrate and invertebrate neurons

The next two examples will compare and attempt to explain the differing
efficiencies between vertebrate and invertebrate attributes. Given that the
former has a smaller $N_{e}$ than the latter, we argue that when explaining
comparisons about the same level of phenotype for both groups, an appeal to
non-adaptive forces is less inappropriate for vertebrates.

Vertebrate neurons are typically multi-polar999We emphasize that they are
typically multi-polar. They are not always multi-polar.. That is, they
resemble the structures often seen in textbooks, where some post-synaptic
dendritic processes converge onto a cell body, before becoming a pre-synaptic
axon. In this way, for a given neuron, neural impulses, or information flow,
must pass through the cell body, in order to exit and pass on to a post-
synaptic cell [18, 25]. Simultaneous voltage recordings of a single mammalian
cortical neuron’s cell body and axon show correlated signals of identical sign
and similar shape, but with a reduced amplitude and a slightly delayed onset
for the axonal signal [24]. That is, the cell body integrates then propagates
a single signal, with some minor decay, to the axon (Figure 4B). In this
sense, multi-polar neurons typical of vertebrates are limited to a single
computation, whose dynamics can be represented by a single cell body
recording.

In contrast, invertebrate neurons are almost always unipolar, meaning that the
cell possesses only a single neurite. In such a morphology, the cell body is
not a point of information convergence. Rather, from the cell body’s one
neurite, the neurite branches in many complex patterns, such that some arbours
are pre-synpatic, and others are post-synaptic. Information flow can pass
through various branches independent of others, and in this way, multiple
computations can be spatially multi-plexed onto a single neuron. Two studies
demonstrate this idea. The first is anatomical. The examination of spiking
local interneurons in the locust metathoracic ganglion reveals two fields of
neuropilar branches that a single process links together. One of these fields
possess numerous finte neurites with relatively uniform diameters, and is
located in a ventral area where afferents from a hind leg hair terminate. The
other field possesses sparser more varicose neurites, and is located in a more
dorsal area, alongside the neurites of many leg muscle motor neurons. The
majority of the dorsal field are output synapses, although they can also
receive inputs, whereas the ventral field consists mostly of input synapses
[69]. These two fields, both of which belong to a single local interneuron,
likely participate in two completely distinct and compartmentalized functions.

Neural recording data in support of this hypothesis can be seen in the
invertebrate Caenorhabditis elegans. Calcium imaging reveals spatially
compartmentalized and multi-plexed computations within a single interneuron,
RIA. The RIA neuron consists of three axonal segments: the loop, the nrV, and
the nrD (Figure 4B). Of these segments, calcium transients in the nrV and the
nrD correlate with ventral and dorsal bends of the animal head, respectively.
Although the loop segment does not correlate with any obvious behaviours, its
dynamics were distinct from those of the nrV and nrD domains. The RIA neuron’s
cell body did not exhibit calcium responses [20]. This multi-plexing of
computations across space in single neurons is largely absent from the multi-
polar neurons typical of smaller $N_{e}$ species, such as vertebrates. A
consideration of both effective population size and phenotypic level informs a
context-dependent worldview for appealing to both adaptive and non-adaptive
evolutionary processes.

####  5.2.3 Vertebrate and invertebrate optics

In addition to differing morphologies and computations at the single-cell
level, vertebrates and invertebrates possess distinct anatomies. These grosser
differences again suggest a greater contribution from neutral forces for
smaller $N_{e}$ vertebrates, than for larger $N_{e}$ invertebrates.

Namely, when compared to the invertebrate eye, the vertebrate eye appears
inefficient. An intuitive and optimal design would place the photo-sensors at
the front of the eye, and then pass those signals to neural processing cells
behind the photo-sensors. In this way, the neurons would not interfere with
the incoming light, and contribute to tissue scattering. Instead, the
vertebrate retina lies directly on the optical path, such that the light
passes through the ganglion cells, then the inner synaptic layer, then the
amacrine cells, then the bipolar cells, then the horizontal cells, then the
outer synaptic layer, then the photoreceptor cell bodies, and then finally,
the actual photoreceptive rods and cones [66, 34]. The retina then processes
the received light back out the way it came, such that the ganglion cells
perform the final computations, despite being the first retinal cells the
light encounters.

