A variational approach to niche construction

In evolutionary biology, niche construction is sometimes described as a genuine evolutionary process whereby organisms, through their activities and regulatory mechanisms, modify their environment such as to steer their own evolutionary trajectory, and that of other species. There is ongoing debate, however, on the extent to which niche construction ought to be considered a bona fide evolutionary force, on a par with natural selection. Recent formulations of the variational free-energy principle as applied to the life sciences describe the properties of living systems, and their selection in evolution, in terms of variational inference. We argue that niche construction can be described using a variational approach. We propose new arguments to support the niche construction perspective, and to extend the variational approach to niche construction to current perspectives in various scientific fields.

Keywords: evolutionary biology, niche construction theory, ecological inheritance, variational free-energy principle, active inference, situated learning

Niche construction refers to any (implicit or explicit) modification by organisms of the (biotic or abiotic) states of the niche that they and others inhabit [1–3]. Niche construction theory (NCT) casts niche construction and ecological inheritance (the inheritance of selection pressures modified by organisms) as bona fide evolutionary processes acting in tandem with standard evolutionary processes like natural selection. NCT studies the way organisms (i) generate non-random biases on selection pressures, (ii) stabilize environmental conditions [1], (iii) and secure organism–niche complementarity (adaptation) [2]. Central to NCT is the view of reciprocal causation, which refers to the fact that developing systems can be both the products and causes of evolution [4].

Reciprocal causal dynamics that pertain to niche construction are expressed at two temporal scales: the timescale of ontogeny and the timescale of phylogeny [5]. Developmental niche construction (DNC) allows for the optimization of phenotypes over ontogenetic timescales, via feedback interactions between organisms and resources of the niche (e.g. parental care and culture acquisition). Selective niche construction (SNC) acts in tandem with natural selection to optimize phenotypes over intergenerational timescales by modifying selection pressures. It concerns consequences of feedback interactions that span over multiple generations (e.g. ecological inheritance).

There is much debate among proponents of the modern synthesis (MS) in biology as to whether niche construction is a bona fide evolutionary process [6,7]. Proponents of MS acknowledge the effects of constructed niches on evolutionary processes [8], but tend to underemphasize their significance. For instance, environmental modifications emanating from organisms' activity are generally cast as being on a par with random environmental changes, e.g. the effects of tsunamis, or volcanic eruptions [8].

The aim of this paper is to review and integrate recent theoretical work on niche construction in neuroscience, biology and anthropology [1,5,9–18]. We present the theoretical foundations and modelling heuristics for a novel computational framework for niche construction dynamics. The variational approach casts evolutionary processes in general as approximate Bayesian (variational) inference, serving the attainment of maximum attunement between the states of an organism and the states of its environment [19] (i.e. the occupation of local free-energy minima in the organism–niche state space). For instance, natural selection can be cast as a process of variational inference, in the sense that the fittest phenotype for a given ecological niche is also the one most likely to be found in that niche and populate it, given a set of environmental constraints. Somatic changes can be cast as a Bayesian update of the parameters of the model embodied by the organism, and genotypic change through natural selection can be cast as a process of Bayesian model selection [20–24] (see the electronic supplementary material for further details).

Central to this paper, the variational (free-energy) approach supports the view of niche construction as a bona fide evolutionary process. Specifically, it may provide a principled method of quantifying the complementarity that obtains between organisms and their niche via niche construction, as well as a computationally tractable definition of algorithmic information [25] and its transmission via ecological inheritance [3]. We discuss the implications of this framework with respect to extensions of the niche construction perspective in developmental psychology (e.g. [26]). Overall, the variational approach could provide a promising modelling tool for research on the niche construction perspective.

In this section, we review recent developments in the literature on NCT, namely the views on DNC and SNC, and present the standard critiques of NCT, which we interpret under the lens of the variational approach in the final section of the paper.

From the point of view of SNC, the ecological niche comprises the set of environmental factors that causally influence the inclusive fitness (rates of survival and reproduction) of organisms, emphasizing those produced by organisms. SNC encompasses all such environmental changes, ranging from the constitution of a layer of warm, moist air around homeothermic organisms [27], or the ability of earthworms and benthic diatoms to self-impose selection pressure through changes in structure and chemical composition of their local environment [28,29], to development of complex behavioural patterns like human communication and cultural systems [30–33].

