Adaptive plasticity in activity modes and food web stability

Akihiko Mougi

doi:10.1371/journal.pone.0267444

Abstract

Natural ecosystems are comprised of diverse species and their interspecific interactions, in contrast to an ecological theory that predicts the instability of large ecological communities. This apparent gap has led ecologists to explore the mechanisms that allow complex communities to stabilize, even via environmental changes. A standard approach to tackling this complexity-stability problem is starting with a description of the ecological network of species and their interaction links, exemplified by a food web. This traditional description is based on the view that each species is in an active state; that is, each species constantly forages and reproduces. However, in nature, species’ activities can virtually stop when hiding, resting, and diapausing or hibernating, resulting in overlooking another situation where they are inactive. Here I theoretically demonstrate that adaptive phenotypic change in active and inactive modes may be the key to understanding food web dynamics. Accurately switching activity modes can greatly stabilize otherwise unstable communities in which coexistence is impossible, further maintaining strong stabilization, even in a large complex community. I hypothesize that adaptive plastic change in activity modes may play a key role in maintaining ecological communities.

Citation: Mougi A (2022) Adaptive plasticity in activity modes and food web stability. PLoS ONE 17(4): e0267444. https://doi.org/10.1371/journal.pone.0267444

Editor: Takefumi Nakazawa, National Cheng Kung University, TAIWAN

Received: December 15, 2021; Accepted: April 9, 2022; Published: April 21, 2022

Copyright: © 2022 Akihiko Mougi. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Data Availability: All relevant data are within the manuscript and its Supporting Information files.

Funding: (1) Grant-in-Aid for Scientific Research (C) (#20K06826) from the Japan Society for the Promotion of Science. (2) Faculty of Life and Environmental Sciences at Shimane University for providing financial aid to publish this article. (this statement is required for receiving this financial aid). Please specify this statement anywhere in the article. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Competing interests: The authors have declared that no competing interests exist.

Introduction

May [1] mathematically demonstrated that large ecosystems are comprised of diverse species and their interactions become inherently unstable and fragile in response to environmental fluctuations, unlike large natural ecosystems. This contradiction between nature and theory, labeled as the complexity–stability debate, has been investigated by ecologists in an attempt to understand the maintenance of ecological communities in nature [2–5]. A major approach to tackling this problem is to reveal the relationship between the ecological network exemplified by a food web (a classical representation of “who eats whom” in the community), and the stability of population dynamics [6,7]. Based on this traditional approach, for half a century, ecologists have proposed diverse mechanisms that allow large ecological communities to remain stable [8–15]. However, it remains unclear whether this ecological view is applicable to real nature, since along this line, each species within a community always actively forages and reproduces, omitting another world in which each species is not active and has almost no species interactions.

In nature, organisms should have both active and inactive modes [16–18]. Animals actively search for resources, prey, mates, and opportunities to reproduce. Active modes are expected to contribute to the population growth, but they can also increase the opportunity to encounter predators, which negatively affect population growth. Thus, active modes are expected to play a role in driving population fluctuations. In this context, the active mode has been a basal model traditionally used to describe the population dynamics in ecological communities. There is no doubt that the standard community dynamics model, due to its analytical simplicity, has greatly contributed to our understanding of how ecological communities are maintained [5]. On the other hand, it would be impossible for organisms to always be active. Organisms spend significant time in inactive modes for diverse reasons, such as resting, recovering from injury, hiding from enemies, diapausing, and hibernating [16]. The inactive mode largely affects community dynamics in several ways. Once the animal is not active, (i) the interaction strengths will be weakened or even vanish. Because the animal is in safety mode, predation risk from enemies becomes low, but the animal loses the opportunity to forage; and (ii) loses the chance to mate so reproduction will decrease, which will decrease the population growth rate. Generally, this is a cost of inactive modes. For example, if the inactive mode is due to a morphological-inducible defense, the maintenance cost of the defensive phenotype can decrease the growth rate [19–21]. Thus, the inactive mode itself is almost never expected to contribute to population dynamics. More importantly, the expected effect of the inactive mode is related to the interaction network. Once a species switches from active to inactive mode, (iii) the node (focal species) within the interaction network will disappear from the active world, resulting in a disappearance of interaction links; this implies a decrease in community complexity, which can largely affect community stability [1].

Here, using a food web model, I demonstrate that switching activity modes in organisms greatly affects community dynamics stability and plays a key role in maintaining complex communities. The model proposed in this study is based on a food web comprising N species, any pair of which is connected with the probability C (connectance). Population dynamics (population sizes of active and inactive modes in each species are respectively represented by X_1i and X_2i, where i = 1,…,N) are driven by interspecific prey-predator interactions (see Materials and methods). A cascade food web was assumed [22] (a random food web was also tested). Two activity modes were considered: active and inactive. Population growth rates, reproduction rates, and interaction strengths in the inactive mode are lower than in the active one. Each species can switch between activity modes, based on the difference between the fitness (or per capita growth rate) of each activity mode [23,24]. A degree of adaptation is characterized by the speed and accuracy of switching between activity modes. The parameter G controls the speed of plastic changes in activity modes. θ denotes the plastic sensitivity to differences in fitness between activity modes (accuracy), and may be interpreted as the ability to catch environmental information; a larger θ represents a higher certainty of environmental information and θ = 0 indicates that no environmental information is available. Hence, when θ = 0, phenotypic changes are random and when θ is high, the model approaches a step function of differences in each fitness (Fig 1A). I controlled the adaptation level (G and θ) to examine how activity mode affects the stability of ecological communities as evaluated by community persistence, with the probability that all species persist for a given time [24,25] (see Materials and methods for further details).

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Fig 1. Plastic changes in activity modes and community stability.

