Regular patterns link individual behavior to population persistence

Resisting and recovering from disturbances is a necessity for most species. The strategy is sometimes collective, depending on the aggregation of interacting individuals into regular patterns. However, relating patterns of abundance across scales to both individual behavior and population persistence remains a major challenge for ecology. Such patterns are found in many ecosystems (1), ranging from microbes to forests, with their regularity taking the form of evenly sized and spaced bands and patches of aggregated individuals. Regular patterns are said to be self-organized when they emerge from local interactions among individuals that are a combination of positive and negative feedbacks (2). Positive feedbacks mean that growth and survival increase with the density of individuals. Such “safety in numbers” is found in many natural systems (3), including saltmarshes (4), arid vegetation (5, 6), and mussel beds (7), where individuals can gain protection from physical disturbances, such as waves or erosion. However, aggregation also means competing for limited resources, which leads to negative feedbacks between density and growth. The combination of positive and negative feedbacks illustrates the “balance of nature” (8), and could lead to a homogeneous distribution, but their properties can produce much more complex dynamics. First, their nonlinearity means that growth and survival can show abrupt changes with small changes in density, which can prevent populations from reaching an equilibrium state. Second, most ecological interactions among individuals occur over limited spatial scales (i.e., between neighbors). When the spatial extent of positive effects is shorter than the extent of negative competitive effects, regular patterns of aggregation can emerge (Fig. 1B). When it is the temporal scales of feedbacks that differ instead, self-organized patterns can emerge as a scale-free distribution of aggregated individuals (Fig. 1C). The regular “pattern” can then be defined as the ratio of small to large patches, which remains constant independent of the scale of observation (9). In this case, the regularity is one across scales rather than over space, and it has been documented in highly disturbed rain forests (10), arid ecosystems (11), and mussel beds (12), where the local propagation of a disturbance, such as fire or waves, is much faster than the local aggregation of individuals. In PNAS, de Paoli et al. (13) document a new class of pattern formation mechanisms based on scale- and density-dependent movement (Fig. 1A), which is shown to operate on fast temporal scales and to act synergistically with scale-dependent feedbacks to form large-scale regular patterns in natural mussel bed ecosystems.

Fig. 1.

Mechanisms of pattern formation, based on positive (green arrows) and negative (red arrows) feedbacks documented in mussel bed ecosystems. (A) Movement rate of individual mussels as a function of density, and resulting small-scale regular bands of mussels (5–10 cm wide) aggregated over fast temporal scales. The blue line shows a quadratic regression model fitted to data, and the red line shows the fit to a diffusion model (adapted from ref. 18). (B) Separation of spatial scales between positive (e.g., attachment strength) and negative (e.g., competition) feedbacks leads to regular bands (5–7 m wide) of mussel beds (adapted from ref. 1). (C) In highly disturbed systems (e.g., fires, strong waves), the separation of temporal scales between fast negative feedbacks (e.g., the local propagation of wave disturbance across mussel beds) and slow positive feedbacks (e.g., aggregation) can lead to scale-free distribution of patches over whole landscapes. (Inset) Illustration of how scale-free patterns are unchanged by varying the scale of observation from 5 to 500 square meters (adapted from ref. 9).

Self-organized patterns can occur over large spatial scales and result from collective interactions among individuals, often from modifications to their physical habitat. These patterns are also relevant to conservation and for the understanding of whole ecosystems when pattern-forming species are ecological engineers: By forming dense aggregates and modifying their physical environments, species such as Spartina (14) and mussels (15) create novel habitats for the assembly of communities and drive the productivity and stability of whole ecosystems. Theory and empirical evidence abound to document benefits of self-organized patterns for the persistence of ecosystem engineers and their association with maximum biomass and productivity in whole communities and ecosystems (5). However, establishing causal relationships linking individual behavior, pattern formation, population persistence, and ecosystem functions is a daunting task because of the range of scales involved and the emerging complexity that must be harnessed through experimental control. de Paoli et al. (13) provide experimental support for the behavioral basis of aggregation in marine mussel beds leading to self-organized patterns over multiple scales, as well as for their ecological implications for the persistence of mussel populations disturbed by waves and predation.

