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in EcologySelfishness driving reductive evolution shapes interdependent patterns in spatially structured microbial communities
The logic of the model
Our spatially-resolved model was simulated in discrete grid boxes of a 100 × 100 array, which included four basic assumptions: (1) Initial individuals were assumed to secrete three public goods but may randomly mutate to lose any of those functions with a certain probability; (2) Secreting a public good created a corresponding metabolic burden, therefore in losing a function the individual would gain a benefit; (3) All public goods were essential for growth. The net growth rates of individuals were dependent on the local concentrations of public goods; (4) Substrate and public goods diffused between two grid boxes at rates proportional to the concentration gradient.
For the 1st assumption, we included three functions because it is the minimal unit and tersest design to simulate complex communities, allows for the emergence of three categories of interaction patterns, and a single cooperative LOF genotype might evolve from differential evolutionary paths (Fig. 1A, B). The genotypes were described by bit strings containing 1 and 0 which indicated the genotype could produce the corresponding public good or not, respectively. Eight genotypes could emerge during the simulations, which were the initial autonomous producer [1, 1, 1], three one-function loss genotypes (OFLGs, i.e., [1, 1, 0], [1, 0, 1], and [0, 1, 1]), three two-function loss genotypes (TFLGs, i.e., [1, 0, 0], [0, 1, 0], and [0, 0, 1]), and a nonproducing cheater [0, 0, 0] (Fig. 1A).
Fig. 1: Logic of the individual-based model.A Possible genotypes and evolutionary relationships among them emerging from reductive evolution when starting with an autonomous genotype that performs three essential public functions. Note that in this three-function model, some genotypes, i.e., Two-function loss genotypes and cheaters, might evolve from different mother genotypes. B Interaction patterns that could possibly be established in the spatially structured communities. C Schematic of the individual-based simulations. A 100 × 100 array initialization with all autonomous phenotypic individuals (left) was conducted with a long-term stepwise iteration to investigate if diverse interaction patterns could form (right). At each time step, calculations were done from the level of individual grids (top) to whole lattice (bottom). Within each grid box, Monod equation modified by basic assumptions of the Black Queen Hypothesis was used to calculate the microbial growth, while minimum and maximum thresholds of biomass were defined to decide the division and death of individuals (top middle). Microbial individuals were allowed to randomly mutate to lose functions (top middle). Classical discretization of the diffusion equation gave local rules for updating the concentrations of public goods and nutrients in each box (middle). State changes at the individual level lead to the evolutionary dynamics of the communities, which may give rise to the formation of diverse interaction patterns (bottom).
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The 2nd and 3rd assumptions were developed from the basic mathematical assumption of the BQH [19], and defined individual growth by integrating the benefit and cost of function loss (Fig. 1C). To conceptualize the cost of performing a function, we supposed a parameter (α) which is the fraction of biomass used to produce a public good per unit time of an individual. In addition, we defined a second parameter (β) as the ratio of the amount of public goods required during each step to account for the produced public goods. Therefore the redundant fraction of public goods production was 1−βj, and lower βj reflected a higher amount of redundant public goods that could be gained from the producers by the LOF genotypes, resulting in decreased risk in association with function loss (see Supporting Information S1 for more details). During the model simulation, spatiotemporal dynamic variables, i.e., positioning of genotypes and the time points at which genotypes evolved, would be collected. We initiated the simulations by randomly distributing 100 ancestor cells [1, 1, 1] into the grid boxes and iterated for at least 1,500,000 time steps. During each time step, individuals grew, decayed, reproduced, and mutated according to the previously mentioned assumptions (Fig. 1C). We paid attention to whether stable communities with various interdependent patterns could be formed after a specified number of iterations, as well as recorded the spatiotemporal dynamics of the communities.