(a) Switching function of activity modes, P_i (Eq 2 in Methods); (b) Effects of the speed and accuracy of phenotypic switching on community stability. See S8 Fig for the confidence interval. The white circle in (b) is the result of no adaptation. N = 40 and C = 0.3. Parameters are R = 0.04, E = 0.01, A₁ = 0.1, and A₂ = 0.05.

https://doi.org/10.1371/journal.pone.0267444.g001

Materials and methods

A cascade food web [22] is considered, in which pairs of species i and j (i, j = 1,…, N) are connected by a trophic interaction with a probability of C, which is defined as the proportion of realized interaction links L in the possible maximum interaction links L_max of a given network model (L = CL_max). For each pair of species, i, j = 1,…, N with i < j, species i never consumes species j, whereas species j may consume species i. To examine the generalization of the main result, random food webs were also tested (S3 Fig). The maximum link number L_max is calculated from N(N−1)/2 in both the random and cascade models. The food web model is defined by the following ordinary differential equation: (1A) (1B) where X_ki is the abundance of species i, r_ki is the intrinsic rate of change in species i, s_i is the density-dependent self-regulation of species i, and M_kij is the interaction coefficient between species i and j. Interaction coefficients are defined as M_kij = e_kija_kij and M_kji = −a_kij, where a_ij is the consumption rate of resource species j by species i and e_kij (<1) is the conversion efficiency. The subscript k represents the activity modes, where 1 is active and 2 is inactive. The last two terms in r.h.s. of Eq (1) represent the dynamics due to plastic changes between the active and inactive modes. G is the constant parameter that controls the speed of plastic changes in activity modes, γ_i is the species-specific phenotypic change rate, and P_i is the switching probability from an active to inactive mode, described by the following non-linear function: (2) where F_ki (k = 1 or 2) is the fitness of the active and inactive modes, defined as F_ki = r_ki–s_iX_ki + Σ_jM_kijX_kj. θ denotes the plastic sensitivity to differences in fitness between the activity modes, and may be interpreted as the ability to catch the information on environments. A larger θ represents a higher certainty of environmental information, while θ = 0 indicates that no environmental information is available. Hence, when θ = 0, phenotypic changes are random and when θ increases, the model approaches a step function of differences in each fitness.

The active and inactive models are defined as follows: (i) r_1i > r_2i (= Rr_1i, where R < 1 is a constant parameter that controls the degree of growth rate reduction from the active to inactive modes); this reflects a cost, due to the phenotypic change to the inactive modes and/or a reduction of the utilization of extra resources. (ii) e_1ij > e_2ij (= Ee_1ij, where E < 1 is a constant parameter that controls the degree of conversion efficiency reduction from the active to inactive modes); this also reflects a cost due to the phenotypic change to the inactive modes. (iii) a_1ij > a_2ij (= A₂a_1ij, where A₂ < 1 is a constant parameter that controls the degree of reduction of interaction strengths from active to inactive modes); this reflects that phenotypic change to the inactive modes makes each species more defensive, but reduces foraging activity. This considers a special case where the refuge in inactive mode is common among each species and very safety against active predators. If they use different habitats in active and inactive individuals, the interaction between active and inactive individuals would be rare. This strong assumption will be relaxed afterward.

It is assumed that r_1i = c_ir, a_1ij = c_iA₁, and γ_i = c_i, where c_i is a constant randomly determined from a uniform distribution (0.0–1.0), r is the absolute growth rate of the active mode (assumed as r = 5), and A₁ is the absolute interaction strength (consumption rate) of the active mode. In this study, for convenience purposes, A₁ and A₂ are referred to as the interaction strength of the active and inactive modes, respectively.

In each iterated simulation, the initial species abundance and parameters were randomly selected from a uniform distribution (X_ki, 0 to 1.0; c_i, 0 to 1.0). The values for s_i and e_1ij were set to constants of 1 (rescaling the species abundances) and 0.2 [26,27], respectively. A positive growth rate in the absence of interaction links was used in all species to avoid a confounding effect, in which an increase in interspecific links decreases the number of heterotrophic species with no potential diet present in the web [14]. From a biological perspective, each species is either autotrophic or makes use of external resources.

Community persistence [24,25] was calculated by measuring the fraction of simulations in which all coexistent species (Σ_kX_ki > 10⁻¹³ for all i) after a sufficiently long time (t = 5 × 10³, which corresponded to the time taken for community persistence to reach an asymptote) in 500 runs.

Results and discussion

Consider an extreme case without inactive mode (G = 0 and X_2i = 0 for all i). Then, in a complex community with diverse species, virtually no community persists (white circle in Fig 1B), as shown via previous food web models. In a world where each species is always active, the population dynamics are predicted to be unstable.

Another case with the inactive mode (i.e., defense, but less foraging/reproduction) is considered. Here, an extreme case, where the inactive mode does not interact with active other species, is assumed first. In this situation, it is expected that inactive individuals remain completely at rest in a safe refuge. Once each species can change their activity mode (G > 0) or switch between active and inactive modes, the community can persist. The stabilization effects critically depend on the fitness sensitivity θ and adaptation speed G. Under slow adaptation (G≪1), the community becomes highly stable and virtually all communities persist, regardless of fitness sensitivity (Fig 1B). However, further increases in the speed of adaptation can alter the stabilization effect, depending on fitness sensitivity. Without sensitivity (θ = 0), stability decreases as the speed of adaptation increases (Fig 1B); the destabilization is so strong that almost no community can persist. However, if each species has high fitness sensitivity, the destabilization due to faster adaptation can vanish (Fig 1B). Under much faster adaptation, the times required for each species to overcome the less adaptive situation are short; thus, if they cannot accurately change their activity modes depending on the environmental situation, phenotypic changes would not play a stabilizing role in community dynamics. As such, under what conditions, in an alternate world, can adaptive phenotypic plasticity play a key role in stabilizing community dynamics?

