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We untangled how the direct and indirect paths of forest cover and water quality variables interact and shape anopheline assemblages in two seasons. Although previous studies determined how environmental variables at different spatial extents affected anopheline distributions in Amazônia, most studies focused on a single effect of an environmental variable or focused on single habitat types (terrestrial or aquatic)22,23,41,42. Our most important finding is that seasonality modulates the direct and indirect effects of forest cover on Amazônian anopheline larval distributions. In particular, we found that forest cover had stronger direct and indirect influence on larval anopheline assemblage composition in the rainy season than the dry season.The different paths and strengths of forest cover influences on anopheline assemblages during the rainy and dry seasons can be associated with the responses of adults and larvae to forest characteristics. Forest cover influences water quality variables of ponds by shading, organic matter inputs and erosion processes43. These effects have consequences for pond water quality44 and favor the establishment of different culicid species45. We showed that during the rainy season, forest cover directly and indirectly influenced site water quality. Greater forest cover in the rainy season directly and indirectly affected A. nimbus and the secondary malaria vectors A. triannulatus and A. braziliensis positively. In the dry season, greater forest cover positively but marginally affected A. peryassui, A. nuneztovari and A. albitarsis, but only indirectly through water quality. Some species like A. triannulatus, A. nuneztovari and A. braziliensis coexist with the malaria vector, A. darlingi, in breeding sites46, and these species have been positively associated with pH, dissolved oxygen and total suspended solids in natural and artificial habitats20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47, which are environmental conditions favored by greater forest cover. The marginal indirect effect of forest cover on anopheline assemblage in the dry season suggests that we need caution in the interpretation of this result and long-term temporal data is required to confirm if this effect is corroborated.Forest conditions influence mosquito vectors and their hosts. For example, some mosquitoes are zoophiles that feed on the blood of birds, reptiles, and mammals48, which are often more abundant in conserved areas. Other species are anthropophilic and prefer to feed on human blood49 and altered environments can force these species to migrate and, consequently, to change hosts48. In our study, A. triannulatus and A. minbus were more abundant in sites with more natural characteristics, whereas A. darlingi and A. nuneztovari were more abundant in altered landscapes. In addition, urbanization and deforestation increase the proximities of humans and domestic animals to mosquito vectors and their hosts, thereby maintaining and increasing transmission cycles50.Forest conditions influence anopheline diversity by different paths, which may alter the strength of their seasonal effects. During the dry season, mosquito survival is also affected by altered microclimate (e.g., lower humidity)51 and lentic habitats contain less water, increased nutrient concentrations and decreased abundance and richness of mosquitoes52,53. We observed that rainfall plays an important role in the larval abundance of Anopheles in artificial larval habitats in Manaus. In addition, climatic factors such as rainfall and river levels are strongly associated with vector abundance and malaria cases in the region54,55. During the rainy season, increased water volume in artificial habitats provides more areas for distribution and development of mosquito species56 and we detected a significant increase in abundance of A. triannulatus, A. darlingi and A. nuneztovari. These observations may partially explain why we found a direct effect of forest cover on mosquitoes only during the rainy season.Our results add more evidence that managing and conserving forest cover is important to control anophelines, thereby decreasing the contact of potential vectors (e.g., A. darlingi) with humans. In general, our results support the idea that mosquitoes are directly affected by the loss of native forest cover57 in the rainy season. Mosquitoes associated with serious human diseases (e.g., malaria, yellow fever, dengue, leishmaniasis) are more abundant in areas with low levels of native forest cover14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58. This is a critically important finding because recent studies have shown that forest cover plays an important role in the vector dynamics of mosquitoes and forest conservation keeps pathogens within the forest, avoiding spillover to human settlements59. On the other hand, deforestation provides favorable conditions for these vectors, thereby increasing malária cases and decreasing scores of the Human Development Index60. In addition, there is a positive correlation between mosquito abundance in fragmented forests and the prevalence of Plasmodium, the protozoan that causes malaria61.Artificial larval habitats promote conditions for malaria vectors in Amazônia62,63. Therefore, the best way to develop control techniques would be to understand larval ecology in these habitats, where they are more sensitive to infections by pathogens, parasites, predation, larvicides