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    Millimeter-sized smart sensors reveal that a solar refuge protects tree snail Partula hyalina from extirpation

    Smart solar sensor designTo prevent interference with the movements of the highly mobile E. rosea predators, we developed a custom smart solar sensor using the Michigan Micro Mote (M3) platform27,36. The M3 platform consists of a family of chips that can be integrated together through die-stacking in various ways, allowing its functionality to be customized. M3 achieves this degree of miniaturization by directly stacking bare-die chips, thus avoiding individual chip packaging, and custom-designed low-power circuits, reducing consumption to only 228 nW. The resulting systems can be powered for >1 week by a chip-scale battery36 measuring only 1.7 × 3.6 × 0.25 mm. For the solar sensor, we selected chips from this set with the following functionalities and stacked them as shown in Fig. 4: (1) two custom-designed thin-film lithium-chemistry batteries37, each with 8-µAh capacity and 4.2-V battery voltage, connected in parallel; (2) a power management chip to generate and regulate the three supply voltages used by the M3 chips from the battery supply voltage; (3) a microprocessor chip containing an ARM Cortex-M038 processor that executes the program controlling the sensor and 8 kB of SRAM for storing program and sensor data; (4) a short-range (5 cm) radio chip with on-chip antenna for retrieving data from the sensor; (5) a decoupling capacitor chip for stabilizing supply voltages; (6) a harvester chip that up-converts the voltage from the photovoltaic (PV) cells to the battery voltage and regulates battery charging; (7) a temperature sensor chip; (8) an inactive spacer chip that provides physical separation between the PV cell, which is exposed to light, and the remainder of the chips below it, which must be blocked from light; and (9) a PV chip for harvesting solar energy, containing also a small PV cell for receiving optical communication.Fig. 4: Structure and testing of custom-designed smart solar sensors.a Smart sensor before encapsulation showing the interconnected stack of chips. b Smart sensor after encapsulation with black and clear epoxy. c Sensor readings of eight randomly selected smart sensors, each indicated by a distinct symbol, at three light intensities across the temperature and battery voltage ranges observed during the sensor deployment with the σ/µ annotated.Full size imageThe battery chips measured 1.7 × 3.6 × 0.25 mm while the remaining chips were 1.05 mm wide, 150 μm thick and varied in length from 1.33 to 2.08 mm. The chips were stacked in staircase fashion (Fig. 4a) using die-attach film and connected electrically using wire bonding with gold 18-μm diameter wire. The radio die extended beyond the other chips at the back to expose the antenna. The chips communicated using a common bus protocol, called M-bus36. The final chip stack was encased in epoxy (Fig. 4b). The top portion of the sensor was encased with clear epoxy to allow light penetration, thereby enabling energy harvesting and optical communication. The bottom portion was encapsulated with black epoxy to protect the sensitive electronics from light. Finally, the entire sensor was coated with 4 μm of parylene. The sensor was tested to withstand immersion in brine at pressures up to 600 atm for 1 h and in saline solution for 2 weeks.The principal approach to reduce the M3 sensor’s power consumption is to duty-cycle its operation, meaning the processor executes code briefly (ms range) every 10–60 min and is in “sleep mode” for the remainder of the time. Sleep power is highly optimized to ~100 of nW using a number of recently developed circuit techniques39,40,41. In active mode, the processor is operating and obtains and stores sensor data. The processor clock frequency was set to 80 kHz, and at 0.6 V supply, the power consumption was 1.0 μW. In sleep mode, the processor and logic are power-gated42, and only the SRAM, timer, optical receiver, and power management remain on, reducing the power consumption to only 160 nW. The 10-min sleep mode period length was selected to amortize the high power in active mode and minimize overall power consumption while retaining a sufficiently small sensor acquisition interval for the proposed study. The average power consumption of the entire sensor including all peripherals was 228 nW, and in tests, it was able to operate on a battery charge alone for 1 week. With PV-based harvesting, the sensor becomes energy autonomous at light levels >850 lux. For this study, the sensors were retrieved and recharged using a light station after each deployment.Although duty-cycling lowers the average current draw from the battery, it limits measurements to times when the sensor is awake. This raised a particular difficulty for measuring the solar ecology of snails where continuous light monitoring is essential, preventing the use of duty-cycling. Typical