As predicted by earlier studies [9,13,14], interaction strengths play a major role in community stability. Fig 2 illustrates the effect of the relationship of the interaction between active and inactive modes on community stability. When the interaction strengths in inactive modes are much lower than those in active modes, communities are likely to persist; the requirement of lower interaction strengths in inactive modes to ensure high stability weakens as the interaction strengths in active modes decrease or fitness sensitivity increases. In addition, with high fitness sensitivity, high community stability is maintained in the broad parameter space of interaction strengths (Fig 2).

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Fig 2. Effects of the interaction strengths of each activity mode on community stability, with the variation of switching accuracy (θ).

Color represents the level of community stability as shown within panel (f). N = 40 and C = 0.3. Parameters are R = 0.04, E = 0.01, and G = 1.

https://doi.org/10.1371/journal.pone.0267444.g002

In the above analysis, I have assumed lower growth or reproduction in inactive modes than in active modes, in addition to lower interaction strengths in inactive modes. Here, I relax the strong conditions. The analysis demonstrates that stability is almost not influenced by the asymmetry of growth and reproduction rates between the two modes (S1 Fig). This suggests that stabilization due to adaptive phenotypic plasticity critically depends on the asymmetry of interaction strengths between the two phenotypic modes.

Adaptive phenotypic plasticity has an intriguing consequence on the ongoing complexity-stability debate. Increased complexity (high species richness and connectance) destabilizes community dynamics and can cause species extinctions in food webs without inactive modes (Fig 3). However, with inactive modes, phenotypic change weakens or even cancels the destabilization effects of complexity. Particularly with high sensitivity, communities are not at all destabilized by increased complexity, and can maintain high community stability (Figs 3 and S2). This insensitivity in response to an increase in complexity can be also observed in other network types, like the random model (S3 Fig).

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Fig 3. Relationships between food web complexity and stability.

(a) Effects of species richness (N), C = 0.3; (b) Effects of connectance (C), N = 40. See S8 Fig. for the confidence interval. Black lines represent cases with no inactive mode. Color represents different values of θ. Parameters are R = 0.04, E = 0.01, A₁ = 0.1, A₂ = 0.01, and G = 1.

https://doi.org/10.1371/journal.pone.0267444.g003

Here, the model is extended into more general situations. The above analysis assumed no interactions between the active and inactive modes. In addition, intraspecific interaction (self-regulation) does not change among the different activity modes. These strong assumptions are relaxed, and it is first assumed that intraspecific interaction becomes weak in the inactive mode. Although intraspecific competition among the inactive modes should not weaken if species compete for a refuge, it should do so if the inactive mode is a defensive phenotype, such as inducible defense, because species do not use the refuge and activity is low. Second, the following relations between consumption rates are assumed: a_11ij > a_12ij, a_21ij and a_12ij > a_21ij, a_22ij, where a_klij is the consumption rate of active prey j by active species i if k = l = 1, that of inactive prey j by active species i if k = 1 and l = 2, that of active prey j by inactive species i if k = 2 and l = 1, and that of inactive prey j by inactive species i if k = l = 2, respectively. This is because active individuals encounter other individuals more frequently. In particular, active predators are likely to find active prey more frequently than inactive prey, while inactive predators are less likely to find inactive prey than active prey. The abovementioned novel assumptions corroborate with the main results.

The result shows that a key species interaction for community stability is that between active predator and inactive prey. As the interaction strength of an active predator to inactive prey decreases, the stability increases (S4 Fig). However, the other interactions (inactive predator to active prey and inactive predator to inactive prey) have less or virtually no effects on stability. This suggests that the adaptive plasticity in activity modes can contribute to community stability if the inactive mode strongly acts as a defense. In fact, in such a case, the main results are held. High adaptation ability (high θ and G) is likely to stabilize the system (Fig 4A). Even if θ varies, its effect on stability does not change qualitatively (S5 Fig). In addition, complex communities with rich species and dense interactions can maintain high community stability due to adaptive plasticity (S6 Fig).

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Fig 4. Plastic changes in activity modes and community stability in the case of interaction between the active and inactive modes.

(a) Effects of the speed and accuracy of phenotypic switching on community stability; (b) Effects of the speed and accuracy of phenotypic switching on mean switching probability. See S8 Fig for the confidence interval in (a). The white circle in (a) is the result of no adaptation and the gray circle in (a) is the result of a system with only inactive mode. The mean switching probability is calculated as the mean of species mean P_i in a community after a sufficiently long time (at an equilibrium) in simulation runs. Each bar in (b) represents the standard deviation. N = 40 and C = 0.3. Parameters are A₁₂ = 0.01, A₂₁ = 0.005 and A₂₂ = 0.001. Other parameters are the same as those in S4 Fig.

https://doi.org/10.1371/journal.pone.0267444.g004

In order to understand how the phenotypic changes in the activity modes contribute to community stability, the analysis of switching dynamics among the activity modes is particularly useful. Phenotypic switching is largely affected by adaptive speed and accuracy (S7 Fig). When adaptive speed is slow, the switching probability from the active to inactive mode is nearly 0.5 at the equilibrium, irrespective of accuracy (Fig 4B). Due to a long stay in the active mode, each species should face a high predation risk. In such a situation, switching to the inactive mode is likely to be adaptive. Because inactive modes are more stable (gray circle in Fig 4A), the inactive mode acts to rescue the persistence of the whole system. In contrast, when adaptive speed is fast, the equilibrium switching probability from the active to inactive mode decreases, and largely differs depending on the accuracy (Fig 4B). As accuracy increases, the switching to the inactive mode decreases. Due to a short stay in each mode, individuals are not likely to receive a merit of each activity mode if they inaccurately switch between the two modes. If the accuracy is high, inactive individuals would be able to avoid a high predation risk and active individuals would be able to enjoy high foraging rate and growth rate by avoiding a long-term predation risk, resulting in the low switching to the inactive mode. In this situation, interaction strengths in the active modes become weak because the species interacting in the active mode may not be present. On the other hand, a high switching from the inactive to active mode will act to rescue the persistence of the whole system.