Mussels feed on phytoplankton by filtering the water, and competition can thus arise between nearby individuals that deplete food transported with currents. However, competition builds up over a distance because it takes many individuals to deplete phytoplankton transported by current down to concentrations that will induce competitive interactions (16). On the other hand, being very close to conspecifics can provide many benefits, including better attachment strength and protection against wave disturbances or protection against desiccation of intertidal populations during low tide. All those benefits typically occur over a shorter distance than competition. The combination of short-range positive interactions and longer range negative competition can, in theory, lead to self-organized patterns, which has been predicted by theory and observed in nature (17). The aggregation behavior of mussels has also been demonstrated and suggested to lead to patchiness over multiple scales (17). de Paoli et al. (13) achieved experimental control of mussel distribution and measured both individual behavior (movement) and population response (persistence) to aggregation into regular patterns. What is important is the experimental confirmation of the positive feedbacks between local density (proximity between individuals), aggregation behavior (movement toward conspecifics), and population persistence.

de Paoli et al. (13) refer to the limited impact of self-organized patterns in conservation. Ecologists have made recent efforts to demonstrate the ecological importance of regular patterns, but it is true that much of our fascination with regular patterns comes from their association with general mechanisms regulating natural systems, ranging from the molecule to whole ecosystems. The study of regular patterns involving the interplay between positive and negative interactions has a long history in both chemistry and biology. Alan Turing discovered regular patterns emerging from chemical reactions between short-range activators (positive feedback) and long-range inhibitors (negative feedback), and gave a name to this general class of spatial (Turing) instabilities. In biology, Turing instabilities have been applied to developmental patterns leading to the specialization of tissues and organs, as well as to color patterns on the coats of zebras and leopards (2). The idea that the complex dynamics between molecules and cells could also drive regular patterns over landscapes, given all their complexity and variability, is sufficient grounds for fascination. In ecology, Turing instabilities are typically slow at producing regular patterns through the differential growth, reproduction, and survival of individuals across facilitation and competition gradients. de Paoli et al. (13) also bring experimental support to the idea that small-scale self-organization driven by fast behavioral response to density (Fig. 1A) can facilitate larger scale band formation (Fig. 1B). This faster response is not interpreted as a Turing instability; instead, it has been linked to phase separation (18), another class of pattern formation mechanism based on density-dependent movement and originally applied to pattern formation in mixed fluids. Phase separation confers more resistance to both alloy materials and mussel beds by initiating conspecific aggregation into high local densities. Mussel bed ecosystems, and perhaps other ecosystems, display this unique interaction between universal mechanisms, Turing instabilities and phase separation, that combine to bring competing conspecifics to high densities so that they can find safety in numbers while sharing food. Again, this emergence of regularity across a broad range of scales should be enough to fascinate and capture our attention, but there are lessons for conservation biology as well.

Conservation and restoration biology could integrate regular patterns into their respective toolboxes. de Paoli et al. (13) show that imposing regular patterns greatly increases population persistence. On the one hand, the pattern itself might not be the key component because high local density is the proximal cause of resistance to wave disturbance. Self-organized patterns become central as the optimal trade-off between competition and facilitation; they allow for maximum density and aggregation under limited resources. What is even more important for conservation is that a strong departure from this optimal trade-off can lead to catastrophic shifts to alternate stable states characterized by much lower productivity and biomass (19). For restoration, it also means setting regular patterns as a goal because they constitute a stable state; other spatial configurations could naturally evolve toward self-organized patterns, but they also run the risk of collapsing to alternate, less productive states. Importantly, a general integration of regular patterns to conservation strategies requires a general understanding of different classes of regular patterns and of their interactions (Fig. 1). Highly disturbed systems might be more prone to scale-free regularity than to evenly distributed patches, with similar implications for conservations, including the maintenance of high productivity and stability against catastrophic shifts (9). de Paoli et al. (13) provide an important example of interactions among classes of regular patterns across scales; more examples could be discovered across disturbance gradients, and could inform the mitigation of climate change effects on ecosystem functions.

The conservation of regular patterns emphasizes the challenge of setting conservation strategies that target both patterns and underlying processes (8): preserving environmental conditions for the behavioral response of mussels to density, as well as regional planning that sets regular patterns as a target. By formulating conservation biology as a problem of scale, this study demonstrates how large spatial scales of self-organized patterns are functionally significant for spatial management strategies, such as networks of protected areas (20). These patterns, it turns out, are as important as the scale of their underlying behavioral and ecological mechanisms.