- Email: [email protected]
Connectance and nestedness as stabilizing factors in response to pulse disturbances in adaptive antagonistic networks
Journal of Theoretical Biology 486 (2020) 110073
Contents lists available at ScienceDirect
Journal of Theoretical Biology journal homepage: www.elsevier.com/locate/jtb
Connectance and nestedness as stabilizing factors in response to pulse disturbances in adaptive antagonistic networks Matheus T. Baumgartner Graduate Course in Ecology of Freshwater Environments, Department of Biology, Centre for Biological Sciences, State University of Maringá, Maringá, Paraná, Brazil
a r t i c l e
i n f o
Article history: Received 19 June 2019 Revised 23 October 2019 Accepted 5 November 2019 Available online 6 November 2019 Keywords: Stability Community robustness Ecological interaction networks Food webs Lotka-Volterra
a b s t r a c t Understanding how network architectures are related to community robustness is essential to investigating the effects of disturbances on biological systems. Regarding the perturbations that are observed in disturbance regimes, frequency and intensity are two main descriptors, specifically for those events with short duration. Here, I used the architecture of 45 real-world weighted bipartite networks to assess whether network size, connectance, and nestedness are related to the effects of pulse disturbances in antagonistic communities. Networks were simulated under five scenarios with different combinations of frequency and intensity of perturbations. The dynamics of resource-consumer interactions followed the adaptive interaction switching behavior, which is the key topological process underlying most of the architectures of antagonistic webs. As opposed to most studies considering the effects of disturbances as species extinctions explicitly, the effects of disturbances here were modeled as changes in the abundance of consumers following immediate reductions in the abundance of resources. Simulations revealed that community robustness to pulse disturbances increased with both connectance and nestedness overall, with no effect of network size. Community networks with highly connected and nested topologies were more robust to disturbances, particularly under high frequency and intensity perturbations. By considering disturbances that are not directly related to species’ extinctions, this study provides valuable insights that connectance and nestedness have an important stabilizing role in ecological networks. © 2019 Elsevier Ltd. All rights reserved.
1. Introduction The effects of disturbances on communities have been investigated extensively in the last five decades (Levin and Paine, 1974; Connell, 1978). Although there is no consensus on the process, understanding how these events affect community structure is fundamental because of the potential impacts on ecosystem services (Turner, 2010). Due to the increased human activities in recent years, the disturbance regimes are changing rapidly across several regions of the world (Dornelas, 2010; Turner, 2010; Johnstone et al., 2016; Newman, 2019), which is the main reason that the effects of disturbances on ecological communities have been in the frontline of biological research (Eklöf and Ebenman, 2006; Thebault and Fontaine, 2010; Rohr et al., 2014). Therefore, we must understand how some of the properties of ecological communities are related to the robustness against disturbances in order to increase the predictive power of theoretical research (Estrada, 2007; Stouffer and Bascompte, 2011).
E-mail address: [email protected] https://doi.org/10.1016/j.jtbi.2019.110073 0022-5193/© 2019 Elsevier Ltd. All rights reserved.
Disturbance can be defined following Pickett and White (1985) as any discrete event in time that disrupts community structure and changes resources availability, whereas disturbance regimes are described as repetitive disturbances that constitute a temporal pattern (Turner, 2010). Within this context, short-term discrete disturbances may be also commonly referred to as pulse disturbances. More specifically, pulse disturbances that are in the control of the experimentalist can be treated as “perturbations” (Pickett and White, 1985; McCabe and Gotelli, 20 0 0). We are then able to build a theoretical framework focusing on how communities respond to different disturbance regimes described by different perturbations. In most natural ecosystems, perturbations are usually related to fire, grazing, extreme weather events, flooding, and other environmental stressors (Battisti et al., 2016). Regardless of their nature, two important features of disturbance regimes, which may influence predictability, can describe these perturbations: intensity and frequency (Jentsch and White 2019). For instance, a fire event in a savannah can burn half of the plant biomass in the system (intensity), every year (frequency), whereas a seasonal flood pulse can reduce the biomass of the marginal vegetation of a lake during
2
M.T. Baumgartner / Journal of Theoretical Biology 486 (2020) 110073
each rainy season. In both situations, a perturbation event that is the consequence of an environmental factor (e.g., fire or flood) reduces the abundance of resources (plants) with important effects on consumers (e.g., herbivores). Antagonist communities can be described as a diverse number of resources and consumers coexisting and interacting with each other through predation and parasitism, such as in networks (Borrett et al., 2014). Considering the dynamics of antagonistic interactions, a hybrid behavior combining two main topological processes underlies resources-consumers networks: interaction switch and random drift. These adaptive processes depicts the tradeoff between natural selection, by the elimination of the unfit (by disposing the resource that contributes the least to its fitness), and the random trial of new resources (Valdovinos et al., 2010; Suweis et al., 2013), which explain most of the empirical architectures of antagonistic networks (Nuwagaba et al., 2015). Many recent studies have investigated the relationships between how communities respond to disturbances and network properties as connectance and nestedness, usually finding a positive relationship for both metrics (Dunne et al., 2002; Bascompte et al., 2003; Burgos et al., 2007; Staniczenko et al., 2010; Landi et al., 2018). However, most studies consider disturbances as species extinction explicitly. Although this is a recognized approach, extinction is only the summit of the abundance decline for a given species, and investigating the robustness of communities (i.e., the ability to sustain its structure in the face of perturbations) by focusing on the relative changes in abundances after each event may provide valuable insights. Species abundance is a sufficiently general descriptor of community state because it does not depend on species identity, and can therefore be used to assess changes in the community state broadly (McGill et al., 2007; Dornelas et al., 2009). Here, I explored whether network properties as connectance and nestedness are related to how antagonist communities respond to different disturbance regimes, considering alternative intensities and frequencies of perturbations. To achieve this objective, I considered the architecture of 45 weighted bipartite (resource-consumer) networks. The dynamics of the networks were considered under a realistic background by incorporating adaptive interaction switching and random drift (Nuwagaba et al., 2015). Networks were subjected to different disturbance regimes by considering five alternative scenarios regarding the intensity and frequency of perturbations. The effect of perturbations was measured as the average change in the abundance of consumers, following discrete reductions in the abundance of resources. Particularly, this study is a specific investigation of the yet underexplored relationship between network properties and the effects of disturbances affecting species’ abundances, rather than their persistence, in ecological networks. In accordance with previous findings (Dunne et al., 2002; Nuwagaba et al., 2017; Mougi and Kondoh, 2016; Traveset et al., 2017), the results underline the fundamental role of connectance and nestedness in decreasing the extent of disturbances and stabilizing the dynamics of biological communities.