The present study demonstrated that adaptive plastic change in activity modes can play a key role in stabilizing complex food webs, with weak interactions in inactive mode and quick and accurate changes in activity modes being important stabilizing factors. The adaptive plasticity causes much higher stability than the system with only inactive individuals (Fig 4A). The stabilization effect of adaptive plasticity in activity is so strong that inherent instability due to community complexity can vanish, providing a new mechanism of community maintenance. Roughly speaking, the present framework can relate to diverse temporal and spatial phenomena in organisms, including behavioral refuge use, inducible morphological defense, resting, diapausing, and hibernating, suggesting a general mechanism for maintaining ecological communities.

The present theory is intimately linked to earlier works on adaptive behavior and its consequences on ecological community dynamics [28]. Previous studies have predicted that adaptation in foraging [14,29,30] and defense [31–33] commonly has a stabilizing effect on community dynamics. With adaptive foraging, adaptive consumers decrease their foraging efforts against rare resources, allowing for the recovery of rare species. In a similar way, if defense efforts are specifically allocated to each predator, adaptive defense enables the recovery of rare consumers whose resources decrease their avoidance efforts against them. These can be seen as apparent mutualism phenomena that emerge due to the inherent frequency dependence of adaptive trophic behavior [28]. Adaptive behaviors can increase their own and other species’ fitness, resulting in a whole system balance. In the present model, via different ways due to effort allocations, a similar stabilization would occur. If a focal species largely decreases resources, it is expected to suppress its own activity to wait for resource recovery. On the other hand, if a focal species is overly attacked by predators, it is expected to seek refuge until predation rates decrease. The former and latter situations would indirectly enable the recovery of rare resources and rare consumers, respectively. In this sense, the adaptive plasticity of activity is a comprehensive mechanism of adaptive behaviors. Furthermore, it has a more important stabilization mechanism, in contrast with earlier theories. Activity changes can temporally decrease species node and interaction links within an active community network; switching from active to inactive modes implies a disappearance of the species node and the subsequent disappearance of the related interaction links. Hence, in a complex system with many species and interaction links, inactivity can largely decrease system complexity, even temporarily, with the nodes and links repeatedly appearing and disappearing like flashing fireflies. The key point here is that the system becomes simple, and a simple system is more stable than a complex one, as predicted by May [1]. This is more critical in more complex systems, as they are inherently more unstable than simpler systems [1]. In other words, the present theory supports May’s prediction.

The present result has an important implication for the role of adaptive defense in community dynamics. The “refuge” has received high attention in earlier ecology works, especially in relation to the stabilization of predator-prey interactions [34]. However, it remains unclear whether stabilization works in more complex systems. In this sense, the present study links the classic, important concept of population ecology to community ecology. Inducible defense [35], phenotypic changes activated by a previous encounter with an enemy that confer some resistance to subsequent attacks, is a type of refuge. The plastic activity changes in the present model can also be interpreted as inducible defense. Inactive modes may be considered as a morphological or behavioral defensive phenotype. Previous studies have shown that inducible defense can greatly stabilize predator-prey dynamics [36–38]. Given the present results, strong stabilization may also work in complex systems. On the other hand, few studies have examined adaptive defense in complex food webs [31–33], some of which have shown that adaptive defense effort allocations do not have much of a stabilization effect on complex systems, compared with adaptive foraging. As discussed above, increased defense allocation to offensive consumers can contribute to community stability due to apparent mutualism; however, increased consumers can potentially increase the likelihood that resource competition between consumers overcomes apparent mutualism, resulting in the destabilization of complex systems, contrary to the present theoretical prediction. Speed and accuracy of the adaptive phenotypic changes are critical for community stability. The development of further mechanistic modeling considering condition-dependent adaptive changes in these two parameters [39,40] represents a future challenge. Nevertheless, the simple model presented in this study may have important implications for biological conservation. Evolutionary traps caused by anthropogenically-driven environmental changes, which cause maladaptive fitness between environments [41], may destabilize ecological communities.

Supporting information

S1 Fig. Effects of growth rates and reproduction rates on community stability.

R and E are changed. Colors represent different values of E (red: 0.01, orange: 0.2, yellow; 0.4, green: 0.6, blue: 0.8, purple: 1.0). Other parameters are identical to those in Fig 1B.

https://doi.org/10.1371/journal.pone.0267444.s001

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S2 Fig. Relationships between food web complexity and stability with varying adaptation speed and accuracy.

Note that in (a) and (f), θ did not affect the results (it was always stable). Parameters are identical to those in Fig 3.

https://doi.org/10.1371/journal.pone.0267444.s002

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S3 Fig. Relationships between food web complexity and stability in the random food web model.

(a) Effects of species richness (N). I assume C = 0.3. (b) Effects of connectance (C). I assume N = 40. Black lines represent cases without inactive modes. Color represents deferent values of θ. Parameters are R = 0.04, E = 0.01, A₁ = 0.1, A₂ = 0.01, and G = 1.

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S4 Fig. Effects of interactions among active and inactive modes on stability.