It is important to note, however, that while any modification to the environment is part of niche construction, only those that have an impact on the scales of development, ecology or evolution ought to be considered as meaningful for NCT. For instance, one might argue that to induce a layer of moist air is not a process powerful enough to have a significant impact on the relevant scales. Advocates of NCT generally argue that the extent to which one should cast a given kind of modification of the environment as relevant niche construction is ultimately an empirical matter.

The developmental niche, as a temporal subset of the selective niche, comprises the set of environmental parameters that enable the development of organisms over ontogeny [5]. It is a reliably inherited, intricate structure of physical, social and epistemic resources that enables the reconstruction of the species-typical developmental trajectory (i.e. the adaptive life cycle), as well as the production of adaptive phenotypic variations [34]. By providing reliably inheritable and contextually flexible inputs for developmental plasticity, for instance by canalizing certain forms of phenotypic accommodation, DNC scaffolds phenotypes at mechanistic and ontogenetic scales [5].

Exogenetic factors may comprise complex behavioural patterns like parental care, stimulation of offspring and social learning, and function as crucial resources for normal development ([5,31,35–37], cf. the earlier concept of ‘ontogenetic niche’ [38]). Other exogenetic resources in the developmental niche include myriad social and transgenerational relationships, e.g. cooperative breeding [39], shared patterned cultural practices [40,41] and regimes of attention [42]. Crucially, these factors enable organisms to acquire the expectations (and, in humans, the norms) that regulate communities, and to learn the practices that have adapted to the particular niche through cultural evolution and culture–gene coevolution [37].

Proponents of the MS are critical of NCT. Part of their motivation is that they understand causation in evolution as unidirectional. On this account, evolutionary processes begin with environmental (biotic and abiotic) selection pressures, and culminate in genotypic changes that secure adapted phenotypes. Although MS acknowledges some cases of reciprocal causation in evolution (e.g. sexual selection), it casts environmental modifications stemming from organismic activity as being the same in kind as those that stem from random natural environmental changes, i.e. they do not count as evolutionary processes properly speaking [6,7].

With standard evolutionary processes (e.g. natural selection), traits that enhance fitness are systematically retained, and those that do not are lost. This explains the appearance of adaptive design. With niche construction, it is unclear whether or not niches adapt the environment to the organism in a systematic way, because constructed environments can lead both to increase and decrease of reproductive success [6]. Moreover, the standard model of evolution allows scientists to make predictions about the effects of natural selection on design, and on the optimization of inclusive fitness [43]. Because of the lack of systematicity of niche construction effects, NCT might not be able to generate predictions about adaptation.

Perhaps the most extensive critique of NCT was offered by Richard Dawkins ([44], cf. [45]). He dismisses NCT's claim of cyclical causality between the genome and environmental modifications induced by organisms. On his account, most of the effects of organismic activity of the environment are just ‘too loose and vague to count as … true niche construction’ [44]. For instance, beaver kits (and grandkits) may gain reproductive success from a well-constructed dam, and this might encourage the preservation of alleles underlying the behaviour of dam construction. Effects on other species, however, are not directly relevant to the beaver's, and should, therefore, be considered as mere by-products. One ought not to confusedly cast the dam as an adaptation and the dam as a by-product, or confuse ‘beaver dams with the beaver's dungs’ [46]. The scope of NCT, however, goes beyond the adaptations\by-products dichotomy to emphasize the underestimated role of the latter in evolutionary feedbacks.

The variational approach explored in the remainder of this paper puts into perspective the relevance of the distinction between adaptations and by-products. Consequences of an organism's activity, in either case, can be framed as contributing to the attainment of maximum statistical attunement with the environment, which we cast below as the minimization of variational free energy.

In this section, we present the conceptual foundations and motivation for the variational (free-energy) principle in relation to biological self-organization (see §4.1. for a formal description). The main ideas discussed here are the statistical conception of the phenotype, and the dynamics underwriting its organization.