2. Materials and Methods Consider an antagonist community where i resources are explored by j consumers as in trophic or host-parasite networks. The population dynamics of resource i is determined by its growth rate minus the population depletion by consumption, while the population of consumer j increases by the exploration of resources minus its density-dependent mortality. If a Holling’s type II functional response is considered, the following Lotka-Volterra resource-consumer model can describe the population dynamics of
species:
⎧ ⎨ R1i
⎩1
Nj
dRi dt dN j dt
= r i − ci Ri − = −d j N j +
j 1+h
ai j vi j N j k ak j vk j Rk
b ji ai j vi j Ri i 1+h k ak j vk j Rk
where Ri and Nj are the abundances of resource i and consumer j, respectively; ri and ci are the intrinsic growth rate and the density-dependent self-regulation coefficient of resource i; dj is the density-dependent mortality of consumer j. Explicitly, the binary interaction matrix (aij ) depicts whether resource i is exploited (1) or not (0) by consumer j; the preference matrix (vij ) describes the probability of consumer j feeding on resource i once met; the benefit matrix (bij ) denotes the energetic income of consumer j when feeding on resource i; h is the handling time, assumed to be equal for all consumers (0.1). The networks followed the hybrid rule of adaptive interaction switch and random drift. This dynamics depicts the tradeoff predicted by natural selection through the elimination of the unfit and the random trial of new resources (Valdovinos et al., 2010; Suweis et al., 2013). At each time step, a random consumer disposes the resource that contributes the least to its per capita growth rate (the resource with the lowest bji aij vij Ri in the equation above) and a new resource is added to the diet of another random consumer, with a random preference. The initial architecture of networks (numbers of resources, consumers, and link density) mirrored those from 45 empirical bipartite networks (14 herbivore-plant and 31 host-parasite; Online Resource 1). The entries of the matrix aij were randomly assigned controlling for no isolated species by ensuring that every species had at least one resource or consumer, and initial population sizes and parameters (ri , ci , dj , vij , and bij ) were assigned at random between 0 and 1; mirroring the structure from Nuwagaba et al. (2015). This random assignment of values for parameters and initial abundances was assumed as not affecting the results, following Nuwagaba et al. (2015, 2017). Moreover, the focus herein was on the discrete effects of disturbances on the overall community structure, which were investigated through highly controlled simulations, rather than on the ability of communities to preserve their original structure. To simulate disturbance regimes, the abundances of resources were reduced following five different scenarios. The first scenario was referred to as “baseline” (Fig. 1A) and consisted of a 40% reduction in abundances every 25 time steps. The second scenario was called “medium frequency” (Fig. 1B) and consisted of 40% reduction in abundances every 20 time steps. The third scenario was treated as “medium intensity” (Fig. 1C) and depicted a 60% decrease in abundances every 25 time steps. The fourth scenario was called “high frequency” (Fig. 1D) and represented a reduction of 40% in abundances every 10 time steps. Finally, the fifth scenario was referred to as “high intensity” (Fig. 1E), representing a 90% decrease in abundances every 25 time steps. The five different scenarios did not follow any specific theoretical basis in respect to the frequency and intensity of disturbance regimes. This decision, coupled with the different combinations of frequency and intensity of perturbations in each scenario, were fundamental to ensure the generalizations of the model. The effect of disturbances was quantified as the average rate of change (after/before) in the overall abundance of consumers (Ab), recorded one time step before and after each perturbation as Ab = ( N jt / N jt−1 )/d, where Nj t is the abundance of consumer j one time step after the disturbance, N j t−1 is the abundance of consumer j one time step before the disturbance, and d is the number of perturbation events for each scenario. This metric quantifies the proportional decrease in the abundance of consumers after each perturbation event, thus the inverse of community robustness (i.e., greater shifts in the abundance of consumers
M.T. Baumgartner / Journal of Theoretical Biology 486 (2020) 110073
Fig. 1. Disturbance scenarios were established based on the frequency and intensity of reductions in the abundance of resources. (A) Baseline scenario caused a 40% reduction every 25 time steps; (B) Medium frequency caused a 40% reduction every 20 time steps; (C) Medium intensity caused a 60% reduction every 25 time steps; (D) High frequency caused a 40% reduction every 10 time steps; (E) High intensity caused a 90% reduction every 25 time steps.
3
are expected in less robust communities). Although intuitively general, changes in the relative abundance of species are consistent descriptors of community dynamics because it precedes shifts in community structure and further species extinctions (Gaston and Fuller, 2008). Particularly, the arbitrary short-term evaluation of the effects of perturbations was essential to avoid potential confounding effects related to the stochastic dynamics of the communities (Dornelas, 2010). Networks were simulated under 100 time steps without perturbations to reach an equilibrium state (usually reached at t = 50; Figure S1), then additional 200 time steps under each of the disturbance regimes were performed. To simplify the model and to focus on the abundance decrease, resources were not allowed to go extinct and were instantly respawned (with random values between 0 and 0.2) if their abundances were below 10−6 , while eventual extinctions of consumers were allowed. This condition was implemented to prevent community collapse due to spurious resources extinctions, which, in fact, rarely occurred overall. Because we were interested in the short-term effects, resources were able to recover immediately after each reduction in abundance. The performance of the model was evaluated by supervising the temporal trajectories of the abundances of both resources and consumers, and simulations were restarted for those communities that ≥ 20% of consumers were lost or eventually collapsed before reaching equilibrium. To assess whether network properties were related to the effects of disturbances, the mean change in the abundance of consumers was tested for correlation with both connectance and nestedness, using Spearman’s rank correlation. Connectance is defined and calculated as the proportion of realized links between species related to the maximum of a given network (realized links/species²; Memmott et al., 2004), while nestedness is a tendency of specialists to interact only with a subset of those species interacting with more generalist species (Nielsen and Bascompte, 2007). These two metrics are recognized as related to community robustness against species extinctions (Memmott et al., 2004; Burgos et al., 2007), and were calculated for each final interaction matrix after simulations. Nestedness was calculated using the Nestedness Metric Based on Overlap and Decreasing Fill (NODF; Almeida-Neto et al., 2008). Because network size (calculated as the number of species or nodes) is frequently correlated with connectance, which may plausibly contribute to stabilization (Fowler, 2009; Landi et al., 2018), this network metric was also considered. Model construction, simulations, and analyses were conducted in the R Environment (R Core Team, 2019). 3. Results
Fig. 2. Mean and standard errors for the effects of disturbances measured as the change in the abundance of consumers at each of the five simulated disturbance regimes. See Methods for details.
The effects of disturbances on the decrease in the abundance of consumers varied across the disturbance scenarios (Fig. 2). Since the Levene’s test revealed that the homogeneity of variances was violated (Levene’s F(4220) = 3.08; P = 0.02), a Welch’s ANOVA was applied. This analysis revealed significant differences (Welch’s F(4105.64) = 14.35; P < 0.01), specifically between the scenario with disturbances at high intensity and all other scenarios (P < 0.01), and between medium intensity and high frequency scenarios (P = 0.01). The effects of disturbances, quantified as the average decrease in the abundance of consumers (Ab), had no correlation with network size (Table 1). However, connectance had significant negative correlations with Ab in all five scenarios representing different disturbance regimes (Table 1; Figs. 3 and 4). An analogous negative correlation with Ab was observed for nestedness, whereas significant values were observed under baseline, medium intensity and high frequency scenarios (Table 1; Fig. 4). At the final architecture, network size was negatively correlated with connectance (Spearman’s rank correlation (ρ ) = −0.60; P < 0.01) and nested-
4
M.T. Baumgartner / Journal of Theoretical Biology 486 (2020) 110073 Table 1 Spearman’s rank correlation between the mean decrease in the abundance of consumers (Ab) following perturbations and network properties (network size, connectance, and nestedness). Scenario
Network size
Connectance
Nestedness
Baseline Medium frequency Medium intensity High frequency High intensity
0.08 0.06 0.10 0.08 −0.05
−0.40 −0.32 −0.37 −0.35 −0.38
−0.36 −0.29 −0.38 −0.31 −0.29
Perturbations were considered as reductions in the abundance of resources under five alternative frequency and intensity scenarios (see Methods for details). Significant correlations at α = 0.05 are in bold.
ness (ρ = −0.72; P < 0.01), whereas connectance and nestedness were highly correlated (ρ = 0.93; P < 0.01), as expected under realistic circumstances for real-world networks (Figure S2). Detailing how network properties were related to the effects of disturbances, the high frequency and high intensity scenarios caused immediate reductions in the abundance of consumers up to 15% and 12%, respectively (Fig. 4). Although the network size was not correlated with the effects of disturbances, there was a decreasing trend in the reduction in consumers abundance after perturbation events as the number of species increased under the medium intensity scenario (Fig. 4A). The stabilizing effect of con-
Fig. 3. Relationships between the mean decrease in the consumers abundance (Ab) following perturbations and network metrics (connectance and nestedness). Connectance was controlled prior to the simulations using link density from 45 real bipartite networks (see Online Resource 1). Nestedness architecture emerged during simulations.
nectance was consistent across all disturbance scenarios, specifically under highly frequent and intense perturbations (Fig. 4B). Finally, the scenarios that provided the clearest stabilizing effects of nestedness were the baseline, medium intensity, and high frequency, with a clear decreasing trend of the decrease in consumers’ abundance as nestedness increased (Fig. 4C).