(a) A₁₂ = 0.01. (b) A₁₂ = 0.02. (c) A₁₂ = 0.05. (d) A₁₂ = 0.1. A_kl is redefined as: a_11ij = c_iA₁₁, a_12ij = A₁₂a_11ij, a_21ij = A₂₁a_11ij, and a_22ij = A₂₂a_11ij, where A₁₁ is the absolute interaction strength (consumption rate) of the active predator to active prey (a normal interaction strength), and A₁₂, A₂₁ and A₂₂ are constant parameters that controls the degree of reduction of interaction strengths from normal to the other three cases. Different colors represent different values of A₂₁. In (a), blue, red, yellow, and green are A₂₁ = 0.001, 0.002, 0.005, and 0.01, respectively; in (b), blue, red, yellow, and green are A₂₁ = 0.001, 0.002, 0.005, and 0.02, respectively; in (c), blue, red, yellow, and green are A₂₁ = 0.001, 0.002, 0.01, and 0.05, respectively; and in (d), blue, red, yellow, and green are A₂₁ = 0.001, 0.002, 0.01, and 0.1, respectively. N = 40 and C = 0.3. Parameters are s₁ = 1, s₂ = 0.5, A₁₁ = 0.1, R = 0.04, E = 0.01, θ = 20, and G = 1.

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S5 Fig. Effects of variation of θ on community stability.

θ_i values are randomly chosen by a uniform distribution with a mean shown on the horizontal axis. Parameters are the same as those in Fig 4.

https://doi.org/10.1371/journal.pone.0267444.s005

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S6 Fig. Relationships between food web complexity and stability in a system with the interactions between active and inactive modes.

(a) Effects of species richness (N), C = 0.3; (b) Effects of connectance (C), N = 40. Parameters are s₁ = 1, s₂ = 0.5, A₁₁ = 0.1, A₁₂ = 0.01, A₂₁ = 0.005, A₂₂ = 0.001. r = 1, R = 0.2, E = 0.01, and G = 1.

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S7 Fig. Transient dynamics of switching probability P_i.

(a) θ = 5, G = 0.001; (b) θ = 5, G = 10; (c) θ = 20, G = 0.001; (d) θ = 20, G = 10. Each color represents a species. Other parameters are the same as those in Fig 4.

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S8 Fig. Confidence interval of the main results.

(a), (b), (c) and (d) correspond to Fig 1B, Fig 4A, Fig 3A and Fig 3B, respectively. Bar indicates the confidence interval.

https://doi.org/10.1371/journal.pone.0267444.s008

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S1 File.

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Acknowledgments

A.M. deeply appreciates the referees’ useful comments and suggestions. A.M. thanks the faculty of life and environmental sciences at Shimane University for providing financial aid to publish this article.