and growth regulators64. This information is necessary to minimize failures in programs to control or eradicate the vector and the disease. Under this perspective, our study adds a new piece in the puzzle of mosquito control in Amazônia. For example, during the rainy season when forest cover directly and indirectly influences larval habitats, control programs can strengthen the control of key limnological variables, habitat structure, and entomological aspects, intensifying the environmental filter, particularly in areas with little forest cover and greater human concentrations near those habitats. The limnological study of Anopheles larval habitats is still far from complete, as each case has peculiarities inherent to them. Despite attempts, anophelines demonstrate versatility in relation to abiotic parameters20,21,22,23,24,25,26,65,66. However, we can use approaches that modify the larval environments. For example, more efficient management of water levels in fish farming ponds could decrease larval numbers and anopheline reproduction, Similarly, greater rationing of fish feed would decrease the supply of food resources for mosquito larvae. It is also worth mentioning that some variables are related to the efficiency of others. Regarding biological control via entomopathogenic bacteria, environmental factors (solar radiation) and water quality (amounts of total suspended solids and organic matter), can interfere with the effectiveness of the formulated Bacillus sphaericus applied in habitats for vector control62,63,64,65,66,67. Furthermore, eutrophication decreased the assemblages of aquatic invertebrates predating mosquito larvae.Another alternative is the use of physical control (removal of grasses and macrophytes from the edge of habitats), helping to reduce microhabitats that provide larval refuges. Also, increased light and water temperature at the edges favor natural predation and biological control processes from potential fish and macroinvertebrates. The conservation of natural enemies and the use of biotic agents in the population control of vector mosquitoes have been recommended in small and medium-sized natural and artificial breeding sites19,20,21,22,23,24,25,26,27,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53. A combination of techniques that shape the important environmental variables for the establishment of these species are essential for vector control.The analytical approach used here opens some windows of opportunity for improvements that are important to be recognized. First, our model did not incorporate important complexity of natural systems, such as ecological interactions among vectors and hosts, including human behavior. Agent-based models, including different host behavior, could provide important insights in this way. Second, our study is very limited in terms of temporal climatic variability. Additional information is needed to better understand the effects of long-term changes in land-use, water quality and climate and their interactions with mosquito assemblages in the region, particularly considering an ecological-evolutionary perspective. Third, it is important to highlight that the magnitude of effects of the estimated drivers were not the same in the rainy and dry seasons. Also, they may not remain constant in coming decades, especially considering potential regional process on mosquito assemblages, such as spillover effects, mass effects and host changes. Fourth, our study was carried out in an area of Amazonia that has experienced, a relatively old land use conversion from forest to urban areas (urban expansion rate of around 12% per year for the past 34 years)68. Beginning in the 1970s, human population increased at a rate of around 23% per decade and 25% in Manaus11. Therefore, the region we studied is very relevant in terms of historical interactions among human populations, mosquitoes and land use changes. However, understanding the effect of these changes on mosquito assemblages in areas with different land-use change dynamics, provides us with important information69, particularly those with very rapid urbanization processes, such as in the Arch of Deforestation70. Lastly, we need studies that consider the nexus among climate and land use changes, human and animal population health, economic conditions, and ecosystem services provided by these forest-urban transitional regions. Such information would facilitate including mosquito information in land use planning and climate mitigation programs based on forest management in and around cities.Therefore, identifying ecological factors and paths that affect the composition of species of epidemiological importance are essential because they inform vector integrated management strategies. We emphasize that larval control in lentic habitats requires knowledge about larval ecology and the effects of biotic and abiotic variables on larvae, especially when it comes to biological controls. The application of integrated pest management can be conducted in both dry and rainy seasons. However, we recommend focusing on the dry season when larval habitats are more limited, in smaller volumes and more accessible for entry and application of vector control techniques. These are critically important considerations because over 2 million people live in Amazonas state11 and anophelines transmitted over 59,637 malaria cases in the Amazon region in the first half of 2020, and about 44.4% came from the state of Amazonas71. More