Fig. 4. Relationships between the effects of disturbances, assessed through the mean decrease in consumers abundance (Ab) immediately after reductions in the abundance of resources, and network properties (network size, connectance, and nestedness). See Methods for details on frequency and intensity of perturbations in each of the simulated disturbance regimes. The red lines indicate the overall trends of significant Spearman’s rank correlations at α = 0.05. Raw correlation values are in Table 1.
M.T. Baumgartner / Journal of Theoretical Biology 486 (2020) 110073
4. Discussion Connectance and nestedness decreased the perceived effects of perturbations in antagonistic networks under different scenarios of disturbance regime, thus providing evidence for a positive effect of both metrics on community stabilization. The particularity of this study is that these stabilization effects were observed considering perturbations that affected species’ abundances rather than their persistence (i.e., disturbance regimes that alter biomass but not the number of species directly), in a theoretical complement to previous approaches. There are mechanisms through which connectance and nestedness can operate on community stabilization. Connectance is a major topological structure related to the level of organization of units (e.g., species) across an ecological interaction network. Considering community robustness, increased connectance may ensure that species persist after a primary extinction in ecological networks because the probability of remaining partners per species is increased (Dunne et al., 2002). Moreover, in highly connected networks, the link organization potentially reduce the number of species with few interactions (Gravel et al., 2011; Nuwagaba et al., 2017; Landi et al., 2018). Particularly for antagonistic interactions, increased connectance may supply consumers with a larger fraction of resources, allowing them to scatter their preference and compensate for eventual changes in the abundance of resources (Fowler, 2009; Fahimipour et al., 2017). As expected, the results showed that connectance decreased significantly with the increasing number of species in networks (Yodzis, 1980; Dunne et al., 2002; Landi et al., 2018). However, there was no direct contribution of network size (i.e., number of species) to stabilization, suggesting that the role of connectance may outperform network size in stabilizing consumer response to perturbations. Nestedness is a deterministic pattern and can also contribute to robustness by virtually ensuring that species still have others to interact with, assuming that specialists are those that go extinct at first (Bascompte et al., 2003; Tylianakis et al., 2010). In addition, highly nested networks are likely more robust against random extinctions and certainly less sensitive to the loss of the most interacting species (Memmott et al., 2004; Burgos et al., 2007; AlmeidaNeto et al., 2008). Although these mechanisms were not investigated in this study, we can speculate that both play a synergic role on community robustness, especially under disturbance regimes of more frequent and intense perturbations. Precisely in these cases, the process that increases community robustness might be explained through the enhanced overall benefit of consumers that may occur in highly connected and nested networks, which has potential to stabilize interactions and decrease the negative effects of perturbations. Stability has several components that diverge from tracking the reductions in the abundance of consumers (Ives and Carpenter, 2007; Donohue et al., 2013; Arnoldi et al., 2016; Aufderheide et al., 2013; Landi et al., 2018). However, the component investigated in this study and its relationship with the network properties provides a theoretical basis for understanding the process underlying community robustness in ecological networks. These results increase the predictability of the effects of perturbations on ecological networks under different regimes of disturbances, considering events that alter resources’ densities but do not remove resources or consumers directly. We can suggest this because the effects of connectance and nestedness on community robustness were consistent across the simulated gradient of perturbations. Another factor that contributes to community robustness is the topological plasticity inherent to both the interaction switch and random drift mechanisms (Valdovinos et al., 2010). These random dynamic processes leads to directional changes of the architec-
5
ture of ecological webs towards enhancing the cost-benefit relationships between consumers and their resources, thus increasing community stability (Staniczenko et al., 2010; Ramos-Jiliberto et al., 2012; Nuwagaba et al., 2017). Because the network dynamics was similar for all simulated networks, it is defensible to assume that the rewiring process was not a confounding effect in the study design regarding community robustness. Instead, the fact that all networks shared the same interaction switching dynamics allowed for comparisons among the main factors of interest (e.g., the relationship between network metrics and the perceived effects of different disturbance regimes). However, it is important to state that, for simplicity, other metrics with likely important roles on community stabilization as specialization, modularity, expansibility, and degree distribution (Estrada, 2007; Mello et al., 2011a, 2011b) were not investigated here. In spite of the focus on network metrics and their relationship with how communities respond to perturbations, some specific results worth being discussed here. First, the abundance of consumers was correlated with the number of respawned resources (ρ = 0.67, P < 0.01). This implied that the number of resources that reached the lower abundance threshold was higher whenever there was an increased consumption pressure, which overlaps with the expectation of low prey success under high predation rates (Abrams, 1992; Salo et al., 2010). Second, the average number of respawned resources was similar across the different disturbance regimes (Figure S3). This is evidence that the extinction probabilities were not affected while the model was manipulating the abundances of resources, and rules out potential bias related to inflated extinction rates as the frequency and intensity of perturbations increased. These results assure that the settings and dynamics of the model were reliable within its theoretical assumptions and practical purposes. The present study was based on a new perspective to provide additional evidence that connectance and nestedness increase community robustness against disturbances (i.e., community stabilization) in antagonistic networks. The approach considered the effects of disturbances as a second-stage response by the community because disturbance itself affected the abundance of resources, not consumers. However, abundance alone, which was the measure representing the disturbance effects, is not sufficient to support statements about biodiversity and ecological processes. Because only the immediate effects were of interest in this study, the abundances of resources and consumers were allowed to recover promptly after each disturbance. Therefore, conclusions about the long-term effects of pulse perturbations should not arise from these findings. Furthermore, this study suggests that the combination of frequent and intense disturbances can have unpredictable effects on the stability of ecosystems. Acknowledgements I am grateful to the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) of the Ministry of Education from Brazil for the Ph.D. scholarship provided. Supplementary materials Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.jtbi.2019.110073. References Abrams, P.A., 1992. Why don’t predators have positive effects on prey populations? Evol. Ecol. 6, 449–457. doi:10.1007/BF02270691. Almeida-Neto, M., Guimarães, P., Guimarães Jr, P.R., Loyola, R.D., Ulrich, W, 2008. A consistent metric for nestedness analysis in ecological systems: reconciling concept and measurement. Oikos 117, 1227–1239. doi:10.1111/j.0030-1299.2008. 16644.x.