References

1. May RM. Will a large complex system be stable? Nature. 1972;238(5364):413–4. pmid:4559589.
- View Article
- PubMed/NCBI
- Google Scholar
2. Namba T. Multi-faceted approaches toward unravelling complex ecological networks. Popul Ecol. 2015;57(1):3–19.
- View Article
- Google Scholar
3. McCann KS. The diversity—stability debate. Nature. 2000;405(6783):228–33. pmid:10821283.
- View Article
- PubMed/NCBI
- Google Scholar
4. Pimm SL. The balance of nature?: ecological issues in the conservation of species and communities. University of Chicago Press; 1991.
5. Landi P, Minoarivelo HO, Brännström Å, Hui C, Dieckmann U. Complexity and stability of ecological networks: a review of the theory. Popul Ecol. 2018;60(4):319–45.
- View Article
- Google Scholar
6. McCann KS. Food webs (MPB-50). Princeton University Press; 2011.
7. Pimm SL. Food webs. Food Webs. 1982:1–11.
- View Article
- Google Scholar
8. Brose U, Williams RJ, Martinez ND. Allometric scaling enhances stability in complex food webs. Ecol Lett. 2006;9(11):1228–36. pmid:17040325.
- View Article
- PubMed/NCBI
- Google Scholar
9. Neutel AM, Heesterbeek JAP, De Ruiter PC. Stability in real food webs: weak links in long loops. Science. 2002;296(5570):1120–3. pmid:12004131.
- View Article
- PubMed/NCBI
- Google Scholar
10. Dunne JA, Williams RJ, Martinez ND. Network structure and biodiversity loss in food webs: robustness increases with connectance. Ecol Letters. 2002;5(4):558–67.
- View Article
- Google Scholar
11. Bascompte J, Jordano P, Olesen JM. Asymmetric coevolutionary networks facilitate biodiversity maintenance. Science. 2006;312(5772):431–3. pmid:16627742.
- View Article
- PubMed/NCBI
- Google Scholar
12. Thébault E, Fontaine C. Stability of ecological communities and the architecture of mutualistic and trophic networks. Science. 2010;329(5993):853–6. pmid:20705861.
- View Article
- PubMed/NCBI
- Google Scholar
13. Gellner G, McCann KS. Consistent role of weak and strong interactions in high- and low-diversity trophic food webs. Nat Commun. 2016;7:11180. pmid:27068000.
- View Article
- PubMed/NCBI
- Google Scholar
14. Kondoh M. Foraging adaptation and the relationship between food-web complexity and stability. Science. 2003;299(5611):1388–91. pmid:12610303.
- View Article
- PubMed/NCBI
- Google Scholar
15. Mougi A, Kondoh M. Diversity of interaction types and ecological community stability. Science. 2012;337(6092):349–51. pmid:22822151.
- View Article
- PubMed/NCBI
- Google Scholar
16. Herbers JM. Time resources and laziness in animals. Oecologia. 1981;49(2):252–62. pmid:28309319.
- View Article
- PubMed/NCBI
- Google Scholar
17. Korstjens AH, Lehmann J, Dunbar RIM. Resting time as an ecological constraint on primate biogeography. Anim Behav. 2010;79(2):361–74.
- View Article
- Google Scholar
18. Houston AI, McNamara JM. Foraging currencies, metabolism and behavioural routines. J Anim Ecol. 2014;83(1):30–40. pmid:23730810.
- View Article
- PubMed/NCBI
- Google Scholar
19. DeWitt TJ, Sih A, Wilson DS. Costs and limits of phenotypic plasticity. Trends Ecol Evol. 1998;13(2):77–81. pmid:21238209.
- View Article
- PubMed/NCBI
- Google Scholar
20. Agrawal AA. Phenotypic plasticity in the interactions and evolution of species. Science. 2001;294(5541):321–6. pmid:11598291.
- View Article
- PubMed/NCBI
- Google Scholar
21. Kishida O, Trussell GC, Mougi A, Nishimura K. Evolutionary ecology of inducible morphological plasticity in predator–prey interaction: toward the practical links with population ecology. Popul Ecol. 2010;52(1):37–46.
- View Article
- Google Scholar
22. Chen X, Cohen JE. Transient dynamics and food—web complexity in the Lotka—Volterra cascade model. Proc R Soc Lond B. 2001;268:869–77. pmid:11345334
- View Article
- PubMed/NCBI
- Google Scholar
23. Kondoh M, Mougi A, Ushimaru A, Nakata K. Adaptive movement and food-chain dynamics: towards food-web theory without birth—death processes. Theor Ecol. 2016;9(1):15–25.
- View Article
- Google Scholar
24. Mougi A. Adaptive migration promotes food web persistence. Sci Rep. 2019;9(1):12632. pmid:31477790.
- View Article
- PubMed/NCBI
- Google Scholar
25. Mougi A. Diversity of biological rhythm and food web stability. Biol Lett. 2021;17(2):20200673. pmid:33563135
- View Article
- PubMed/NCBI
- Google Scholar
26. Humphreys WF. Production and respiration in animal populations. J Anim Ecol. 1979;48(2):427–53.
- View Article
- Google Scholar
27. Robbins CT. Wildlife feeding and nutrition. 2nd ed. San Diego: Academic Press; 1993.
28. Valdovinos FS, Ramos-Jiliberto R, Garay-Narváez L, Urbani P, Dunne JA. Consequences of adaptive behaviour for the structure and dynamics of food webs. Ecol Lett. 2010;13(12):1546–59. pmid:20937057.
- View Article
- PubMed/NCBI
- Google Scholar
29. Uchida S, Drossel B. Relation between complexity and stability in food webs with adaptive behavior. J Theor Biol. 2007;247(4):713–22. pmid:17543344.
- View Article
- PubMed/NCBI
- Google Scholar
30. Uchida S, Drossel B, Brose U. The structure of food webs with adaptive behaviour. Ecol Modell. 2007;206(3–4):263–76.
- View Article
- Google Scholar
31. Matsuda H, Hori M, Abrams PA. Effects of predator-specific defence on community complexity. Evol Ecol. 1994;8(6):628–38.
- View Article
- Google Scholar
32. Matsuda H, Hori M, Abrams PA. Effects of predator-specific defence on biodiversity and community complexity in two-trophic-level communities. Evol Ecol. 1996;10(1):13–28.
- View Article
- Google Scholar
33. Kondoh M. Anti-predator defence and the complexity—stability relationship of food webs. Proc Biol Sci. 2007;274(1618):1617–24. pmid:17456452.
- View Article
- PubMed/NCBI
- Google Scholar
34. Berryman AA, Hawkins BA, Hawkins BA. The refuge as an integrating concept in ecology and evolution. Oikos. 2006;115(1):192–6.
- View Article
- Google Scholar
35. Tollrian R, Harvell CD. The ecology and evolution of inducible defenses. Princeton University Press; 1999.
36. Vos M, Kooi BW, DeAngelis DL, Mooij WM. Inducible defences and the paradox of enrichment. Oikos. 2004;105(3):471–80.
- View Article
- Google Scholar
37. Mougi A, Kishida O. Reciprocal phenotypic plasticity can lead to stable predator–prey interaction. J Anim Ecol. 2009;78(6):1172–81. pmid:19622080.
- View Article
- PubMed/NCBI
- Google Scholar
38. Kovach-Orr C, Fussmann GF. Evolutionary and plastic rescue in multitrophic model communities. Philos Trans R Soc Lond B Biol Sci. 2013;368(1610):20120084. pmid:23209166.
- View Article
- PubMed/NCBI
- Google Scholar
39. Chittka L, Skorupski P, Raine NE. Speed-accuracy tradeoffs in animal decision making. Trends Ecol Evol. 2009;24(7):400–7. pmid:19409649.
- View Article
- PubMed/NCBI
- Google Scholar
40. Sih A, Del Giudice M. Linking behavioural syndromes and cognition: a behavioural ecology perspective. Philos Trans R Soc Lond B Biol Sci. 2012;367(1603):2762–72. pmid:22927575.
- View Article
- PubMed/NCBI
- Google Scholar
41. Robertson BA, Rehage JS, Sih A. Ecological novelty and the emergence of evolutionary traps. Trends Ecol Evol. 2013;28(9):552–60. pmid:23756104.
- View Article
- PubMed/NCBI
- Google Scholar

[ref1] 1. May RM. Will a large complex system be stable? Nature. 1972;238(5364):413–4. pmid:4559589.
View Article
PubMed/NCBI
Google Scholar

[2] View Article

[3] PubMed/NCBI

[4] Google Scholar

[ref2] 2. Namba T. Multi-faceted approaches toward unravelling complex ecological networks. Popul Ecol. 2015;57(1):3–19.
View Article
Google Scholar

[6] View Article

[7] Google Scholar

[ref3] 3. McCann KS. The diversity—stability debate. Nature. 2000;405(6783):228–33. pmid:10821283.
View Article
PubMed/NCBI
Google Scholar

[9] View Article

[10] PubMed/NCBI

[11] Google Scholar

[ref4] 4. Pimm SL. The balance of nature?: ecological issues in the conservation of species and communities. University of Chicago Press; 1991.