This inverted configuration not only scatters the incoming light, but also
results in a literal blind spot [34]. In order for the retinal information to
leave the eye and enter the central nervous system, it must, at some point,
route through all the lower cell layers, including the rods and cones. The
spot where the neural information leaves the eye cannot receive stimulus
information, and the animal is blind in this region (Figure 4B). The obviously
more efficient retinal layout that would both preclude a blind spot and
mitigate light scattering from tissues would arrange the retina in the everted
order. That is, it would place the photoreceptive cells at the front, relative
to the incoming light, and the neurons behind the preceding cell would always
do the subsequent computation [34]. In doing so, the proceeding computations
will not interfere with the light path, and routing the neural information out
of the eye will not require transecting the retina.

There is little reason to think that such an everted structure is not possible
in nature. In fact, invertebrate eyes possess exactly this configuration
(Figure 4B). The apposition compound eyes of most diurnal insects and the
superposition compound eyes of nocturnal insects and deep-water crustaceans
position their photoreceptive cells closest to the incoming light, and route
the neural processing behind the photosensors, so that the information enters
the central nervous system with no blind spot [34]. This comparison is
somewhat incommensurable, however, because compound eyes operate quite
differently from the cornea-lens mechanism of terrestrial animals. Rather, we
should compare the vertebrate terrestrial eye against the one major
terrestrial invertebrate group with a cornea-lens structure: spiders. The
anterior median eyes, or primary eyes, of spiders are everted, and as a
result, they are not subject to the light scattering and blind spots seen in
its vertebrate counterparts [34, 49]. Moreover, several ancient invertebrate
phyla such as polychaetes [56], and both the scyphomedusae and hydromedusae
jellyfish [17] possess everted retina. Given the relative small $N_{e}$ values
of the more recent vertebrate species, we speculate that the inverted retina
may have originated from ancient large $N_{e}$ animals via a series of
stochastic drift-driven contributions.

Despite the clear evidence for an inefficient vertebrate retina,
neurobiologists continue to investigate the structure in terms of a design
problem. That is, they hypothesize some goal for the system, and argue that
retinal properties are subservient to the goal. For example, vision
researchers have argued that the inverted retinal configuration affords some
modest degree of space-saving efficiency, so that more retinal cells can be
compacted in a given volume [33]. This argument, however, fails to address
whether such a modest advantage is worth the light scattering and blind spot
that comes with the inverted design. Indeed, the functional relevance of
packing in more retinal cells, in general, is unclear. Similar arguments have
been made regarding the retinal layers. Given that the retina lies on the
optical path, neuroscientists have argued that the retina has optimized itself
to be as thin as possible, so that it minimally scatters the incoming light
[66]. We emphasize, however, that an everted retina would circumvent this
problem, as well as the blind spot. A consideration for neutral evolutionary
processes may address this overcommitment to an efficiency-based framework.
That being said, we do not disagree that natural selection has contributed
significantly to retinal structures, including those of vertebrates. Several
compelling arguments exist for the vertebrate retina’s signal processing and
general computational abilities. We merely aim to identify contexts where an
appeal to neutral evolutionary forces may provide needed explanatory power.
The small $N_{e}$ of vertebrates, relative to invertebrates, for a given
phenotypic level, is one.

####  5.2.4 Speculations on brainwide activity across species

How might a framework that acknowledges non-adaptive processes be relevant for
explaining the origins of recent results in neuroscience? In this brief
example, we provide interpretations of contemporary data to demonstrate the
ongoing relevance of neutral evolutionary forces.

Recent technological innovations have enabled neuroscientists to record at an
unprecedented scale and resolution, across species. These brainwide recordings
identify highly redundant representations of spontaneous ongoing behaviours,
across the entire brain. In particular, smaller $N_{e}$ vertebrates appear to
contribute a larger fraction of neural activity for representing their
behaviours, than their larger $N_{e}$ counterparts, such that even dedicated
visual processing areas, like V1, are found representing ongoing motor actions
[67, 27, 1, 58, 26]. In contrast, for the invertebrate C. elegans, the sensory
neurons fail to represent ongoing behaviours, and in this sense, do not
contribute to the dominant redundant representation [27, 26]. Similarly, in
flies, although a significant fraction of brainwide activity represents
ongoing behaviours, residual activity is high-dimensional, and appears to
represent non-behavioural information, such as sensory cues and internal
states [1, 58]. Neutral evolutionary forces may, in part, explain the origins
of this greater redundancy reduction for large $N_{e}$ invertebrates over
small $N_{e}$ vertebrates. In general, for all species, the central nervous
system’s limited interaction with the natural environment, relative to the
peripheral processing systems, may explain the subjection to possible neutral
forces, and the resulting neural redundancy and lack of a clear objective
function. We emphasize, however, that such redundancy does not mean natural
selection does not operate, whatsoever. Indeed, for many macroevolutionary
processes, the outcomes of neutral events can be co-opted for more adaptive
means, such that they facilitate functional dependencies and
neofunctionalizations [35, 8, 28]. Speculating on possible systems-level
functions and goals is still essential for neuroscience. Evolutionary
explanations are more powerful, however, when one can appeal to both non-
adaptive and adaptive processes.