6
M.T. Baumgartner / Journal of Theoretical Biology 486 (2020) 110073
Arnoldi, J.-F., Loreau, M., Haegeman, B., 2016. Resilience, reactivity and variability: a mathematical comparison of ecological stability measures. J. Theor. Biol. 389, 47–59. doi:10.1016/j.jtbi.2015.10.012. Aufderheide, H., Rudolf, L., Gross, T., Lafferty, K.D, 2013. How to predict community responses to perturbations in the face of imperfect knowledge and network complexity. Proc. R. Soc. B 280, 20132355. doi:10.1098/rspb.2013.2355. Bascompte, J., Jordano, P., Melian, C.J., Olesen, J.M, 2003. The nested assembly of plant-animal mutualistic networks. Proc. Natl. Acad. Sci. 100, 9383–9387. doi:10. 1073/pnas.1633576100. Battisti, C., Poeta, G., Fanelli, G, 2016. Categories of natural disturbances. An Introduction to Disturbance Ecology. Environmental Science and Engineering. Springer, Cham. Borrett, S.R., Moody, J., Edelmann, A, 2014. The rise of network ecology: maps of the topic diversity and scientific collaboration. Ecol. Model. 293, 111–127. Burgos, E., Ceva, H., Perazzo, R.P.J., Devoto, M., Medan, D., Zimmermann, M., María Delbue, A, 2007. Why nestedness in mutualistic networks? J. Theor. Biol. 249, 307–313. doi:10.1016/j.jtbi.2007.07.030. Connell, J.H., 1978. Diversity in tropical rain forests and coral reefs. Science 199, 1302–1310. doi:10.1126/science.199.4335.1302. Donohue, I., et al., 2013. On the dimensionality of ecological stability. Ecol. Lett. 16, 421–429. doi:10.1111/ele.12086. Dornelas, M., 2010. Disturbance and change in biodiversity. Philos. Trans. R. Soc. Lond. B Biol. Sci. 365, 3719–3727. doi:10.1098/rstb.2010.0295. Dornelas, M., Moonen, A.C., Magurran, A.E., Bàrberi, P, 2009. Species abundance distributions reveal environmental heterogeneity in modified landscapes. J. Appl. Ecol. 46, 666–672. doi:10.1111/j.1365-2664.2009.01640.x. Dunne, J.A., Williams, R.J., Martinez, N.D, 2002. Network structure and biodiversity loss in food webs: robustness increases with connectance. Ecol. Lett. 5, 558–567. doi:10.1046/j.1461-0248.20 02.0 0354.x. Eklöf, A., Ebenman, B., 2006. Species loss and secondary extinctions in simple and complex model communities. J. Anim. Ecol. 75, 239–246. doi:10.1111/j. 1365-2656.2006.01041.x. Estrada, E., 2007. Food webs robustness to biodiversity loss: the roles of connectance, expansibility and degree distribution. J. Theor. Biol. 244, 296–307. doi:10.1016/j.jtbi.20 06.08.0 02. Fahimipour, A.K., Anderson, K.E., Williams, R.J, 2017. Compensation masks trophic cascades in complex food webs. Theor. Ecol. 10, 245–253. doi:10.1007/ s12080- 016- 0326- 8. Fowler, M.S., 2009. Increasing community size and connectance can increase stability in competitive communities. J. Theor. Biol. 258, 179–188. doi:10.1016/j.jtbi. 2009.01.010. Gaston, K., Fuller, R., 2008. Commonness, population depletion and conservation biology. Trends Ecol. Evol. 23, 14–19. doi:10.1016/j.tree.20 07.11.0 01. Gravel, D., Canard, E., Guichard, F., Mouquet, N., 2011. Persistence increases with diversity and connectance in trophic metacommunities. PLoS ONE 6, e19374. doi:10.1371/journal.pone.0019374. Ives, A.R., Carpenter, S.R., 2007. Stability and diversity of ecosystems. Science 317, 58–62. doi:10.1126/science.1133258. Jentsch, A., White, P., 2019. A theory of pulse dynamics and disturbance in ecology. Ecology 100, e02734. doi:10.1002/ecy.2734. Johnstone, J.F., et al., 2016. Changing disturbance regimes, ecological memory, and forest resilience. Front. Ecol. Environ. 14, 369–378. doi:10.1002/fee.1311. ˚ Hui, C., Dieckmann, U, 2018. Complexity Landi, P., Minoarivelo, H.O., Brännström, A., and stability of ecological networks: a review of the theory. Popul. Ecol. 60, 319–345. doi:10.1007/s10144-018-0628-3. Levin, S.A., Paine, R.T., 1974. Disturbance, patch formation, and community structure. Proc. Natl. Acad. Sci. 71, 2744–2747. doi:10.1073/pnas.71.7.2744. McCabe, D.J., Gotelli, N.J., 20 0 0. Effects of disturbance frequency, intensity, and area on assemblages of stream macroinvertebrates. Oecologia 124, 270–279. doi:10. 10 07/s0 04420 0 0 0369.
McGill, B.J., et al., 2007. Species abundance distributions: moving beyond single prediction theories to integration within an ecological framework. Ecol. Lett. 10, 995–1015. doi:10.1111/j.1461-0248.2007.01094.x. Mello, M.A.R., Marquitti, F.M.D., Guimarães, P.R., Kalko, E.K.V., Jordano, P., de Aguiar, M.A.M., 2011a. The missing part of seed dispersal networks: structure and robustness of bat-fruit interactions. PLoS ONE 6, e17395. doi:10.1371/ journal.pone.0017395. Mello, M.A.R., Marquitti, F.M.D., Guimarães, P.R., Kalko, E.K.V., Jordano, P., de Aguiar, M.A.M., 2011b. The modularity of seed dispersal: differences in structure and robustness between bat– and bird–fruit networks. Oecologia 167, 131–140. doi:10.10 07/s0 0442- 011- 1984- 2. Memmott, J., Waser, N.M., Price, M.V, 2004. Tolerance of pollination networks to species extinctions. Proc. R. Soc. Lond. B Biol. Sci. 271, 2605–2611. doi:10.1098/ rspb.2004.2909. Mougi, A., Kondoh, M., 2016. Food-web complexity, meta-community complexity and community stability. Sci. Rep 6, 24478. doi:10.1038/srep24478. Newman, E.A., 2019. Disturbance ecology in the anthropocene. Front. Ecol. Evol. 7, 147. doi:10.3389/fevo.2019.00147. Nielsen, A., Bascompte, J., 2007. Ecological networks, nestedness and sampling effort. J. Ecol. 95, 1134–1141. doi:10.1111/j.1365-2745.2007.01271.x. Nuwagaba, S., Zhang, F., Hui, C, 2015. A hybrid behavioural rule of adaptation and drift explains the emergent architecture of antagonistic networks. Proc. R. Soc. B Biol. Sci. 282, 20150320. doi:10.1098/rspb.2015.0320. Nuwagaba, S., Zhang, F., Hui, C., 2017. Robustness of rigid and adaptive networks to species loss. PLoS ONE 12, e0189086. doi:10.1371/journal.pone.0189086. Pickett, S., White, P., 1985. The Ecology of Natural Disturbance and Patch Dynamics. Academic Press, NewYork. R Core Team, 2019. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria https://www.R-project. org/. Ramos-Jiliberto, R., Valdovinos, F.S., Moisset de Espanés, P., Flores, J.D, 2012. Topological plasticity increases robustness of mutualistic networks. J. Anim. Ecol. 81, 896–904. doi:10.1111/j.1365-2656.2012.01960.x. Rohr, R.P., Saavedra, S., Bascompte, J., 2014. On the structural stability of mutualistic systems. Science 345, 1253497. doi:10.1126/science.1253497. Salo, P., Banks, P.B., Dickman, C.R., Korpimäki, E, 2010. Predator manipulation experiments: impacts on populations of terrestrial vertebrate prey. Ecol. Monogr. 80, 531–546. doi:10.1890/09-1260.1. Staniczenko, P.P.A., Lewis, O.T., Jones, N.S., Reed-Tsochas, F, 2010. Structural dynamics and robustness of food webs. Ecol. Lett. 13, 891–899. doi:10.1111/j. 1461-0248.2010.01485.x. Stouffer, D.B., Bascompte, J., 2011. Compartmentalization increases food-web persistence. Proc. Natl. Acad. Sci. 108, 3648–3652. doi:10.1073/pnas.1014353108. Suweis, S., Simini, F., Banavar, J.R., Maritan, A., 2013. Emergence of structural and dynamical properties of ecological mutualistic networks. Nature 500, 449–452. doi:10.1038/nature12438. Thebault, E., Fontaine, C., 2010. Stability of ecological communities and the architecture of mutualistic and trophic networks. Science 329, 853–856. doi:10.1126/ science.1188321. Traveset, A., Tur, C., Eguíluz, V.M, 2017. Plant survival and keystone pollinator species in stochastic coextinction models: role of intrinsic dependence on animal-pollination. Sci. Rep. 7. doi:10.1038/s41598- 017- 07037- 7. Turner, M.G., 2010. Disturbance and landscape dynamics in a changing world. Ecology 91, 2833–2849. doi:10.1890/10-0097.1. Tylianakis, J.M., Laliberté, E., Nielsen, A., Bascompte, J, 2010. Conservation of species interaction networks. Biol. Conserv. 143, 2270–2279. doi:10.1016/j.biocon.2009. 12.004. Valdovinos, F.S., Ramos-Jiliberto, R., Garay-Narváez, L., Urbani, P., Dunne, J.A, 2010. Consequences of adaptive behaviour for the structure and dynamics of food webs. Ecol. Lett. 13, 1546–1559. doi:10.1111/j.1461-0248.2010.01535.x. Yodzis, P., 1980. The connectance of real ecosystems. Nature 284 (5756), 544.