[ref5] 5. Landi P, Minoarivelo HO, Brännström Å, Hui C, Dieckmann U. Complexity and stability of ecological networks: a review of the theory. Popul Ecol. 2018;60(4):319–45.
View Article
Google Scholar

[14] View Article

[15] Google Scholar

[ref6] 6. McCann KS. Food webs (MPB-50). Princeton University Press; 2011.

[ref7] 7. Pimm SL. Food webs. Food Webs. 1982:1–11.
View Article
Google Scholar

[18] View Article

[19] Google Scholar

[ref8] 8. Brose U, Williams RJ, Martinez ND. Allometric scaling enhances stability in complex food webs. Ecol Lett. 2006;9(11):1228–36. pmid:17040325.
View Article
PubMed/NCBI
Google Scholar

[21] View Article

[22] PubMed/NCBI

[23] Google Scholar

[ref9] 9. Neutel AM, Heesterbeek JAP, De Ruiter PC. Stability in real food webs: weak links in long loops. Science. 2002;296(5570):1120–3. pmid:12004131.
View Article
PubMed/NCBI
Google Scholar

[25] View Article

[26] PubMed/NCBI

[27] Google Scholar

[ref10] 10. Dunne JA, Williams RJ, Martinez ND. Network structure and biodiversity loss in food webs: robustness increases with connectance. Ecol Letters. 2002;5(4):558–67.
View Article
Google Scholar

[29] View Article

[30] Google Scholar

[ref11] 11. Bascompte J, Jordano P, Olesen JM. Asymmetric coevolutionary networks facilitate biodiversity maintenance. Science. 2006;312(5772):431–3. pmid:16627742.
View Article
PubMed/NCBI
Google Scholar

[32] View Article

[33] PubMed/NCBI

[34] Google Scholar

[ref12] 12. Thébault E, Fontaine C. Stability of ecological communities and the architecture of mutualistic and trophic networks. Science. 2010;329(5993):853–6. pmid:20705861.
View Article
PubMed/NCBI
Google Scholar

[36] View Article

[37] PubMed/NCBI

[38] Google Scholar

[ref13] 13. Gellner G, McCann KS. Consistent role of weak and strong interactions in high- and low-diversity trophic food webs. Nat Commun. 2016;7:11180. pmid:27068000.
View Article
PubMed/NCBI
Google Scholar

[40] View Article

[41] PubMed/NCBI

[42] Google Scholar

[ref14] 14. Kondoh M. Foraging adaptation and the relationship between food-web complexity and stability. Science. 2003;299(5611):1388–91. pmid:12610303.
View Article
PubMed/NCBI
Google Scholar

[44] View Article

[45] PubMed/NCBI

[46] Google Scholar

[ref15] 15. Mougi A, Kondoh M. Diversity of interaction types and ecological community stability. Science. 2012;337(6092):349–51. pmid:22822151.
View Article
PubMed/NCBI
Google Scholar

[48] View Article

[49] PubMed/NCBI

[50] Google Scholar

[ref16] 16. Herbers JM. Time resources and laziness in animals. Oecologia. 1981;49(2):252–62. pmid:28309319.
View Article
PubMed/NCBI
Google Scholar

[52] View Article

[53] PubMed/NCBI

[54] Google Scholar

[ref17] 17. Korstjens AH, Lehmann J, Dunbar RIM. Resting time as an ecological constraint on primate biogeography. Anim Behav. 2010;79(2):361–74.
View Article
Google Scholar

[56] View Article

[57] Google Scholar

[ref18] 18. Houston AI, McNamara JM. Foraging currencies, metabolism and behavioural routines. J Anim Ecol. 2014;83(1):30–40. pmid:23730810.
View Article
PubMed/NCBI
Google Scholar

[59] View Article

[60] PubMed/NCBI

[61] Google Scholar

[ref19] 19. DeWitt TJ, Sih A, Wilson DS. Costs and limits of phenotypic plasticity. Trends Ecol Evol. 1998;13(2):77–81. pmid:21238209.
View Article
PubMed/NCBI
Google Scholar

[63] View Article

[64] PubMed/NCBI

[65] Google Scholar

[ref20] 20. Agrawal AA. Phenotypic plasticity in the interactions and evolution of species. Science. 2001;294(5541):321–6. pmid:11598291.
View Article
PubMed/NCBI
Google Scholar

[67] View Article

[68] PubMed/NCBI

[69] Google Scholar

[ref21] 21. Kishida O, Trussell GC, Mougi A, Nishimura K. Evolutionary ecology of inducible morphological plasticity in predator–prey interaction: toward the practical links with population ecology. Popul Ecol. 2010;52(1):37–46.
View Article
Google Scholar

[71] View Article

[72] Google Scholar

[ref22] 22. Chen X, Cohen JE. Transient dynamics and food—web complexity in the Lotka—Volterra cascade model. Proc R Soc Lond B. 2001;268:869–77. pmid:11345334
View Article
PubMed/NCBI
Google Scholar

[74] View Article

[75] PubMed/NCBI

[76] Google Scholar

[ref23] 23. Kondoh M, Mougi A, Ushimaru A, Nakata K. Adaptive movement and food-chain dynamics: towards food-web theory without birth—death processes. Theor Ecol. 2016;9(1):15–25.
View Article
Google Scholar