The variational free-energy principle (FEP) has been applied fruitfully to yield a statistical conception of the dynamics of life [47]. The key idea behind this principle is that the bounded set of characteristic states in which an organism maintains itself most of the time, and in which it is most likely to find itself, can be interpreted as the set of its phenotypic states, i.e. its specific repertoire of functional or adaptive states, its physiology and morphology, and its sensorimotor patterns. Since these characteristic states are visited more frequently than others, they are associated with a higher probability than other states (e.g. a fish is more likely to find itself in water than anywhere else). This statistical conception of the phenotype is supported by simulation studies of the emergence of biological self-organization and morphogenesis [47,48], and further evidence comes from the study of early myelopoiesis in real biological systems (e.g. [49]).

Phenotypic states subsume all states of an agent, from quickly fluctuating ones (e.g. its temperature or visually evoked responses), to slowly fluctuating states that constrain fast dynamics (e.g. its morphology, structure and neuronal connectivity). Later, we will consider this distinction in terms of the distinction between stable and unstable dynamics in synergetics [50], where the latter (unstable, slow) modes correspond to order parameters, and will be associated with ‘traits’ of phenotypes, which can include states of the niche. Thus, the conception of the phenotype that interests us here can be framed in terms of a joint phenotypic space that includes states internal (e.g. phenotypic states) and external (e.g. phenotypic traits) to the organism, biotic and abiotic.

Organisms are open systems. Yet, they maintain their organization over time in the face of environmental perturbations. Therefore, one must assume (a priori) that they manage to limit the entropy of their states [51]. Technically, entropy (as an information theoretic quantity) is the long-term average of self-information or ‘surprisal’. Surprisal reflects the likelihood of an outcome—it is the negative log probability of any sensory state being encountered. Organisms that maintain their continued existence spend most of their time in attracting states, and will, therefore, have a low average surprisal and low entropy. Note that one could also define entropy (as a thermodynamic quantity) in the following way. Under ergodic assumptions (that is, under the assumption that the system has properties that can be measured more than once), surprisal is equivalent to a thermodynamic potential energy [52]. Although the stationary distributions involved do not necessarily have a Boltzmann–Gibbs form, recent developments finesse the difficulties in identifying potential functions that play the role of an adaptive landscape: see [53] for a technical discussion. Only the information theoretic definition concerns us directly in this paper.

Because surprisal depends on hidden causes in the environment, the organism (e.g. its brain) cannot directly assess it. Here is where the variational free energy comes in. Mathematically, it constitutes an upper bound on surprisal, and thereby implicitly bounds its average, namely, entropy. Variational free-energy reports a deviation from, and is conditioned on, a set of priors, which are operationalized in a hierarchical, probabilistic generative model of the hidden causes of sensory inputs (observations) [20]. Priors are probability distributions or Bayesian beliefs that provide constraints on lower levels, in hierarchical models. Because they are themselves parametrized, they can be optimized via hyperparameters that depend upon the sensory observations (refer figure 1 and §4.1 below for technical details).

A generative model is a mapping from sensory observations, action policies, to external (hidden) causes. These causes constitute the generative process, which describes the transitions among hidden causes in the world (including the organism's own actions) that generate sensory inputs [55]. The generative model is conditioned on the prior (Bayesian) beliefs of the organism. These beliefs are parametrized by a density that is encoded by the internal states of the organism (e.g. brain states). See figure 1 for a discussion. This density represents the ‘best guess’ of the organism as to the causes of its sensations. Updates of the generative model conform to the principles of variational inference. This involves approximating the generative process by optimizing parameters of the internal density, with respect to the free energy bound on Bayesian model evidence (sometimes referred to as an evidence bound). This bound means that if one changes some probability distribution (i.e. beliefs) over the causes of observed data to minimize variational free energy, one is effectively maximizing model evidence [52].

Thus, although it cannot track surprisal directly, the organism can track a proxy quantity (an upper bound), the variational free energy. By minimizing free energy (or maximizing model evidence), the organism can estimate surprise, and thereby avoid deleterious phase transitions and maintain its phenotypic organization. Hence, the long-term, evolutionary (distal) imperative for the organism to minimize entropy translates into the short-term (proximal) imperative to avoid surprisal by minimizing free energy (see §4.2. for the mathematical details).