##  6 Non-adaptive explanations and the origins of neural codes

Evolution explains the origins of biological things. It provides a process-
based explanation for how a biological observation came to be. It can explain
the efficiencies of neural codes, but it can also explain relative
inefficiencies seen across phyla. Doing so, however, requires neuroscientists
to not limit their evolutionary explanations to adaptive processes, like
natural selection (Figure 1B). We began this paper with a historical and
speculative diagnosis as to why neuroscientists limit their explanations. The
success of an efficiency-based worldview in neuroscience invites teleological
implementations of an adaptive evolutionary process. To address this
epistemological shortcoming, we introduced in this paper the concept of
neutral stochastic evolutionary forces. We explained why the concept was first
articulated, and we illustrate its accepted success for explaining biological
features outside of neuroscience. We showed that evolutionary theory predicts
that neutral processes make some non-negligible contribution to the origins of
neurobiological features, and that, in addition, these processes comprise a
useful epistemological tool for explaining neurobiological phenomena that
natural selection struggles with.

More precisely, we articulated a framework for providing intuitions about the
relative contributions of adaptive and non-adaptive evolutionary forces, when
thinking about the origins of a neurobiological feature. We theorize that the
effective population size, just like for all of evolutionary biology, is a key
parameter for hypothesizing the relative efficacy of natural selection on
neurobiological traits. In addition, to $N_{e}$ values, we contend that the
‘level’ of phenotype under evolutionary question is also germane for
hypothesizing the relative contributions of drift. Phenotypes are the objects
for selection [44, 64], because they are what directly interact with the
environment. Not all phenotypes interact with the environment to the same
degree, however, and for this reason, lower levels that are more obfuscated
from the environment’s effects are less subject to selective pressures. These
lower levels, including the actual units of inheritance—the objects of
selection [44, 64]—are increasingly free to drift, because they are of less
consequence to the species phenotypes that actually interact with the world.
Even if the exact nature of this framework is questionable, we contend that
one of the overall goals of this paper still stands: neurobiological features,
like all biological features, are subject to the full repertoire of
evolutionary forces, including non-adaptive and stochastic processes. Such
processes can provide satisfactory explanations, just like natural selection
can, and in some cases, more so.

Evolution is a complex process. Rarely does it operate exclusively in adaptive
or non-adaptive terms [19]. For this reason, we can still rightfully appeal to
natural selection when explaining the many efficiencies of neural coding, but
we can also speculate on the contributions of stochastic forces when we
observe an obvious relative inefficiency. Neuroscientists must still
hypothesize cost functions and goals for neural systems, but need not do so
without acknowledging the non-teleological evolutionary means by which those
functions arose. A careful consideration for all evolutionary forces has the
greatest explanatory power. Evolution explains the origins of neural codes,
including the occasional inefficiency.

## Acknowledgements

I thank Bingni W. Brunton, Markus Meister, Joseph Parker, Zitong (Jerry) Wang,
Alex Farhang, Kelly Kadlec, Guruprasad Raghavan, and Tara Chari for critical
discussions and/or careful readings of the evolving manuscript. I thank Bingni
W. Brunton for invaluable conversations and BLT sandwiches. I thank Markus
Meister for teaching Principles of Neural Science (Bi154) at the California
Institute of Technology and for encouraging me to share the paper with a
broader audience. I am extremely grateful to Joseph Parker for his invaluable
support, trust, and encouragement. I am supported by the Natural Sciences and
Engineering Research Council of Canada’s Postgraduate Scholarship.

## Author contributions

Conceptualization: HK. Writing: HK. Editing and review: HK. Visualization: HK.

## Competing interests

The authors have no competing interests.

## Code availability

Code for Figure 2A and the original LaTeX text are available at
https://github.com/hanhanhan-kim/neuroevo_paper.

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