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Metacommunity model and asymptotic community assemblyWe built a large set of model metacommunities (detailed in full in “Methods”) describing competitive dynamics within a single guild of species across a landscape. Each metacommunity consisted of a set of patches, or local communities, randomly placed in a square arena and linked by a spatial network. The dynamics of each population are governed by three processes: inter- and intraspecific interactions, heterogeneous responses to the environment and dispersal between adjacent patches (Fig. 1). Competition coefficients between species are drawn at random and the population dynamics within each patch are described by a Lotka-Volterra competition model. We control the level of environmental heterogeneity across the network directly by generating an intrinsic growth rate for each species at each patch from a random, spatially correlated distribution. To ensure any turnover is purely autonomous, we keep the environment fixed throughout simulations. Dispersal between neighbouring patches declines exponentially with distance between sites. This formulation allows precise and independent control of key properties of the metacommunity–the number of patches, the characteristic dispersal length and the heterogeneity of the environment.Fig. 1: Elements of the Lotka-Volterra metacommunity model and the emergence of autonomous population dynamics.Environmental heterogeneity, represented by the intrinsic growth rate matrix R, is modelled using a spatially autocorrelated Gaussian random field. A random spatial network, represented by the dispersal matrix D, defines the spatial connectivity of the landscape. The network of species interactions, represented by the competitive overlap matrix A, is modelled by sampling competition coefficients at random (perpendicular bars indicate recipients of a deleterious competitive impact). The resulting dynamics of local population biomasses, given by the colour-coded equation, are numerically simulated. The Hadamard product ‘∘’ represents element-wise matrix multiplication. For large metacommunities, local populations exhibit persistent dynamics despite the absence of external drivers. In the 3D boxes, typical simulated biomass dynamics of dominating species are plotted on linear axes over 2500 unit times. The graphs illustrate the complexity of the autonomous dynamics and the propensity for compositional change (local extinction and colonisation).Full size imageTo populate the model metacommunities, we iteratively introduced species with randomly generated intrinsic growth rates and interspecific interaction coefficients. Between successive regional invasions we simulated the model dynamics, and removed any species whose abundance fell below a threshold across the whole network. Through this assembly process and the eventual onset of ecological structural instability, both average local diversity, the number of species coexisting in a given patch, and regional diversity, the total number of species in the metacommunity, eventually saturate and then fluctuate around an equilibrium value—any introduction of a new species then leads on average to the extinction of one other species (Supplementary Fig. 1). In these intrinsically regulated metacommunities we then studied the phenomenology of autonomous community turnover in the absence of regional invasions or abiotic change.In our metacommunity model, local community dynamics and therefore local limits on species richness depend on a combination of biotic and abiotic filtering (non-uniform responses of species to local conditions)33,34,35 and immigration from adjacent patches, generating so called mass effects in the local community36,37,38. Biotic filtering via interspecific competition is encoded in the interaction coefficients Aij, while abiotic filtering occurs via the spatial variation of intrinsic growth rates Rix. For simplicity, and since predator-prey dynamics are known to generate oscillations39 through mechanisms distinct from those we report here, we restrict our analysis to competitive communities for which all ecological interactions are antagonistic. The off-diagonal elements of the interaction matrix A describe how one species i affects another species j. These are sampled independently from a discrete distribution, such that the interaction strength Aij is set to a constant value in the range 0 to 1 (in most cases 0.5) with fixed probability (connectance, in most cases 0.5) and otherwise set to zero. Intraspecific competition coefficients Aii are set to 1 for all species. This discrete distribution of the interaction terms was chosen for its relative efficiency. In the Supplementary discussion (and Supplementary Fig. 2) we show that outcomes remain unaffected when more complex distributions are modelled. Intrinsic growth rates Rix are sampled from spatially correlated normal distributions with mean 1, autocorrelation length ϕ and variance σ2 (Supplementary Fig. 3).Dispersal is modelled via a spatial connectivity matrix with elements Dxy. The topology of the model metacommunity, expressed through D, is generated by sampling the spatial coordinates of N patches from a uniform distribution ({mathcal{U}}(0,sqrt{N})times {mathcal{U}}(0,sqrt{N})), i.e., an area of size N. Thus, under variation of the number of patches, the inter-patch distances remain fixed on average. Spatial connectivity is defined by linking these patches through a Gabriel graph40, a planar graph generated by an algorithm that, on average, links each local community to four close neighbours41. Avoidance of direct long-distance dispersal and the sparsity of the resulting dispersal matrix permit the use of efficient numerical methods. The exponential dispersal kernel defining Dxy is tuned by the dispersal length ℓ, which is fixed for all species.The dynamics of local population biomasses Bix = Bix(t) are modelled using a system of spatially coupled Lotka-Volterra (LV) equations that, in matrix notation, takes the form23$$frac{d{bf{B}}}{dt}={bf{B}}circ ({bf{R}}-{bf{A}}{bf{B}})+{bf{B}}{bf{D}},$$