Contents lists available at ScienceDirect
Journal of Theoretical Biology journal homepage: www.elsevier.com/locate/jtb
Connectance and nestedness as stabilizing factors in response to pulse disturbances in adaptive antagonistic networks Matheus T. Baumgartner Graduate Course in Ecology of Freshwater Environments, Department of Biology, Centre for Biological Sciences, State University of Maringá, Maringá, Paraná, Brazil
a r t i c l e
i n f o
Article history: Received 19 June 2019 Revised 23 October 2019 Accepted 5 November 2019 Available online 6 November 2019 Keywords: Stability Community robustness Ecological interaction networks Food webs Lotka-Volterra
a b s t r a c t Understanding how network architectures are related to community robustness is essential to investigating the effects of disturbances on biological systems. Regarding the perturbations that are observed in disturbance regimes, frequency and intensity are two main descriptors, specifically for those events with short duration. Here, I used the architecture of 45 real-world weighted bipartite networks to assess whether network size, connectance, and nestedness are related to the effects of pulse disturbances in antagonistic communities. Networks were simulated under five scenarios with different combinations of frequency and intensity of perturbations. The dynamics of resource-consumer interactions followed the adaptive interaction switching behavior, which is the key topological process underlying most of the architectures of antagonistic webs. As opposed to most studies considering the effects of disturbances as species extinctions explicitly, the effects of disturbances here were modeled as changes in the abundance of consumers following immediate reductions in the abundance of resources. Simulations revealed that community robustness to pulse disturbances increased with both connectance and nestedness overall, with no effect of network size. Community networks with highly connected and nested topologies were more robust to disturbances, particularly under high frequency and intensity perturbations. By considering disturbances that are not directly related to species’ extinctions, this study provides valuable insights that connectance and nestedness have an important stabilizing role in ecological networks. © 2019 Elsevier Ltd. All rights reserved.
1. Introduction The effects of disturbances on communities have been investigated extensively in the last five decades (Levin and Paine, 1974; Connell, 1978). Although there is no consensus on the process, understanding how these events affect community structure is fundamental because of the potential impacts on ecosystem services (Turner, 2010). Due to the increased human activities in recent years, the disturbance regimes are changing rapidly across several regions of the world (Dornelas, 2010; Turner, 2010; Johnstone et al., 2016; Newman, 2019), which is the main reason that the effects of disturbances on ecological communities have been in the frontline of biological research (Eklöf and Ebenman, 2006; Thebault and Fontaine, 2010; Rohr et al., 2014). Therefore, we must understand how some of the properties of ecological communities are related to the robustness against disturbances in order to increase the predictive power of theoretical research (Estrada, 2007; Stouffer and Bascompte, 2011).
E-mail address: [email protected] https://doi.org/10.1016/j.jtbi.2019.110073 0022-5193/© 2019 Elsevier Ltd. All rights reserved.
Disturbance can be defined following Pickett and White (1985) as any discrete event in time that disrupts community structure and changes resources availability, whereas disturbance regimes are described as repetitive disturbances that constitute a temporal pattern (Turner, 2010). Within this context, short-term discrete disturbances may be also commonly referred to as pulse disturbances. More specifically, pulse disturbances that are in the control of the experimentalist can be treated as “perturbations” (Pickett and White, 1985; McCabe and Gotelli, 20 0 0). We are then able to build a theoretical framework focusing on how communities respond to different disturbance regimes described by different perturbations. In most natural ecosystems, perturbations are usually related to fire, grazing, extreme weather events, flooding, and other environmental stressors (Battisti et al., 2016). Regardless of their nature, two important features of disturbance regimes, which may influence predictability, can describe these perturbations: intensity and frequency (Jentsch and White 2019). For instance, a fire event in a savannah can burn half of the plant biomass in the system (intensity), every year (frequency), whereas a seasonal flood pulse can reduce the biomass of the marginal vegetation of a lake during
2
M.T. Baumgartner / Journal of Theoretical Biology 486 (2020) 110073
each rainy season. In both situations, a perturbation event that is the consequence of an environmental factor (e.g., fire or flood) reduces the abundance of resources (plants) with important effects on consumers (e.g., herbivores). Antagonist communities can be described as a diverse number of resources and consumers coexisting and interacting with each other through predation and parasitism, such as in networks (Borrett et al., 2014). Considering the dynamics of antagonistic interactions, a hybrid behavior combining two main topological processes underlies resources-consumers networks: interaction switch and random drift. These adaptive processes depicts the tradeoff between natural selection, by the elimination of the unfit (by disposing the resource that contributes the least to its fitness), and the random trial of new resources (Valdovinos et al., 2010; Suweis et al., 2013), which explain most of the empirical architectures of antagonistic networks (Nuwagaba et al., 2015). Many recent studies have investigated the relationships between how communities respond to disturbances and network properties as connectance and nestedness, usually finding a positive relationship for both metrics (Dunne et al., 2002; Bascompte et al., 2003; Burgos et al., 2007; Staniczenko et al., 2010; Landi et al., 2018). However, most studies consider disturbances as species extinction explicitly. Although this is a recognized approach, extinction is only the summit of the abundance decline for a given species, and investigating the robustness of communities (i.e., the ability to sustain its structure in the face of perturbations) by focusing on the relative changes in abundances after each event may provide valuable insights. Species abundance is a sufficiently general descriptor of community state because it does not depend on species identity, and can therefore be used to assess changes in the community state broadly (McGill et al., 2007; Dornelas et al., 2009). Here, I explored whether network properties as connectance and nestedness are related to how antagonist communities respond to different disturbance regimes, considering alternative intensities and frequencies of perturbations. To achieve this objective, I considered the architecture of 45 weighted bipartite (resource-consumer) networks. The dynamics of the networks were considered under a realistic background by incorporating adaptive interaction switching and random drift (Nuwagaba et al., 2015). Networks were subjected to different disturbance regimes by considering five alternative scenarios regarding the intensity and frequency of perturbations. The effect of perturbations was measured as the average change in the abundance of consumers, following discrete reductions in the abundance of resources. Particularly, this study is a specific investigation of the yet underexplored relationship between network properties and the effects of disturbances affecting species’ abundances, rather than their persistence, in ecological networks. In accordance with previous findings (Dunne et al., 2002; Nuwagaba et al., 2017; Mougi and Kondoh, 2016; Traveset et al., 2017), the results underline the fundamental role of connectance and nestedness in decreasing the extent of disturbances and stabilizing the dynamics of biological communities.