Diverse interdependent patterns emerged with high level of function cost and varied level of functional redundancy
For model simulations, the function cost (parameter α) and functional redundancy (parameter β) were assigned to 0.0001, 0.0005, 0.001, and 0.4, 0.6, 0.8, respectively. A total of 2891 independent simulations with 9 parameter sets displayed different community structures (Fig. 2A). When the function cost was assigned to a low level, i.e., 0.0001, the autonomous ancestor dominated the community. When function costs were assigned to higher levels, 0.0005 and 0.001, new genotypes evolved and later interacted to form three distinct types of interdependent patterns even within the same α and β combination, i.e., asymmetric functional complementation (AFC), complete functional division pattern, and one-way dependency, with the relative amounts of 1677/2891, 143/2891, and 48/2891, respectively. In addition, higher functional redundancies favored the loss of more functions, increasing complexity of the community structures.
Fig. 2: Reductive evolution shapes diverse interdependent patterns in microbial communities.A The final (steady state) community structures across gradients of function cost (α) and functional redundancy (1-β). Results were summarized from at least 300 interdependent runs for each parameter set. Community structures were assessed after simulation for 170,000 iterations, where 98.9% (2891/2923) of runs reached steady state. According to the structures, replicates were clustered into several scenarios for each parameter set, which are shown separately in the area plots. Note that the values of β is the proportion of public goods that is required for growth, and thus 1-β reflects the level of function redundancy. B, C Six representative community dynamics on the spatial lattices were selected from one interdependent simulation with the given conditions (mut = 10−5, α = 0.001, β = 0.8), showing the evolution of three types of asymmetric functional complementary pairs (AFCPs) (B), three different paths for the evolution of pairs [0, 0, 1] & [1, 1, 0] (C). Left images indicate the distribution of different genotypes at different points in evolutionary time. Curve plot in the middle describes the community dynamics of the corresponding simulation. Schematics at right briefly summarize the spatiotemporal dynamics of each simulation: the arrays in (B) indicate one type of AFCP directly dominated the communities without competition from others; the boxes in (C) indicates the composition of ancestor or AFCP in the related time points, while the windows inside indicate the spatial coexistence of multiple AFCPs and the size of the windows represents the relative fraction of different AFCPs.
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Among the three possible kinds of interactions, the AFC pattern was the most widespread, which was the combination of a two-function-loss genotype (TFLG) and its complementary one-function-loss genotype (OFLG). For example, [0, 0, 1], which produced a single essential public good, depended on its functional complement one-function-loss partner [1, 1, 0], for the other two public goods. Specifically, three types of the asymmetric functional complementary pairs (AFCPs), that is, [0, 0, 1] coupled with [1, 1, 0], [0, 1, 0] coupled with [1, 0, 1], and [1, 0, 0] coupled with [0, 1, 1], colonized most of the grid with a similar frequency of emergence. Interestingly, under the condition of high level of cost, the emergence of AFC patterns was accompanied by some nonproducing cheaters, whose relative abundance rose with the increase in functional redundancy (Fig. 2A top row). The addition of cheaters significantly reduced the total biomass of the communities, suggesting that high functional redundancy favors the evolution of cheaters which may decrease the community productivity. In addition, function loss happened more easily with high function cost. As the function cost parameter α increased from 0.0005 to 0.001, relative abundance of TFLGs increased approximately from 55 to 70% (Fig. 2A).
Besides the AFC patterns, two additional types of interdependent patterns evolved at a relatively lower frequency. The complete functional division pattern, that is, coexistence of [0, 0, 1], [0, 1, 0], and [1, 0, 0], only evolved when both factors were at high levels (α = 0.001, β = 0.4) with a frequency of approximately 45% (143 of 319 simulations, Fig. 2A, top right), which described a scenario with high benefit and low cost of function loss, favoring the loss of more functions and consequently more likely to maintain the evolution of TFLPs. Another form of interactions that emerged was one-way dependency, where one partner performs all functions and other none (i.e., coexistence of [1, 1, 1] and [0, 0, 0]). This form emerged at a low frequency (48 out of all 2891 simulations shown in Fig. 2A), but evolved with a higher probability under the condition of a mid-level function cost and low level of functional redundancy (α = 0.0005, β = 0.6, Fig. 2A, middle left), where the extinction of [1, 1, 1] was ~2.5 times slower than in other scenarios (Supplementary Fig. 1), leading to a higher potential for the spatial proximity between [1, 1, 1] and [0, 0, 0] during evolution.