(1)
with ∘ denoting element-wise multiplication. Hereafter this formalism is referred to as the Lotka-Volterra Metacommunity Model (LVMCM). Further technical details are provided in Methods and the Supplementary Discussion.In order to numerically probe the impacts of ℓ, ϕ and σ2 on the emergent temporal dynamics, we initially fixed N = 64 and varied each parameter through multiple orders of magnitude (Supplementary Fig. 4). In order to obtain a full characterisation of autonomous turnover in the computationally accessible spatial range (N ≤ 256), we then selected a parameter combination found to generate substantial fluctuations for further analysis. Thereafter we assembled metacommunities of 8–256 patches (Fig. 2a) until regional diversity limits were reached (with tenfold replication) and generated community time series of 104 unit times from which the phenomenology of autonomous turnover could be explored in detail. We found no evidence to suggest that the phenomenology described below depends on this specific parameter combination. While future results may confirm or refute this, autonomous turnover arises over a wide range of parameters (Supplementary Fig. 4) and as such the phenomenon is robust.Fig. 2: Autonomous turnover in model metacommunities.a Typical model metacommunities: a spatial network with N nodes representing local communities (or patches) and edges, channels of dispersal. Patch colour represents the number of clusters in local community state space detected over 104 unit times t using hierarchical clustering of the Bray-Curtis (BC) dissimilarity matrix, Supplementary Fig. 6. b Colour coded matrices of pairwise temporal BC dissimilarity corresponding to the circled patches in (a). Insets represent 102 unit times. For small networks (N = 8) local compositions converge to static fixed points. As metacommunity extent increases, however, persistent dynamics emerge. Initially this autonomous turnover is oscillatory in nature with communities fluctuating between small numbers of states which can be grouped into clusters (16 ≤ N ≤ 32). Intermediate metacommunities (32 ≤ N ≤ 64) manifest “Clementsian” temporal turnover, characterised by sharp transitions in composition, implying species turn over in cohorts. Large metacommunities (N ≥ 128) turn over continuously, implying “Gleasonian” assembly dynamics in which species’ temporal occupancies are independent. c The mean number of local compositional clusters detected for metacommunities of various numbers of patches N (error bars represent standard deviation across all replicated simulations). While the transition from static to dynamic community composition at the local scale is sharp (see text), non-uniform turnover within metacommunities (a) blurs the transition at the regional scale. Aij = 0.5 with probability 0.5, ϕ = 10, σ2 = 0.01, ℓ = 0.5.Full size imageAutonomous turnover in model metacommunitiesFor small (N ≤ 8) metacommunities assembled to regional diversity limits, populations attain equilibria, i.e., converge to fixed points, implying the absence of autonomous turnover23. With increasing metacommunity size N, however, we observe the emergence of persistent population dynamics (Supplementary Fig. 5 and external video) that can produce substantial turnover in local community composition. This autonomous turnover can be represented through Bray-Curtis42 (BC) dissimilarity matrices comparing local community composition through time (Fig. 2b), and quantified by the number of compositional clusters detected in such matrices using hierarchical cluster analysis (Fig. 2a, c).At intermediate spatial scales (Fig. 2, 16 ≤ N ≤ 32) we often find oscillatory dynamics, which can be perfectly periodic or slightly irregular. With increasing oscillation amplitude, these lead to persistent turnover dynamics where local communities repeatedly transition between a small number of distinct compositional clusters (represented in Fig. 2 by stripes of high pairwise BC dissimilarity spanning large temporal ranges). At even larger scales (N ≥ 64) this compositional coherence begins to break down, and for very large metacommunities (N ≥ 128) autonomous dynamics drive continuous acyclic change in community composition. The number of compositional clusters detected over time typically varies within a given metacommunity (Fig. 2a node colour), however we find a clear increase in the average number of compositional clusters, i.e., an increase in turnover, with increasing total metacommunity size (Fig. 2c).Metacommunities in which the boundaries of species ranges along environmental gradients are clumped are termed Clementsian, while those for which range limits are independently distributed are  referred to as Gleasonian43. We consider the block structure of the temporal dissimilarity matrix at intermediate N to represent a form of Clementsian temporal turnover, characterised