2. Materials and Methods Consider an antagonist community where i resources are explored by j consumers as in trophic or host-parasite networks. The population dynamics of resource i is determined by its growth rate minus the population depletion by consumption, while the population of consumer j increases by the exploration of resources minus its density-dependent mortality. If a Holling’s type II functional response is considered, the following Lotka-Volterra resource-consumer model can describe the population dynamics of
species:
⎧ ⎨ R1i
⎩1
Nj
dRi dt dN j dt
= r i − ci Ri − = −d j N j +
j 1+h
ai j vi j N j k ak j vk j Rk
b ji ai j vi j Ri i 1+h k ak j vk j Rk
where Ri and Nj are the abundances of resource i and consumer j, respectively; ri and ci are the intrinsic growth rate and the density-dependent self-regulation coefficient of resource i; dj is the density-dependent mortality of consumer j. Explicitly, the binary interaction matrix (aij ) depicts whether resource i is exploited (1) or not (0) by consumer j; the preference matrix (vij ) describes the probability of consumer j feeding on resource i once met; the benefit matrix (bij ) denotes the energetic income of consumer j when feeding on resource i; h is the handling time, assumed to be equal for all consumers (0.1). The networks followed the hybrid rule of adaptive interaction switch and random drift. This dynamics depicts the tradeoff predicted by natural selection through the elimination of the unfit and the random trial of new resources (Valdovinos et al., 2010; Suweis et al., 2013). At each time step, a random consumer disposes the resource that contributes the least to its per capita growth rate (the resource with the lowest bji aij vij Ri in the equation above) and a new resource is added to the diet of another random consumer, with a random preference. The initial architecture of networks (numbers of resources, consumers, and link density) mirrored those from 45 empirical bipartite networks (14 herbivore-plant and 31 host-parasite; Online Resource 1). The entries of the matrix aij were randomly assigned controlling for no isolated species by ensuring that every species had at least one resource or consumer, and initial population sizes and parameters (ri , ci , dj , vij , and bij ) were assigned at random between 0 and 1; mirroring the structure from Nuwagaba et al. (2015). This random assignment of values for parameters and initial abundances was assumed as not affecting the results, following Nuwagaba et al. (2015, 2017). Moreover, the focus herein was on the discrete effects of disturbances on the overall community structure, which were investigated through highly controlled simulations, rather than on the ability of communities to preserve their original structure. To simulate disturbance regimes, the abundances of resources were reduced following five different scenarios. The first scenario was referred to as “baseline” (Fig. 1A) and consisted of a 40% reduction in abundances every 25 time steps. The second scenario was called “medium frequency” (Fig. 1B) and consisted of 40% reduction in abundances every 20 time steps. The third scenario was treated as “medium intensity” (Fig. 1C) and depicted a 60% decrease in abundances every 25 time steps. The fourth scenario was called “high frequency” (Fig. 1D) and represented a reduction of 40% in abundances every 10 time steps. Finally, the fifth scenario was referred to as “high intensity” (Fig. 1E), representing a 90% decrease in abundances every 25 time steps. The five different scenarios did not follow any specific theoretical basis in respect to the frequency and intensity of disturbance regimes. This decision, coupled with the different combinations of frequency and intensity of perturbations in each scenario, were fundamental to ensure the generalizations of the model. The effect of disturbances was quantified as the average rate of change (after/before) in the overall abundance of consumers (Ab), recorded one time step before and after each perturbation as Ab = ( N jt / N jt−1 )/d, where Nj t is the abundance of consumer j one time step after the disturbance, N j t−1 is the abundance of consumer j one time step before the disturbance, and d is the number of perturbation events for each scenario. This metric quantifies the proportional decrease in the abundance of consumers after each perturbation event, thus the inverse of community robustness (i.e., greater shifts in the abundance of consumers
M.T. Baumgartner / Journal of Theoretical Biology 486 (2020) 110073
Fig. 1. Disturbance scenarios were established based on the frequency and intensity of reductions in the abundance of resources. (A) Baseline scenario caused a 40% reduction every 25 time steps; (B) Medium frequency caused a 40% reduction every 20 time steps; (C) Medium intensity caused a 60% reduction every 25 time steps; (D) High frequency caused a 40% reduction every 10 time steps; (E) High intensity caused a 90% reduction every 25 time steps.
3
are expected in less robust communities). Although intuitively general, changes in the relative abundance of species are consistent descriptors of community dynamics because it precedes shifts in community structure and further species extinctions (Gaston and Fuller, 2008). Particularly, the arbitrary short-term evaluation of the effects of perturbations was essential to avoid potential confounding effects related to the stochastic dynamics of the communities (Dornelas, 2010). Networks were simulated under 100 time steps without perturbations to reach an equilibrium state (usually reached at t = 50; Figure S1), then additional 200 time steps under each of the disturbance regimes were performed. To simplify the model and to focus on the abundance decrease, resources were not allowed to go extinct and were instantly respawned (with random values between 0 and 0.2) if their abundances were below 10−6 , while eventual extinctions of consumers were allowed. This condition was implemented to prevent community collapse due to spurious resources extinctions, which, in fact, rarely occurred overall. Because we were interested in the short-term effects, resources were able to recover immediately after each reduction in abundance. The performance of the model was evaluated by supervising the temporal trajectories of the abundances of both resources and consumers, and simulations were restarted for those communities that ≥ 20% of consumers were lost or eventually collapsed before reaching equilibrium. To assess whether network properties were related to the effects of disturbances, the mean change in the abundance of consumers was tested for correlation with both connectance and nestedness, using Spearman’s rank correlation. Connectance is defined and calculated as the proportion of realized links between species related to the maximum of a given network (realized links/species²; Memmott et al., 2004), while nestedness is a tendency of specialists to interact only with a subset of those species interacting with more generalist species (Nielsen and Bascompte, 2007). These two metrics are recognized as related to community robustness against species extinctions (Memmott et al., 2004; Burgos et al., 2007), and were calculated for each final interaction matrix after simulations. Nestedness was calculated using the Nestedness Metric Based on Overlap and Decreasing Fill (NODF; Almeida-Neto et al., 2008). Because network size (calculated as the number of species or nodes) is frequently correlated with connectance, which may plausibly contribute to stabilization (Fowler, 2009; Landi et al., 2018), this network metric was also considered. Model construction, simulations, and analyses were conducted in the R Environment (R Core Team, 2019). 3. Results
Fig. 2. Mean and standard errors for the effects of disturbances measured as the change in the abundance of consumers at each of the five simulated disturbance regimes. See Methods for details.
The effects of disturbances on the decrease in the abundance of consumers varied across the disturbance scenarios (Fig. 2). Since the Levene’s test revealed that the homogeneity of variances was violated (Levene’s F(4220) = 3.08; P = 0.02), a Welch’s ANOVA was applied. This analysis revealed significant differences (Welch’s F(4105.64) = 14.35; P < 0.01), specifically between the scenario with disturbances at high intensity and all other scenarios (P < 0.01), and between medium intensity and high frequency scenarios (P = 0.01). The effects of disturbances, quantified as the average decrease in the abundance of consumers (Ab), had no correlation with network size (Table 1). However, connectance had significant negative correlations with Ab in all five scenarios representing different disturbance regimes (Table 1; Figs. 3 and 4). An analogous negative correlation with Ab was observed for nestedness, whereas significant values were observed under baseline, medium intensity and high frequency scenarios (Table 1; Fig. 4). At the final architecture, network size was negatively correlated with connectance (Spearman’s rank correlation (ρ ) = −0.60; P < 0.01) and nested-
4
M.T. Baumgartner / Journal of Theoretical Biology 486 (2020) 110073 Table 1 Spearman’s rank correlation between the mean decrease in the abundance of consumers (Ab) following perturbations and network properties (network size, connectance, and nestedness). Scenario
Network size
Connectance
Nestedness
Baseline Medium frequency Medium intensity High frequency High intensity
0.08 0.06 0.10 0.08 −0.05
−0.40 −0.32 −0.37 −0.35 −0.38
−0.36 −0.29 −0.38 −0.31 −0.29
Perturbations were considered as reductions in the abundance of resources under five alternative frequency and intensity scenarios (see Methods for details). Significant correlations at α = 0.05 are in bold.
ness (ρ = −0.72; P < 0.01), whereas connectance and nestedness were highly correlated (ρ = 0.93; P < 0.01), as expected under realistic circumstances for real-world networks (Figure S2). Detailing how network properties were related to the effects of disturbances, the high frequency and high intensity scenarios caused immediate reductions in the abundance of consumers up to 15% and 12%, respectively (Fig. 4). Although the network size was not correlated with the effects of disturbances, there was a decreasing trend in the reduction in consumers abundance after perturbation events as the number of species increased under the medium intensity scenario (Fig. 4A). The stabilizing effect of con-
Fig. 3. Relationships between the mean decrease in the consumers abundance (Ab) following perturbations and network metrics (connectance and nestedness). Connectance was controlled prior to the simulations using link density from 45 real bipartite networks (see Online Resource 1). Nestedness architecture emerged during simulations.
nectance was consistent across all disturbance scenarios, specifically under highly frequent and intense perturbations (Fig. 4B). Finally, the scenarios that provided the clearest stabilizing effects of nestedness were the baseline, medium intensity, and high frequency, with a clear decreasing trend of the decrease in consumers’ abundance as nestedness increased (Fig. 4C).