Taken together, these phenomena demonstrated that the mutualistic exchange of complementary functions happened only when function cost was high. The emergence of different interdependent interaction patterns was related to the function cost and function redundancy, especially for the complete functional division and one-way dependency pattern, which only emerged within a limited parameter range. However, even for a given combination of α and β, it still remained possible for the evolution of distinct interaction patterns, suggesting that stochastic processes may play a role.
Same interdependent patterns might evolve via different modes
Because the evolution of three kinds of AFCPs were the most common scenarios in our simulations, we then focused on the role of stochastic processes, i.e., the key random events, in deciding the winning complementary pair among the three similar but different AFCPs. As a first step, we traced the variation in the spatiotemporal dynamics, trying to cluster the numerous evolutionary dynamics into limited modes and divide the complex evolutionary courses into several stages. These simplifications would facilitate the search for key random events.
Therefore, we analyzed the dynamics of 296 simulations with a typical parameter set (α = 0.001, β = 0.8), because under this condition, only the three types of AFCPs evolved, with a similar frequency of emergence (Fig. 2A, Top left), in order to avoid interference from the other interaction patterns. As described above, any of the three types of AFCPs could potentially take over the final community under this condition (Fig. 2B; Supplementary video 1–3). Using the emergence of AFCP [0, 0, 1] & [1, 1, 0] as an example, three categories of dynamic modes could give rise to its final domination. (1) After pair [0, 0, 1] & [1, 1, 0] emerged and formed a spatial aggregation, it rapidly expanded and took over the entire grid (Fig. 2C, first line; Supplementary video 3). (2) In addition to the pair [0, 0, 1] & [1, 1, 0], spatial aggregations of another AFCP also emerged (e.g., pair [0, 1, 0] & [1, 0, 1] in Fig. 2C, second line and Supplementary video 4). In this scenario, a special spatial pattern was established in a short period after the evolution of both AFCPs e, where pairs of two complementary members exhibited strong spatial mixing, while the two different AFCPs were totally segregated. Community succession was then governed by spatial competition between the two AFCPs. If pair [0, 0, 1] & [1, 1, 0] won the competition, it would dominate the final community. (3) Spatial aggregations of all three AFCPs emerged, and then pair [0, 0, 1] & [1, 1, 0] dominated the community after outcompeting the other two AFCPs (Fig. 2C, third line; Supplementary video 5). The clustering of these three possible modes of AFC patterns was also shown by the temporal dynamics of the α-diversity across different parameter sets (Supplementary Fig. 2), where the evolution modes of the AFC patterns were clearly clustered into three possible categories, suggesting that this clustering is independent of the determined factors α and β.
In sum, the succession of interdependent patterns could be divided into two stages: (1) the emergence of spatial aggregations composed of two interdependent members with strong connections; (2) spatial competition among different aggregations drive the community to evolve to the final state, composed of only one type of interdependent interactions. Of course, if only one type of AFCP emerged, the spatial competition stage would be unnecessary during succession.
Evolutionary random events play important roles in deciding the dominant AFCP in equilibrium communities
The presence of two evolutionary stages lead us to hypothesize that the random events affecting ecological outcomes should arise from two aspects. First, in the initial evolutionary stage, the emergence of interdependent spatial aggregations should be related to the order in which new genotypes emerge. Second, the outcome of the spatial competition should be also influenced by the initial positioning of the new genotypes.