[78] View Article

[79] Google Scholar

[ref24] 24. Mougi A. Adaptive migration promotes food web persistence. Sci Rep. 2019;9(1):12632. pmid:31477790.
View Article
PubMed/NCBI
Google Scholar

[81] View Article

[82] PubMed/NCBI

[83] Google Scholar

[ref25] 25. Mougi A. Diversity of biological rhythm and food web stability. Biol Lett. 2021;17(2):20200673. pmid:33563135
View Article
PubMed/NCBI
Google Scholar

[85] View Article

[86] PubMed/NCBI

[87] Google Scholar

[ref26] 26. Humphreys WF. Production and respiration in animal populations. J Anim Ecol. 1979;48(2):427–53.
View Article
Google Scholar

[89] View Article

[90] Google Scholar

[ref27] 27. Robbins CT. Wildlife feeding and nutrition. 2nd ed. San Diego: Academic Press; 1993.

[ref28] 28. Valdovinos FS, Ramos-Jiliberto R, Garay-Narváez L, Urbani P, Dunne JA. Consequences of adaptive behaviour for the structure and dynamics of food webs. Ecol Lett. 2010;13(12):1546–59. pmid:20937057.
View Article
PubMed/NCBI
Google Scholar

[93] View Article

[94] PubMed/NCBI

[95] Google Scholar

[ref29] 29. Uchida S, Drossel B. Relation between complexity and stability in food webs with adaptive behavior. J Theor Biol. 2007;247(4):713–22. pmid:17543344.
View Article
PubMed/NCBI
Google Scholar

[97] View Article

[98] PubMed/NCBI

[99] Google Scholar

[ref30] 30. Uchida S, Drossel B, Brose U. The structure of food webs with adaptive behaviour. Ecol Modell. 2007;206(3–4):263–76.
View Article
Google Scholar

[101] View Article

[102] Google Scholar

[ref31] 31. Matsuda H, Hori M, Abrams PA. Effects of predator-specific defence on community complexity. Evol Ecol. 1994;8(6):628–38.
View Article
Google Scholar

[104] View Article

[105] Google Scholar

[ref32] 32. Matsuda H, Hori M, Abrams PA. Effects of predator-specific defence on biodiversity and community complexity in two-trophic-level communities. Evol Ecol. 1996;10(1):13–28.
View Article
Google Scholar

[107] View Article

[108] Google Scholar

[ref33] 33. Kondoh M. Anti-predator defence and the complexity—stability relationship of food webs. Proc Biol Sci. 2007;274(1618):1617–24. pmid:17456452.
View Article
PubMed/NCBI
Google Scholar

[110] View Article

[111] PubMed/NCBI

[112] Google Scholar

[ref34] 34. Berryman AA, Hawkins BA, Hawkins BA. The refuge as an integrating concept in ecology and evolution. Oikos. 2006;115(1):192–6.
View Article
Google Scholar

[114] View Article

[115] Google Scholar

[ref35] 35. Tollrian R, Harvell CD. The ecology and evolution of inducible defenses. Princeton University Press; 1999.

[ref36] 36. Vos M, Kooi BW, DeAngelis DL, Mooij WM. Inducible defences and the paradox of enrichment. Oikos. 2004;105(3):471–80.
View Article
Google Scholar

[118] View Article

[119] Google Scholar

[ref37] 37. Mougi A, Kishida O. Reciprocal phenotypic plasticity can lead to stable predator–prey interaction. J Anim Ecol. 2009;78(6):1172–81. pmid:19622080.
View Article
PubMed/NCBI
Google Scholar

[121] View Article

[122] PubMed/NCBI

[123] Google Scholar

[ref38] 38. Kovach-Orr C, Fussmann GF. Evolutionary and plastic rescue in multitrophic model communities. Philos Trans R Soc Lond B Biol Sci. 2013;368(1610):20120084. pmid:23209166.
View Article
PubMed/NCBI
Google Scholar

[125] View Article

[126] PubMed/NCBI

[127] Google Scholar

[ref39] 39. Chittka L, Skorupski P, Raine NE. Speed-accuracy tradeoffs in animal decision making. Trends Ecol Evol. 2009;24(7):400–7. pmid:19409649.
View Article
PubMed/NCBI
Google Scholar

[129] View Article

[130] PubMed/NCBI

[131] Google Scholar

[ref40] 40. Sih A, Del Giudice M. Linking behavioural syndromes and cognition: a behavioural ecology perspective. Philos Trans R Soc Lond B Biol Sci. 2012;367(1603):2762–72. pmid:22927575.
View Article
PubMed/NCBI
Google Scholar

[133] View Article

[134] PubMed/NCBI

[135] Google Scholar

[ref41] 41. Robertson BA, Rehage JS, Sih A. Ecological novelty and the emergence of evolutionary traps. Trends Ecol Evol. 2013;28(9):552–60. pmid:23756104.
View Article
PubMed/NCBI
Google Scholar

[137] View Article

[138] PubMed/NCBI

[139] Google Scholar

Figures

Abstract

Introduction

Materials and methods

Results and discussion

Supporting information

S1 Fig. Effects of growth rates and reproduction rates on community stability.

S2 Fig. Relationships between food web complexity and stability with varying adaptation speed and accuracy.

S3 Fig. Relationships between food web complexity and stability in the random food web model.

S4 Fig. Effects of interactions among active and inactive modes on stability.

S5 Fig. Effects of variation of θ on community stability.

S6 Fig. Relationships between food web complexity and stability in a system with the interactions between active and inactive modes.

S7 Fig. Transient dynamics of switching probability Pi.

S8 Fig. Confidence interval of the main results.

S1 File.

Acknowledgments

References

S7 Fig. Transient dynamics of switching probability P_i.