Fig. 4. Relationships between the effects of disturbances, assessed through the mean decrease in consumers abundance (Ab) immediately after reductions in the abundance of resources, and network properties (network size, connectance, and nestedness). See Methods for details on frequency and intensity of perturbations in each of the simulated disturbance regimes. The red lines indicate the overall trends of significant Spearman’s rank correlations at α = 0.05. Raw correlation values are in Table 1.
M.T. Baumgartner / Journal of Theoretical Biology 486 (2020) 110073
4. Discussion Connectance and nestedness decreased the perceived effects of perturbations in antagonistic networks under different scenarios of disturbance regime, thus providing evidence for a positive effect of both metrics on community stabilization. The particularity of this study is that these stabilization effects were observed considering perturbations that affected species’ abundances rather than their persistence (i.e., disturbance regimes that alter biomass but not the number of species directly), in a theoretical complement to previous approaches. There are mechanisms through which connectance and nestedness can operate on community stabilization. Connectance is a major topological structure related to the level of organization of units (e.g., species) across an ecological interaction network. Considering community robustness, increased connectance may ensure that species persist after a primary extinction in ecological networks because the probability of remaining partners per species is increased (Dunne et al., 2002). Moreover, in highly connected networks, the link organization potentially reduce the number of species with few interactions (Gravel et al., 2011; Nuwagaba et al., 2017; Landi et al., 2018). Particularly for antagonistic interactions, increased connectance may supply consumers with a larger fraction of resources, allowing them to scatter their preference and compensate for eventual changes in the abundance of resources (Fowler, 2009; Fahimipour et al., 2017). As expected, the results showed that connectance decreased significantly with the increasing number of species in networks (Yodzis, 1980; Dunne et al., 2002; Landi et al., 2018). However, there was no direct contribution of network size (i.e., number of species) to stabilization, suggesting that the role of connectance may outperform network size in stabilizing consumer response to perturbations. Nestedness is a deterministic pattern and can also contribute to robustness by virtually ensuring that species still have others to interact with, assuming that specialists are those that go extinct at first (Bascompte et al., 2003; Tylianakis et al., 2010). In addition, highly nested networks are likely more robust against random extinctions and certainly less sensitive to the loss of the most interacting species (Memmott et al., 2004; Burgos et al., 2007; AlmeidaNeto et al., 2008). Although these mechanisms were not investigated in this study, we can speculate that both play a synergic role on community robustness, especially under disturbance regimes of more frequent and intense perturbations. Precisely in these cases, the process that increases community robustness might be explained through the enhanced overall benefit of consumers that may occur in highly connected and nested networks, which has potential to stabilize interactions and decrease the negative effects of perturbations. Stability has several components that diverge from tracking the reductions in the abundance of consumers (Ives and Carpenter, 2007; Donohue et al., 2013; Arnoldi et al., 2016; Aufderheide et al., 2013; Landi et al., 2018). However, the component investigated in this study and its relationship with the network properties provides a theoretical basis for understanding the process underlying community robustness in ecological networks. These results increase the predictability of the effects of perturbations on ecological networks under different regimes of disturbances, considering events that alter resources’ densities but do not remove resources or consumers directly. We can suggest this because the effects of connectance and nestedness on community robustness were consistent across the simulated gradient of perturbations. Another factor that contributes to community robustness is the topological plasticity inherent to both the interaction switch and random drift mechanisms (Valdovinos et al., 2010). These random dynamic processes leads to directional changes of the architec-
5
ture of ecological webs towards enhancing the cost-benefit relationships between consumers and their resources, thus increasing community stability (Staniczenko et al., 2010; Ramos-Jiliberto et al., 2012; Nuwagaba et al., 2017). Because the network dynamics was similar for all simulated networks, it is defensible to assume that the rewiring process was not a confounding effect in the study design regarding community robustness. Instead, the fact that all networks shared the same interaction switching dynamics allowed for comparisons among the main factors of interest (e.g., the relationship between network metrics and the perceived effects of different disturbance regimes). However, it is important to state that, for simplicity, other metrics with likely important roles on community stabilization as specialization, modularity, expansibility, and degree distribution (Estrada, 2007; Mello et al., 2011a, 2011b) were not investigated here. In spite of the focus on network metrics and their relationship with how communities respond to perturbations, some specific results worth being discussed here. First, the abundance of consumers was correlated with the number of respawned resources (ρ = 0.67, P < 0.01). This implied that the number of resources that reached the lower abundance threshold was higher whenever there was an increased consumption pressure, which overlaps with the expectation of low prey success under high predation rates (Abrams, 1992; Salo et al., 2010). Second, the average number of respawned resources was similar across the different disturbance regimes (Figure S3). This is evidence that the extinction probabilities were not affected while the model was manipulating the abundances of resources, and rules out potential bias related to inflated extinction rates as the frequency and intensity of perturbations increased. These results assure that the settings and dynamics of the model were reliable within its theoretical assumptions and practical purposes. The present study was based on a new perspective to provide additional evidence that connectance and nestedness increase community robustness against disturbances (i.e., community stabilization) in antagonistic networks. The approach considered the effects of disturbances as a second-stage response by the community because disturbance itself affected the abundance of resources, not consumers. However, abundance alone, which was the measure representing the disturbance effects, is not sufficient to support statements about biodiversity and ecological processes. Because only the immediate effects were of interest in this study, the abundances of resources and consumers were allowed to recover promptly after each disturbance. Therefore, conclusions about the long-term effects of pulse perturbations should not arise from these findings. Furthermore, this study suggests that the combination of frequent and intense disturbances can have unpredictable effects on the stability of ecosystems. Acknowledgements I am grateful to the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) of the Ministry of Education from Brazil for the Ph.D. scholarship provided. Supplementary materials Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.jtbi.2019.110073. References Abrams, P.A., 1992. Why don’t predators have positive effects on prey populations? Evol. Ecol. 6, 449–457. doi:10.1007/BF02270691. Almeida-Neto, M., Guimarães, P., Guimarães Jr, P.R., Loyola, R.D., Ulrich, W, 2008. A consistent metric for nestedness analysis in ecological systems: reconciling concept and measurement. Oikos 117, 1227–1239. doi:10.1111/j.0030-1299.2008. 16644.x.