The fact that each TFLP had two possible evolutionary paths (e.g., [1, 0, 0] could inherit its function from [1, 1, 0] or [1, 0, 1]), suggested that the effects of the random order of emergence for different genotypes were highly correlated with the evolutionary lineage. Therefore, to investigate the effects of this, we analyzed the evolutionary lineage of emergence, colonization, and loss of every genotype within the 296 simulations with the typical parameter set (α = 0.001, β = 0.8). In total, there were 24 evolutionary branches leading to the evolution of the three forms of AFC patterns (8 for each, Fig. 3). Among all these branches, we summarized two key random events (Fig. 3, red and blue boxes).
Fig. 3: The evolutionary trajectories of 296 independent simulations with the typical parameter set (mut = 10−5, α = 0.001, β = 0.8).We analyzed the evolutionary trajectories of every interdependent run and clustered them into 24 types of branches (top, see Methods). The area plot shows the final community structures and the frequencies of each branch (bottom). Blue dashed box shows the evolutionary diversification into four scenarios after the first key event occurs, while the red dashed box indicates the 24 different evolutionary trajectories that diverged after the second key event occurs. Solid boxes with colored circles represent the genotypic composition of communities at different evolutionary time points. Red arrows indicate the branches where one type of asymmetric functional complementary pair (AFCP) directly dominated the communities without competition with other AFCPs, while the blue arrows indicate the branches where one type of AFCP took over the entire space after competitions with other AFCPs. Dashed boxes at the figure labels (right) indicate different AFCPs.
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The first event occurred after two types of OFLGs emerged. After this evolutionary time point, all three public functions were included in OFLGs. With the benefit of the function loss, these two OFLGs would expand and gradually outcompete the autonomous genotype [1, 1, 1]. Thus, the first key event was whether all three OFLGs could emerge before the autonomous genotype entirely disappeared (Fig. 3, blue box). If not, the third type of AFCP would never evolve; if so, all three types of AFCPs would still have a chance to dominate the final community. In the 296 simulations, the frequencies of these two scenarios were nearly same, that is, 147 simulations were clustered to the former, while 149 simulations were clustered to the latter. The 147 simulations, where the third type of AFCP never evolved, could be then divided into three categories with similar frequencies, where two of the three OFLGs occupied the whole space and excluded the ancestral population.
The second key evolutionary event was the emergence of TFLGs (Fig. 3, red box). After the two or three types of OFLGs successfully colonized, whose functional complementary TFLGs first to emerge in the next evolutionary time would lead to the prior formation of the spatial aggregation of the AFCP. It is obvious that if no other AFCP aggregations formed later, this AFCP would dominate the final community (Fig. 3, red arrow indicated branches). Alternatively, if other AFCP aggregations formed during the expansion process, the spatial competition between different AFCPs would decide the dominant AFCP in the equilibrium communities (Fig. 3, blue arrow indicated branches). In our analysis, the chance of only one AFCP evolving reached 64.7% (198 of the 296 simulations). If only two OFLGs evolved after the first event, the frequency of only one AFCP evolving reached 79.6% (121 of the 152 simulations). In contrast, if three OFLGs evolved after the first event, there could be a relative higher possibility of two or three AFCPs evolving (47.4%), meaning that spatial competition could then be an important process.