light-sensing circuits monitor the current from a photodiode and consume ~μW power43, a load that would deplete the batteries in only a few hours. Hence the light intensity had to be monitored during sleep mode. To achieve this without substantially increasing the sleep mode current draw, we observed that the harvester circuit inherently integrates and quantizes the harvested energy from the photovoltaic (PV) cell in a manner proportion to the ambient light level and can be modified to function as a light sensor readout circuit.To up-convert the output voltage of the PV cell (250–450 mV) to that of the battery (3.9–4.2 V), the harvester performs a series of voltage doublings44 using the circuit shown in Supplementary Fig. 6. Each voltage doubling circuit consists of two chains of inverters, configured as a ring oscillator. The two oscillators are coupled through on-chip MIM capacitors and are connected to the supplies Vin and Vdouble, as shown. During one oscillation cycle, each capacitor experiences two different configurations. When the input to its driving inverters is high, a capacitor is placed between Vin and ground (GND), i.e., in parallel with the PV cell, which charges it with a finite amount of charge. When its driving inverter inputs are switched low, the capacitor is placed between Vin and Vdouble, and it delivers the received charge to Vdouble, thereby up-converting the voltage from the PV cell. The amount of charge that is transferred per cycle is kept constant by the frequency regulation circuit. If the PV cell is exposed to intense light and produces a high current, the regulation circuit increases the frequency by reducing the delay of the voltage-controlled delay element to maintain a constant charge transfer per cycle. Conversely, if the light level drops, the regulation circuit slows the oscillation frequency.As a result, the frequency of oscillation is proportional to the PV current to the first order. And, because the current of the PV cell is proportional to the light intensity, the oscillation frequency is a measure of the instantaneous ambient light level. To obtain the light dose over a sleep mode time period, we added a low-power counter (shown in Supplementary Fig. 6), which records the number of oscillations during this period, thereby integrating its total light dose. Each active-mode period, the microprocessor reads the counter value, resulting in a light sensor code, and resets the counter. The counter operates at a low supply voltage of 0.6 V, which reduces its power consumption by ~9× compared to a standard supply of 1.8 V. This allowed us to implement a 24 bit counter with negligible power consumption (5 nW or 2.2% of total average power). The resulting sensors continuously monitor the light level and record a light-dose code for every 10 min interval. The addition of the counter constitutes a relatively small change in the harvester circuit and allows light monitoring without additional chips or an increase in battery capacity or sensor size.Sensor testing and calibrationBecause the harvester oscillation frequency is dependent on temperature and battery voltage, these parameters are stored by the processor in SRAM along with the light sensor code. After data retrieval, the code is then converted to light intensity using a model that accounts for the temperature and battery voltage dependency. To construct this calibration model, four sensor nodes were measured at six light levels (0.5, 1, 5, 10, 50, and 100 klux) and four temperatures (25, 35, 45, and 55 °C), and four battery voltages (3.9, 4.0, 4.1, and 4.2 V); a total of 96 measurements were made for each sensor. After averaging the light sensor codes across the four sensors, a multidimensional, piecewise linear model was extracted to establish the relationship between the recorded digital code and the light intensity at a particular temperature and battery voltage (Supplementary Fig. 7). To calibrate the model for each fabricated sensor, we measured the light sensor code, temperature sensor code and battery voltage sensor code in controlled conditions (temperature: 25, 45, and 55 °C; light: 5 klux; battery voltage: 4.1 V) for each sensor. We then applied three-point calibration of the temperature sensor and one-point calibration of both the battery voltage and light sensors. The calibration conditions were selected based on the expected temperature and battery operating range in the field and on what the discriminating light intensity was expected to be. This was balanced with the time required to measure the 55 deployed systems in a controlled environment.To verify the accuracy of the light readings, eight randomly selected sensor systems were tested at three light levels (0.5, 5, and 50 klux) and three temperatures (25, 30, and 35 °C), a total of nine conditions each. These testing conditions were selected to match the conditions that sensors experienced during the field testing and are representative of the error in light readings