by sudden significant shifts in community composition. Metacommunity models similar to ours have been found to generate such patterns along spatial gradients44, potentially via an analogous mechanism45. Large, diverse model metacommunities manifest Gleasonian temporal turnover. In such cases, species colonisations and extirpations are largely independent and temporal occupancies predominantly uncorrelated, such that compositional change is continuous, rarely, if ever, reverting to the same state.Mechanistic explanation of autonomous turnoverSurprisingly, the onset and increasing complexity of autonomous turnover as system size N increases (Fig. 2) can be understood as a consequence of local community dynamics alone. To explain this, we first recall relevant theoretical results for isolated LV communities. Then we demonstrate that, in presence of weak propagule pressure, these results imply local community turnover dynamics, controlled by the richness of potential invaders, that closely mirror the dependence on system size seen in full LV metacommunities.Application of methods from statistical mechanics to models of large isolated LV communities with random interactions revealed that such models exhibit qualitatively distinct phases46,47,48. If the number of modelled species, S, interpreted as species pool size, lies below some threshold value determined by the distribution of interaction strengths (Supplementary Fig. 7), these models exhibit a unique linearly stable equilibrium (Unique Fixed Point phase, UFP). Some species may go extinct, but the majority persists48. When pool size S exceeds this threshold, there appear to be no more linearly stable equilibrium configurations. Any community formed by a selection from the S species is either unfeasible (there is no equilibrium with all species present), intrinsically linearly unstable, or invadable by at least one of the excluded species. This has been called the multiple attractor (MA) phase47. However, the implied notion that this part of the phase space is in fact characterised by multiple stable equilibria may be incorrect.Population dynamical models with many species have been shown to easily exhibit attractors called stable heteroclinic networks49, which are characterised by dynamics in which the system bounces around between several unstable equilibria, each corresponding to a different composition of the extant community, implying indefinite, autonomous community turnover (Fig. 3, red line). As these attractors are approached, models exhibit increasingly long intermittent phases of slow dynamics, which, when numerically simulated, can give the impression that the system eventually reaches one of several ‘stable’ equilibria, suggesting that turnover comes to a halt. We demonstrate in the Supplementary discussion that the MA phase of isolated LV models is in fact characterised by such stable heteroclinic networks (Supplementary Figs. 8 and 9). Note, we retain the MA terminology here because the underlying complete heteroclinic networks, interpreted as a directed graph50,51 (Fig. 3, inset), might have multiple components that are mutually unreachable through dynamic transitions52, each representing a different attractor.Fig. 3: Approximate heteroclinic networks underlie autonomous community turnover.The main panel shows two trajectories in the state space of a community of three hypothetical species (population biomasses B1, B2, B3) that are in non-hierarchical competition with each other, such that no species can competitively exclude both others (a “rock-paper-scissors game”17). Without propagule pressure, the system has three unstable equilibrium points (P1, P2, P3) and cycles between these (red curve), coming increasingly close to the equilibria and spending ever more time in the vicinity of each. The corresponding attractor is called a heteroclinic cycle (dashed arrows). Under weak extrinsic propagule pressure (blue curve), the three equilibria and the heteroclinic cycle disappear, yet the system closely tracks the original cycle in state space. Such a cycle can be represented as a graph linking the dynamically connected equilibria (inset). With more interacting species, these graphs can become complex “heteroclinic networks”49,50,51 with trajectories representing complex sequences of species composition during autonomous community turnover.Full size imageIf one now adds to such isolated LV models terms representing weak propagule pressure for all S species (Supplementary Eq. (2)), dynamically equivalent to mass effects occurring in the full metacommunity model (Eq. (1)), then none of the S species can entirely go extinct. The weak influx of biomass drives community states away from the unstable equilibria representing coexistence of subsets of the S species and the heteroclinic network connecting them (blue line in Fig. 3). Typically, system dynamics then still follow trajectories closely tracking the original heteroclinic networks (Fig. 3), but now without requiring boundless time to transition from the vicinity of one equilibrium to the next.The nature and complexity of the resulting population dynamics depend on the size and complexity of the underlying heteroclinic network, and both increase with pool size S. In simulations (Supplementary Fig. 10) we find that, as S increases, LV models with weak propagule pressure pass through the same sequence of states as we documented for LVMCM metacommunities in Fig. 2: equilibria, oscillatory population dynamics, Clementsian