What decided the winner of the competition? We observed that after the segregated interdependent spatial pattern was newly established, the relative region sizes occupied by different AFCPs were the key to determining the winner (Fig. 2C, the second and third lines; Supplementary video 4 and 5). We analyzed the time gaps between the emergence of the two AFCPs in the second categories of succession modes and the size of the regions they occupied (Fig. 4A). The result indicated a significantly positive correlation between the length of the time gaps and the region size the prior AFCP occupied (t-test, p 1 indicates pair [0, 0, 1] & [1, 1, 0] is more spatially associated than pair [0, 1, 0] & [1, 0, 1]. Applying these definitions, the simulation results where the advantage of prior space occupancy was not significant (left side of blue line in Fig. 4C, 33 replicates) were selected for analysis, and we found a significantly positive correlation between the relative PAD at the beginning of spatial self-organization and the ‘region size advantage’ (Fig. 5A; p 1 means the prior emerged AFCPs are more spatially associated than the second AFCPs. Red dots indicate the first to emerge AFCP won the competition in the corresponding replicate, while the green dots indicate the second to emerge AFCP won the competition. B Two typical examples of simulations initialized with premixing the two types of AFCPs, [0, 0, 1] & [1, 1, 0] and [0, 1, 0] & [1, 0, 1], which represent scenarios when initial PAI001:010 1, respectively. C The significant positive correlation between the winning frequency of pair [0, 0, 1] & [1, 1, 0] and the initial value of PAI001:010. When initial PAI001:010 > 1, final communities were more likely to be dominated by pair [0, 0, 1] & [1, 1, 0], oppositely, pair [0, 1, 0] & [1, 0, 1] were more favorable when PAI001:010 More213 Shares109 Views
in EcologyDistinct ecotypes within a natural haloarchaeal population enable adaptation to changing environmental conditions without causing population sweeps
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in EcologyEcological responses to flow variation inform river dolphin conservation
Study area
This project was conducted in the downstream segment of the Karnali River basin of Nepal (Fig. 1), which is the largest of Nepal’s three major river systems and is characterized by the steep terrain of the Himalayan Mountains. The highest runoff occurs during the monsoon season (e.g., June–October), and the lowest occurs during the winter season (e.g., December–May). Below the Siwalik Mountain range (a physiographic zone, Fig. 1), a vast network of small tributaries combines to form a single narrow channel of the Karnali River with well-defined banks. Originating from the Tibetan Plateau, the Karnali River is the largest tributary to the Ganges River in India, which harbours the most significant density of GRDs in the world. The lower Karnali River basin provides the furthest upstream range for GRDs, critically endangered gharials (Gavialis gangeticus), smooth Indian otters (Lutrogale perspicillata), and 36 native fish species49. The GRD population size in the Karnali River has declined from 26 to six individuals50. Such a sharp decline in the GRD population is due to the effects of habitat degradation, mainly from water-based development projects (i.e., water diversion,51). Concurrently, several upstream development projects are proposed, under construction, or completed [e.g., planned: the Karnali Chisapani multipurpose dam, 10,800 megawatt (MW); under construction: the upper Karnali hydropower project, 900 MW, and Bhari Babai diversion project; completed: Rani Jamara Kulariya irrigation intakes] and further threaten downstream aquatic life. All projects adopt traditional preconstruction environmental impact assessments procedure to define flow proportions (generally 10–20% of natural regimes) anecdotally and unscientifically. Thus, traditional flow proportions might be inadequate to sustain native aquatic biodiversity. Our study focused on the lower catchment area of the Karnali River basin, which is downstream from all megaprojects. All measurement protocols, including dolphin observation methods, were carried out in accordance with the Department of National Parks and Wildlife Conservation, Government of Nepal, guidelines and regulations. Habitat measurement protocols, including dolphin observation methods, were approved by the Department of National Parks and Wildlife Conservation, Government of Nepal (No 1129; 12 December 2016).
Available habitat assessment
Reduced water levels during the low-water season (e.g., December–May) escalate threats to aquatic biota by limiting physical habitat availability. Here, habitat refers to the hydro-physical habitat, which is defined by the flow and depth interactions at a particular geomorphic condition over space and time. Therefore, habitat availability (i.e. the area accessible to species) is assumed to be the greatest bottleneck, critically limiting species reproduction and survival42,51. We measured the available habitats in the low-water season when suitable habitat is critically limited (i.e., December–May in 2018/2019), excluding the monsoon season (June–November). Further, to capture dynamic flow variation within the dry (i.e., low) water season, we selected three temporal periods—March (mid dry season), May (late dry season), and December (early dry season)—based on 39 years of flow records available from the Department of Hydrology, Government of Nepal. Assessing available habitat includes habitat mapping and bank and instream surveys. We divided the study area into three segments [upper segment (S1): length = 11 km, average width = 218 m; middle segment (S2): length = 29 km, average width = 121 m; and lower segment (S3): length = 10 km, average width = 198 m; Fig. 1] based on uniform flow and channel geomorphology mapped along the selected stretch of the river. The three segments vary hydrologically and structurally. S1 consists of river channels with natural flows without any infrastructural diversion. Because of water diversion operations (e.g., Rani Jamuna irrigation intake and several traditional agricultural irrigation channels) and distributaries, the natural flow volume in S2 was low compared to that in S1. S3 benefited slightly from distributaries and received more water than S2.