for the collected data. Figure 4c shows the resulting measurements after calibration was applied. The x-axis is the reported light level, and the y-axis is the actual light level the sensor was exposed to. The worst-case variation in reported light measurement was sigma/mean = 28%, at 5 klux, showing acceptable stability.Nonlinearity was worse with a sensor light reading to actual controlled light intensity ratio ranging from −37 to +14%. However, because this is a comparative study of prey and predator species, and the same individual sensors were reused for both the prey and the predators, nonlinearity was judged to be less important than sensor-to-sensor variation and variation resulting from temperature change.We manufactured 201 smart solar sensor systems, most of which were used for bench top testing and green house testing at the University of Michigan using locally caught specimens of Cepaea nemoralis land snails (Supplementary Fig. 8). A total of 55 tested units were taken to Tahiti and were reused in multiple deployments while there. Our small batch production cost for these sensors was ~$500 US per unit (including wafer fabrication, wafer dicing, system assembly, encapsulation, and yield loss); however, for large volume ( >200 units) production, this was reduced to ~$150/unit.Field methodsTwo field populations of E. rosea and three of Partula hyalina located in five northern valleys of Tahiti-Nui, the main Tahitian peninsula, were investigated in August 2017 (Fig. 1a). These locations were selected by T. Coote, who had conducted extensive field surveys on Tahiti since 2004, as being the most accessible populations of both species then available.Although E. rosea remains widely distributed throughout Tahiti, it has become less numerous in many valleys in recent years, possibly because of the introduction of another snail predator, the New Guinea flatworm Platydemus manokwari12,35. Dead E. rosea shells were much more common than live specimens at our three Partula hyalina study locations, so we focused instead on the robust predator populations present in the nearby main Fautaua Valley and in its side-valley Fautaua-Iti. In both locations, we picked sites where foraging E. rosea had ready access to both shaded and open habitats. The Fautaua-Iti Valley location consisted of an open sunlit trail through the rainforest (Supplementary Fig. 1d), and the solar ecologies of nine predators were monitored here on two days: 5 on August 8 and 4 on August 11. The Fautaua Valley location consisted of a forest-edge adjoining an open grassy area (Supplementary Fig. 1e), and 29 predators were monitored here over two days: 12 on August 12 and 16 on August 14.All three of our Partula hyalina study sites (Fig. 1a) consisted of discrete patches of vegetation between the edge of the forest and the primary stream, or captage, within each valley. The Tahitian valley of Tipaerui encompasses a small side valley, Tipaerui-Iti, which contained the most robust known surviving population of P. hyalina on Tahiti, consisting of hundreds of individuals. They were restricted to a linear stand of Etlingera cevuga extending for 60–70 m (Supplementary Fig. 1a). The solar ecologies of 28 aestivating Tipaerui-Iti Partula hyalina individuals were recorded over two days: 12 on August 10 and 16 on August 15. Partula hyalina population sizes were much smaller in the other two valleys, Faarapa, and Matatia (Fig. 1a), requiring us to monitor all of the individuals we encountered. The Faarapa Valley site consisted of a mixed stand of Barringtonia asiatica, Alocasia macrorrhiza, and Pisona umbellifera (Supplementary Fig. 1b). We detected six individuals at this site, and their solar environments were monitored on August 5. Our remaining Partula hyalina study site was in Matatia Valley (Fig. 1a), where a small, low-density population occurred in scrubby habitat attached to the foliage of Z. officinale, Pisona umbellifera, and Inocarpus fagifer (Supplementary Fig. 1c). A total of seven individuals were detected and assayed on August 7.Each working day, we entered the study valley in the early morning between 8 and 9 a.m., prior to the appearance of the sun above the valley walls; and searched systematically for our respective target species. Euglandina rosea individuals were found foraging actively, either on the ground or climbing on vegetation, and they typically maintained this searching activity throughout the day. In contrast, Partula hyalina individuals were aestivating attached to the underside of leaves, and specimens typically remained in situ on the same leaf during the observation period.To track the solar ecology of each predator, a smart solar sensor was reversibly attached to the dorsal surface of each E. rosea shell using a nut and screw method. The nut (McMaster-Carr, Brass Hex Nut, narrow, 0–80 thread size) was glued (Loctite, Super Glue) directly on the predator’s shell, and after allowing 10 min for bonding, a sensor, preglued to a