and finally Gleasonian temporal turnover.Above we introduced the number of clusters detected in Bray-Curtis dissimilarity matrices of fixed time series length as a means of quantifying the approximate number of equilibria visited during local community turnover. As shown in Fig. 4a, b, this number increases in LV models with S in a manner strikingly similar to its increase in the LVMCM with the number of species present in the ecological neighbourhood of a given patch. Thus, dynamics within a patch are controlled not by N directly but rather by neighbourhood species richness. For a given neighbourhood, species richness depends on the number of connected patches, the total area and therefore total abiotic heterogeneity encompassed, and the connectivity, all of which can vary substantially within a metacommunity of a given size N. As illustrated in Fig. 4b, there is a tendency for neighbourhood richness to be larger in larger metacommunities, leading indirectly to the dependence of metacommunity dynamics on N seen in Fig. 2.Fig. 4: Ecological mass effects drive autonomous turnover.a The number of compositional clusters detected, plotted against the size of the pool of potential invaders S for an isolated LV community using a propagule pressure ϵ of 10−10 and 10−15, fit by a generalised additive model87. For S 1 compositional cluster) occurs at a pools size of around S = 35 species, consistent with the theoretical prediction47 of the transition between the UFP and MA phases (Supplementary Discussion). Close inspection of this threshold reveals an important and hitherto unreported relationship between the transition into the MA phase and local ecological limits set by the onset of ecological structural instability, which is known to regulate species richness in LV systems subject to external invasion pressure23,24: in the Supplementary Discussion we show that the boundary between the UFP and MA phases47 coincides precisely with the onset of structural instability24 (Supplementary Eqs. (3)–(9)).For LVMCM metacommunities, this relationship (demonstrated analytically in the Supplementary Discussion) is numerically confirmed in Fig. 5. During assembly, local species richness increases until it reaches the limit imposed by local structural instability. Further assembly occurs via the “regionalisation” of the biota53—a collapse in average range sizes23 and associated increase in spatial beta diversity—until regional diversity limits are reached23. The emergence of autonomous turnover coincides with the onset of species saturation at the local scale. Autonomous turnover can therefore serve as an indirect indication of intrinsic biodiversity regulation via local structural instability in complex communities.Fig. 5: The emergence of temporal turnover during metacommunity assembly.a Local species richness, defined by reference to source populations only (({overline{alpha }}_{text{src}}), grey) and regional diversity (γ black) for a single metacommunity of N = 32 coupled communities during iterative regional invasion of random species. We quantify local source diversity ({overline{alpha }}_{text{src}}) as the metacommunity average of the number αsrc of non-zero equilibrium populations persisting when immigration is switched off (off-diagonal elements of D set to zero), since this is the component of a local community subject to strict ecological limits to biodiversity. Note the log scale chosen for easy comparison of local and regional species richness. b Increases in regional diversity beyond local limits arise via corresponding increases in spatial turnover (({overline{beta }}_{text{s}}), black). Autonomous temporal turnover (({overline{beta }}_{text{t}}), grey) sets in (crosses a threshold mean Bray Curtis (BC) dissimilarity of 10−2) precisely when average local species richness ({overline{alpha }}_{text{src}}) has reached its limit, reflecting the equivalence of the transition to the MA phase space and the onset of local structural instability. In both panels, the dashed line marks the point at which autonomous temporal turnover was first detected. Aij = 0.3 with probability 0.3, ϕ = 10, σ2 = 0.01, ℓ = 0.5. Both spatial and temporal turnover computed as the mean BC dissimilarity. In each iteration of the assembly model (regional invasion event), 0.1S + 1 species were introduced. Dynamics were simulated for 2 × 104 unit times, with the second 104 unit times analysed for autonomous turnover, and a total of 104 invasions were modelled.Full size imageThus, we have shown that propagule pressure perturbs local communities away from unstable equilibria and drives compositional change. In order to invade, however, species need to be capable of passing through biotic and abiotic filters33,34,35. We would expect, therefore, that turnover would be suppressed in highly heterogeneous or poorly connected environments where mass effects are weak. Indeed, by manipulating the autocorrelation length ϕ and variance σ2 of the abiotic filter represented by the matrix R and the characteristic dispersal length ℓ, we observe a sharp drop-off in temporal turnover in parameter regimes that maximise between-patch community dissimilarity (short environmental correlation or dispersal lengths, Supplementary Fig. 11). Thus, we conclude that it is not species richness or spatial dissimilarity per se that best predict temporal turnover, but the size of the pool of species with positive invasion fitness, i.e., those not repelled by the combined effects of