6
M.T. Baumgartner / Journal of Theoretical Biology 486 (2020) 110073
Arnoldi, J.-F., Loreau, M., Haegeman, B., 2016. Resilience, reactivity and variability: a mathematical comparison of ecological stability measures. J. Theor. Biol. 389, 47–59. doi:10.1016/j.jtbi.2015.10.012. Aufderheide, H., Rudolf, L., Gross, T., Lafferty, K.D, 2013. How to predict community responses to perturbations in the face of imperfect knowledge and network complexity. Proc. R. Soc. B 280, 20132355. doi:10.1098/rspb.2013.2355. Bascompte, J., Jordano, P., Melian, C.J., Olesen, J.M, 2003. The nested assembly of plant-animal mutualistic networks. Proc. Natl. Acad. Sci. 100, 9383–9387. doi:10. 1073/pnas.1633576100. Battisti, C., Poeta, G., Fanelli, G, 2016. Categories of natural disturbances. An Introduction to Disturbance Ecology. Environmental Science and Engineering. Springer, Cham. Borrett, S.R., Moody, J., Edelmann, A, 2014. The rise of network ecology: maps of the topic diversity and scientific collaboration. Ecol. Model. 293, 111–127. Burgos, E., Ceva, H., Perazzo, R.P.J., Devoto, M., Medan, D., Zimmermann, M., María Delbue, A, 2007. Why nestedness in mutualistic networks? J. Theor. Biol. 249, 307–313. doi:10.1016/j.jtbi.2007.07.030. Connell, J.H., 1978. Diversity in tropical rain forests and coral reefs. Science 199, 1302–1310. doi:10.1126/science.199.4335.1302. Donohue, I., et al., 2013. On the dimensionality of ecological stability. Ecol. Lett. 16, 421–429. doi:10.1111/ele.12086. Dornelas, M., 2010. Disturbance and change in biodiversity. Philos. Trans. R. Soc. Lond. B Biol. Sci. 365, 3719–3727. doi:10.1098/rstb.2010.0295. Dornelas, M., Moonen, A.C., Magurran, A.E., Bàrberi, P, 2009. Species abundance distributions reveal environmental heterogeneity in modified landscapes. J. Appl. Ecol. 46, 666–672. doi:10.1111/j.1365-2664.2009.01640.x. Dunne, J.A., Williams, R.J., Martinez, N.D, 2002. Network structure and biodiversity loss in food webs: robustness increases with connectance. Ecol. Lett. 5, 558–567. doi:10.1046/j.1461-0248.20 02.0 0354.x. Eklöf, A., Ebenman, B., 2006. Species loss and secondary extinctions in simple and complex model communities. J. Anim. Ecol. 75, 239–246. doi:10.1111/j. 1365-2656.2006.01041.x. Estrada, E., 2007. Food webs robustness to biodiversity loss: the roles of connectance, expansibility and degree distribution. J. Theor. Biol. 244, 296–307. doi:10.1016/j.jtbi.20 06.08.0 02. Fahimipour, A.K., Anderson, K.E., Williams, R.J, 2017. Compensation masks trophic cascades in complex food webs. Theor. Ecol. 10, 245–253. doi:10.1007/ s12080- 016- 0326- 8. Fowler, M.S., 2009. Increasing community size and connectance can increase stability in competitive communities. J. Theor. Biol. 258, 179–188. doi:10.1016/j.jtbi. 2009.01.010. Gaston, K., Fuller, R., 2008. Commonness, population depletion and conservation biology. Trends Ecol. Evol. 23, 14–19. doi:10.1016/j.tree.20 07.11.0 01. Gravel, D., Canard, E., Guichard, F., Mouquet, N., 2011. Persistence increases with diversity and connectance in trophic metacommunities. PLoS ONE 6, e19374. doi:10.1371/journal.pone.0019374. Ives, A.R., Carpenter, S.R., 2007. Stability and diversity of ecosystems. Science 317, 58–62. doi:10.1126/science.1133258. Jentsch, A., White, P., 2019. A theory of pulse dynamics and disturbance in ecology. Ecology 100, e02734. doi:10.1002/ecy.2734. Johnstone, J.F., et al., 2016. Changing disturbance regimes, ecological memory, and forest resilience. Front. Ecol. Environ. 14, 369–378. doi:10.1002/fee.1311. ˚ Hui, C., Dieckmann, U, 2018. Complexity Landi, P., Minoarivelo, H.O., Brännström, A., and stability of ecological networks: a review of the theory. Popul. Ecol. 60, 319–345. doi:10.1007/s10144-018-0628-3. Levin, S.A., Paine, R.T., 1974. Disturbance, patch formation, and community structure. Proc. Natl. Acad. Sci. 71, 2744–2747. doi:10.1073/pnas.71.7.2744. McCabe, D.J., Gotelli, N.J., 20 0 0. Effects of disturbance frequency, intensity, and area on assemblages of stream macroinvertebrates. Oecologia 124, 270–279. doi:10. 10 07/s0 04420 0 0 0369.
McGill, B.J., et al., 2007. Species abundance distributions: moving beyond single prediction theories to integration within an ecological framework. Ecol. Lett. 10, 995–1015. doi:10.1111/j.1461-0248.2007.01094.x. Mello, M.A.R., Marquitti, F.M.D., Guimarães, P.R., Kalko, E.K.V., Jordano, P., de Aguiar, M.A.M., 2011a. The missing part of seed dispersal networks: structure and robustness of bat-fruit interactions. PLoS ONE 6, e17395. doi:10.1371/ journal.pone.0017395. Mello, M.A.R., Marquitti, F.M.D., Guimarães, P.R., Kalko, E.K.V., Jordano, P., de Aguiar, M.A.M., 2011b. The modularity of seed dispersal: differences in structure and robustness between bat– and bird–fruit networks. Oecologia 167, 131–140. doi:10.10 07/s0 0442- 011- 1984- 2. Memmott, J., Waser, N.M., Price, M.V, 2004. Tolerance of pollination networks to species extinctions. Proc. R. Soc. Lond. B Biol. Sci. 271, 2605–2611. doi:10.1098/ rspb.2004.2909. Mougi, A., Kondoh, M., 2016. Food-web complexity, meta-community complexity and community stability. Sci. Rep 6, 24478. doi:10.1038/srep24478. Newman, E.A., 2019. Disturbance ecology in the anthropocene. Front. Ecol. Evol. 7, 147. doi:10.3389/fevo.2019.00147. Nielsen, A., Bascompte, J., 2007. Ecological networks, nestedness and sampling effort. J. Ecol. 95, 1134–1141. doi:10.1111/j.1365-2745.2007.01271.x. Nuwagaba, S., Zhang, F., Hui, C, 2015. A hybrid behavioural rule of adaptation and drift explains the emergent architecture of antagonistic networks. Proc. R. Soc. B Biol. Sci. 282, 20150320. doi:10.1098/rspb.2015.0320. Nuwagaba, S., Zhang, F., Hui, C., 2017. Robustness of rigid and adaptive networks to species loss. PLoS ONE 12, e0189086. doi:10.1371/journal.pone.0189086. Pickett, S., White, P., 1985. The Ecology of Natural Disturbance and Patch Dynamics. Academic Press, NewYork. R Core Team, 2019. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria https://www.R-project. org/. Ramos-Jiliberto, R., Valdovinos, F.S., Moisset de Espanés, P., Flores, J.D, 2012. Topological plasticity increases robustness of mutualistic networks. J. Anim. Ecol. 81, 896–904. doi:10.1111/j.1365-2656.2012.01960.x. Rohr, R.P., Saavedra, S., Bascompte, J., 2014. On the structural stability of mutualistic systems. Science 345, 1253497. doi:10.1126/science.1253497. Salo, P., Banks, P.B., Dickman, C.R., Korpimäki, E, 2010. Predator manipulation experiments: impacts on populations of terrestrial vertebrate prey. Ecol. Monogr. 80, 531–546. doi:10.1890/09-1260.1. Staniczenko, P.P.A., Lewis, O.T., Jones, N.S., Reed-Tsochas, F, 2010. Structural dynamics and robustness of food webs. Ecol. Lett. 13, 891–899. doi:10.1111/j. 1461-0248.2010.01485.x. Stouffer, D.B., Bascompte, J., 2011. Compartmentalization increases food-web persistence. Proc. Natl. Acad. Sci. 108, 3648–3652. doi:10.1073/pnas.1014353108. Suweis, S., Simini, F., Banavar, J.R., Maritan, A., 2013. Emergence of structural and dynamical properties of ecological mutualistic networks. Nature 500, 449–452. doi:10.1038/nature12438. Thebault, E., Fontaine, C., 2010. Stability of ecological communities and the architecture of mutualistic and trophic networks. Science 329, 853–856. doi:10.1126/ science.1188321. Traveset, A., Tur, C., Eguíluz, V.M, 2017. Plant survival and keystone pollinator species in stochastic coextinction models: role of intrinsic dependence on animal-pollination. Sci. Rep. 7. doi:10.1038/s41598- 017- 07037- 7. Turner, M.G., 2010. Disturbance and landscape dynamics in a changing world. Ecology 91, 2833–2849. doi:10.1890/10-0097.1. Tylianakis, J.M., Laliberté, E., Nielsen, A., Bascompte, J, 2010. Conservation of species interaction networks. Biol. Conserv. 143, 2270–2279. doi:10.1016/j.biocon.2009. 12.004. Valdovinos, F.S., Ramos-Jiliberto, R., Garay-Narváez, L., Urbani, P., Dunne, J.A, 2010. Consequences of adaptive behaviour for the structure and dynamics of food webs. Ecol. Lett. 13, 1546–1559. doi:10.1111/j.1461-0248.2010.01535.x. Yodzis, P., 1980. The connectance of real ecosystems. Nature 284 (5756), 544.