compatible screw (McMaster-Carr, 18–8 Stainless Steel Socket Head Screw 0–80 thread size, 1/16” long), was attached mechanically. Each predator was numerically labeled using nail polish and released at the exact spot it had been discovered. For the rest of the study period, each predator was visually tracked as it continued its foraging until mid-afternoon, when the sun descended below the valley walls, and the snails and sensors were recovered. These invasive predators were then euthanized.Aestivating Partula hyalina attach to the underside of leaves. Because our permit did not allow the direct attachment of light sensors to this endangered species, we deployed under-leaf sensors next to the aestivating snails using a nut/screw/magnets combination. This involved gluing, in advance, the screw to the sensor base and the nut to a round magnet (Radial Magnet Inc., Magnet Neodymium Iron Boron (NdFeB) N35, 4.78 mm diameter, 1.60 mm thickness). In the field, these components were assembled and held in place using another magnet positioned on the upper leaf surface. In addition to recording the under-leaf light intensities experienced by the aestivating Partula hyalina specimens, we also recorded the ambient light intensity by attaching a sensor to the upper surface of the leaves harboring the aestivating specimens.Each working day, the data recording function of the smart sensors was activated before going into the field and was terminated after returning from the field, and the data were then retrieved via the sensors’ wireless communication link. For each sensor, the recording start time, meaningful time of the measurement start time, meaningful measurement end time, and sensor recording end time were recorded to properly calibrate the time of the recorded samples. The received raw data in digital format were then translated to time and light intensity information using a MATLAB program and the calibration data specific for that sensor.Statistics and reproducibilityRecordings from each of the three categories (Partula hyalina leaf top, P. hyalina under leaf, and Euglandina rosea) over the 8 days of field recording were aggregated into their respective 10-min time intervals from 9:30 to 16:00 h. This recording time window avoided the early morning handling period when sensors were attached to the predator, spanned the midday period of peak solar irradiation (Figs. 2, 3), and enabled us to recover the visually tracked predators before losing them in the gathering darkness of the late afternoon valley forests. We collected light intensity measurements for 40 leaf top sensors, 41 under leaf P. hyalina, and 37 foraging E. rosea snails over the 9:30–16:00 h time period. Most aestivating P. hyalina (N = 26/41) had two under-leaf sensors bracketing the snails to record their immediate light environment (Fig. 1b) and for these individuals we used the mean light intensity of the two sensors to compare to the other two categories.We compared the three categories (leaf top, P. hyalina under leaf, and E. rosea) for the 40 timepoints over the 9:30–16:00 h time period using a repeated measures analysis of variance (ANOVA) in the nlme45 and car46 packages in R v.3.5.047. We first tested the light intensity measurements for conformance to a normal distribution using the R code shapiro.test, with the result being a highly skewed distribution. We thus LOG transformed the measurement data. We specified the following linear mixed model for the 9:30–16:00 time interval using the nlme package in R:$$begin{array}{c}lmeleft({mathrm{LOG}},{mathrm{fullmean}}sim {mathrm{group}}+{mathrm{time}}+{mathrm{group}}ast {mathrm{time}}right.\ left.{mathrm{random}}=;sim 1right|{mathrm{individual}},\ {mathrm{correlation}}=corAR1left({mathrm{from}}=;sim {mathrm{time}}left|{mathrm{individual}}right.right.\ left.{mathrm{method}}={^{primeprime}} {mathrm{{REML}}}{^{primeprime}} ,,{mathrm{na}}.,{mathrm{action}}={mathrm{na}}.{mathrm{exclude}}right)end{array}$$Where LOGfullmean = the LOG transformed light intensity readings, group = leaf top, P. hyalina under leaf, or E. rosea, time = the 40 10-min time intervals from the 9:30–16:00 time period. We considered each individual as a random block and included the correlation between time and individual. The repeated measures ANOVA utilized the restricted loglikelihood (REML) method and excluded any missing timepoint measurements (na.action = na.exclude) from the 9:30–16:00 h time period. After running the linear mixed model in R, we then used the Anova command from the R package car followed by a post-hoc Tukey’s test to determine which categories significantly differed in their light ecologies.Reporting summaryFurther information on research design is available in the Nature Research Reporting Summary linked to this article. More

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    Intrinsic ecological dynamics drive biodiversity turnover in model metacommunities

    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