biotic and abiotic filters.The macroecology of autonomous turnoverWe find good correspondence between temporal and spatio-temporal biodiversity patterns emerging in model metacommunities in the absence of external abiotic change and in empirical data (Fig. 6), with quantitative characteristics lying within the ranges observed in natural ecosystems.Fig. 6: Macroecological signatures of autonomous compositional change.A bimodal distribution in temporal occupancy observed in North American birds54 (a) and in simulations (e N = 64, ϕ = 5, σ2 = 0.01, ℓ = 0.5). Intrisically regulated species richness observed in estuarine fish species59 (b) and in simulations (f N = 64, ϕ = 5, σ2 = 0.01, ℓ = 0.5, 1000 unit times t). The decreasing slopes of the STR with increasing sample area12 (c), and the SAR with increasing sample duration12 (d) for various communities and in simulations (g and h N = 256, ϕ = 10, σ2 = 0.01, ℓ = 0.5, spatial window ΔA, temporal windo ΔT). In (c) and (d) we have rescaled the sample area/duration by the smallest/shortest reported value and coloured by community (see original study for details). In (g) and (h) we study the STAR in metacommunities of various size N, represented by colour. Limited spatio-temporal turnover in the smallest metacommunties (blue colours) greatly reduces the exponents of the STAR relative to large metacommunities (red colours). Aij = 0.5 with probability 0.5 in all cases.Full size imageTemporal occupancyThe proportion of time in which species occupy a community tends to have a bi-modal empirical distribution54,55,56 (Fig. 6a). The distribution we found in simulations (Fig. 6e) closely matches the empirical pattern.Community structureTemporal turnover has been posited to play a stabilising role in the maintenance of community structure57,58. In an estuarine fish community59, for example, species richness (Fig. 6b) and the distribution of abundances were remarkably robust despite changes in population biomasses by multiple orders of magnitude. In model metacommunities with autonomous turnover we found, likewise, that local species richness exhibited only small fluctuations around the steady-state mean (Fig. 6f, three random local communities shown) and that the macroscopic structure of the community was largely time invariant (Supplementary Fig. 12). In the light of our results, we propose the absence of temporal change in community properties such as richness or the abundance distribution despite potentially large fluctuations in population abundances59 as indicative of autonomous compositional turnover.The species-time-area-relation, STARThe species-time-relation (STR), typically fit by a power law of the form S ∝ Tw 12,60,61, describes how observed species richness increases with observation time T. The exponent w of the STR has been found to be consistent across taxonomic groups and ecosystems12,13,62, indicative of some general population dynamical mechanism. However, the exponent of the STR decreases with increasing sampling area12, and the exponent of the empirical Species Area Relation (SAR) (S ∝ Az) consistently decreases with increasing sampling duration12 (Fig. 6c, d). We tested for these patterns in a large simulated metacommunity with N = 256 patches by computing the species-time-area-relation (STAR) for nested subdomains and variable temporal sampling windows (see “Methods”). We observed exponents of the nested SAR in the range z = 0.02–0.44 and for the STR a range w = 0.01–0.44 (Supplementary Fig. 13). We also found a clear decrease in the rate of species accumulation in time as a function of sample area and vice-versa (Fig. 6g, h), consistent with the empirical observations. Meta-analyses of these patterns in nature have reported exponents which are remarkably consistent, with z typically in the range 0.1–0.363, and w typically in the range 0.2–0.413, in both cases largely independent of location or taxonomic group13.Thus, the distribution of temporal occupancy, the time invariance of key macroecological structures and the STAR in our model metacommunities match observed patterns. This evidence suggests that such autonomous dynamics cannot be ruled out as an important driver of temporal compositional change in natural ecosystems.Turnover rate in simulated metacommunitiesHow do the turnover rates that we find in our model compare with those observed? Our current analytic understanding of autonomous turnover is insufficient for estimating the rates directly from parameters, but the simulation results provide some indication of the expected order of magnitude, that can be compared with observations. Key for such a comparison is the fact that, because the elements of R are 1 on average, the time required for an isolated single population to reach carrying capacity is ({mathcal{O}}(1)) unit times. Supplementary Fig. 12b suggests that transitions between community states occur at the scale of around 10–50 unit times. This gives a holistic, rule-of-thumb estimate for the expected rate of autonomous turnover, depending on the typical reproductive rates of the guild of interest. In the case of macroinvertebrates, for example, the time required for populations to saturate in population biomass could be of the order of a month or less. By our rule of thumb, this would mean that autonomous community turnover would occur on a timescale of years. In contrast, for slow growing species like trees, where monoculture stands can take decades to reach maximum population biomass, the predicted