Active inference is the self-evidencing process by which the organism garners and produces evidence for the generative model that it instantiates by existing. At the scale of organisms interacting with their niche, active inference is realized in patterns of action and perception. Action allows the organism to gather more precise (Bayesian) model evidence: sensory samples reduce uncertainty with respect to the causes of sensory states. In turn, the role of perception, sometimes called ‘perceptual inference’, is to update the system's priors while informing action. This process amounts to minimizing the surprisal expected following an action, where expected surprisal is also known as uncertainty. In other words, all action is—at one level—in the game of resolving uncertainty and minimizing surprisal. Given the statistical conception of the phenotype described above, the upshot is that we can interpret active inference as the generalized homeostasis and allostasis of an organism [21,56].

Relating these ideas to the core of our discussion, variational free energy is minimized at all scales of self-organization; from the ensemble behaviour of macromolecules to evolutionary dynamics [57]. It is a purely information theoretic construct that generalizes thermodynamic free energy. It can provide an upper bound on the (log) evidence for the exchange of a structure like a cell with its environment. This evidence can either be interpreted as self-information (a.k.a. surprisal), such that the time integral of self-information becomes the entropy of environmental exchange. By interpreting the evidence in relation to a generative model, one can associate the biophysical states of any living system (cell, brain, phenotype, species, etc.) with the sufficient statistics of the generative model.

The variational free energy is then a functional of the environmental (e.g. sensory) input to the system and the probability distribution over causes of that input parametrized by the system's internal states (e.g. intracellular concentrations, neuronal connectivity, anatomical infrastructure, etc.). Crucially, the generative process generating the input may be formally distinct from the generative model of that process. This construction means that the same free-energy functional is minimized at different spatial and temporal scales, depending on how the system is defined. This minimization describes, for example, the chemotactic behaviour of Escherichia coli, learning in our brains, institutional organization, etc.: see [47,52] for a detailed discussion and [48] for a worked example in morphogenesis.

From the perspective of the organism, minimizing free energy through active inference may feel like constructing ‘designed’ environments [58]. From the niche's perspective encoding the traces of organismic activity, it is just ‘learning’ about the phenotypes that inhabit it: both niche and phenotype are self-evidencing. Mathematically, action on the environment is the same as the niche sensing an organism. This is key to our treatment in what follows. If both the niche and organism are ergodic, then they must both conform to the free-energy principle. This implicit symmetry or circular causality means that free-energy bounding dynamics are also a special case of generalized synchrony, e.g. two swinging pendulums attached to a beam that synchronize over time, or between a phenotype (e.g. me) and (e.g. my) niche, which is usually constituted by other sentient systems (e.g. like me). This synchrony is what we associate with (developmental) niche construction dynamics generating ecological inheritance.

This section summarizes the conceptual and mathematical analysis that underlies the variational principles supporting the modelling heuristics for the variational framework of niche construction.

This section summarizes the conceptual and mathematical analysis that underlies the variational principles we are pursuing. The FEP furnishes an interpretation of an agent's internal dynamics as a gradient flow on a free-energy functional of sensory states and an approximate posterior based on a generative model of external dynamics (and how they map to sensory states). This means that the internal states of an agent acquire a Bayesian mechanics via an implicit (generative) model of its environment. This interpretation rests on a distinction between states that are external and internal to a given agent. This (statistical) separation requires the existence of something called a Markov blanket—that itself can be divided into active and sensory states [47,59,60]. The only requirement (that licenses a distinction between internal and external states) is that internal states cannot directly influence sensory states—and external states cannot directly influence active states (figure 1).

The key move now is to appreciate that the same Bayesian interpretation can be applied to the external states. This follows from the antisymmetry of the conditional dependencies that define the Markov blanket. In other words, we can relabel internal states as external states and relabel sensory states as active states. In so doing, the conditional independencies remain unchanged (figure 1). This means that there must be a description of niche dynamics, where the environment models how the agent's internal dynamics are generating its active states. From the perspective of the environment, the agent's active states now become sensory states and sensory states become active states. The crucial observation here is that the agent and eco-niche share the same Markov blanket and, therefore, mathematically speaking, must be inferring each other.