timescale for autonomous turnover would be on the order of centuries or more. Indeed, macroinvertebrate communities have been observed switching between community configurations with a period of a few years64,65, while the proportional abundance of tree pollen and tree fern spores fluctuates in rain forest bog deposits with a period of the order of 103 years66—suggesting that the predicted autonomous turnover rates are biologically plausible.ConclusionsCurrent understanding of the mechanisms driving temporal turnover in ecological communities is predominantly built upon phenomenological studies of observed patterns2,67,68,69 and is unquestionably incomplete10,59. That temporal turnover can be driven by external forces—e.g., seasonal or long term climate change, direct anthropogenic pressures—is indisputable. A vitally important question is, however, how much empirically observed compositional change is actually due to such forcing. Recent landmark analyses of temporal patterns in biodiversity have detected no systematic change in species richness or structure in natural communities, despite rates of compositional turnover greater than predicted by stochastic null models1,70,71,72. Here we have shown that empirically realistic turnover in model metacommunities can occur via precisely the same mechanism as that responsible for regulating species richness at the local scale. While the processes regulating diversity in natural communities remain insufficiently understood, our theoretical work suggests local structural instability may explain these empirical observations in a unified and parsimonious way. Therefore, we advocate for the application of null models of metacommunity dynamics that account for natural turnover in ecological status assessments and predictions based on ancestral baselines. Future work will involve fitting the model described here to observations by estimating abiotic and biotic parameters from empirical datasets. In the Supplementary Discussion we show how different combinations of parameters lead to different quantitative outcomes (Supplementary Fig. 4), likely representing different types of empirical metacommunities. Understanding where in this parameter space natural systems exist may provide the foundation for a quantitative null model, a baseline expectation of turnover against which observations can be compared.Our simulations revealed a qualitative transition from “small” metacommunities, where autonomous turnover is absent or minimal, to “large” metacommunities with pronounced autonomous turnover (Fig. 2). The precise location of the transition between these cases depends on details such as dispersal traits, the ecological interaction network, and environmental gradients (Supplementary Fig. 4). Taking, for simplicity, regional species richness as a measure of metacommunity size suggests that both ‘small’ and ‘large’ communities in this sense are realised in nature. In our simulations, the smallest metacommunities sustain 10s of species, while the largest have a regional diversity of the order 103, which is not large comparable to the number of tree species in just 0.25 km2 of tropical rainforest (1100–1200 in Borneo and Ecuador73) or of macroinvertebrates in the UK ( >32,00074). Within the ‘small’ category, where autonomous turnover is absent, we would therefore expect to be, e.g., communities of marine mammals or large fish, where just a few species interact over ranges that can extend across entire climatic niches, implying that the effective number of independent “patches” is small and providing few opportunities for colonisation by species from neighbouring communities. Likely to belong to the ‘large’ category are communities of organisms that occur in high diversity with range sizes that are small compared to climatic niches, such as macroinvertebrates. For these, autonomous turnover of local communities can plausibly be expected based on our findings. Empirically distinguishing between these two cases for different guilds will be an important task for the future.For metacommunities of intermediate spatial extent, autonomous turnover is characterised by sharp transitions between cohesive states at the local scale. To date, few empirical analyses have reported such coherence in temporal turnover, perhaps because the taxonomic and temporal resolution required to detect such patterns is not yet widely available. Developments in biomonitoring technologies75 are likely to reveal a variety of previously undetected ecological dynamics, however and by combining high resolution temporal sampling and metagenetic analysis of community composition, a recent study demonstrated cohesive but short-lived community cohorts in coastal plankton76. Such Clementsian temporal turnover may offer a useful signal of autonomous compositional change in real systems.Thus, overcoming previous computational limits to the study of complex metacommunities11,77, we have discovered the existence of two distinct phases of metacommunity ecology—one characterised by weak or absent autonomous turnover, the other by continuous compositional change even in the absence of external drivers. By synthesising a wide range of established ecological theory11,23,24,47,48,49, we have heuristically explained these phases. Our explanation implies that autonomous turnover requires little more than a diverse neighbourhood of potential invaders, a weak immigration pressure, and a complex network of interactions between co-existing species. More