Within each segment, the study reach (the linear segment where cross-sections are established) was established in such a way that the length of each reach was at least higher than the mean width (so the number varies among segments) of the respective segment. We also tried to maintain relatively similar flow at the top and bottom of the reach. Within each reach, random cross-sections were established to capture the hydraulic properties based on flow variation. As the flow variability of the stream increased, the number of cross-sections increased, and each section was kept at least 300 m apart from the other sections. Therefore, the number of cross-sections was based on the flow variation within a reach instead of the length of the reach. Bank and instream surveys started in an upstream direction, wherein directional readings of the cross-sections were noted. For the bank and instream measurements, pin heights were established at either side of the cross-section using GPS and a permanent reference marker for repeated flow measurements. Water surface elevations were estimated using a total station (an optical instrument for land surveying; Leica 772737 Builder 503) across the pin heights for each cross-section required for hydrological simulation. A new benchmark was established for each effort to measure the water surface elevation at each cross-section. The total number of cross-sections examined for the available habitats was 177 (March = 60, May = 47, and December = 60). The hydraulic parameters (see habitat characterization section below) at each cross-section were measured using a RiverSurveyor S5 acoustic water current profile reader [Sontek, Acoustic Doppler Profiler (ADP S5)], which records hydro-parameters continuously at a cell size between 0.02 to 0.5 m offering complete underwater available hydro-physical profile.
Occupied habitat assessment
We conducted a GRD population survey to capture occupied (selectivity) habitat characteristics (n = 97) at three temporal scales (previously mentioned) using the developed approach24. Within each temporal scale, we conducted three replications to capture the temporal and spatial variability in the characteristics of the occupied habitat. When we first detected dolphins, we observed surfacing behaviours for at least five minutes before establishing a cross-section. The habitats that were used for at least five minutes were considered occupied habitats, and then cross-sections were established to measure habitat characteristics using the ADP. If the dolphins disappeared after the location of the first sighting in less than five minutes, we excluded those habitats from our analysis. The Dolphin observation (only observation done) protocols were approved and permitted by the Department of National Parks and Wildlife Conservation, Government of Nepal.
Data analysis
Data preparation and software
The ADP S5 hydraulic data were imported into Excel databases (Microsoft v. 2010) to format for System for Environmental Flow Analysis (SEFA, version 1.5; Aquatic Habitat Analysts Inc.) software. All the hydraulic properties [depth (m), velocity (m/s), wetted perimeter-WP (m), width (m), cross-sectional area-CSA (m2), Froude number, and discharge (m3/s)], suitability, and flow regime determination were calculated using SEFA software and analysed at the cross-section and segment levels. The average flow of each segment was used as a base flow while running the habitat simulation model for the respective segment. We found critical flows ( 417 m3/s, excess flow with a negative contribution to habitat suitability) in May. Therefore, the habitat retention hydraulic simulation model was performed only with excess flow (for May) using 39 years of 90% exceedance flow (the flow that is equaled or exceeded 90% of the time).
Habitat characterization
The cross-sectional hydro-physical parameters—width, flow, depth, velocity, wetted perimeter, cross-sectional area, and habitat (types)—were reported spatially and temporally. The habitat type (e.g., pool, run, and riffle) was classified based on the Froude number (Fr), where Froude is an index of hydraulic turbulence (the ratio of velocity by the acceleration of gravity). Points with Froude numbers exceeding 0.41 were considered riffles, points with Froude numbers less than 0.18 were considered pools, and intermediate values were classified as run habitats. The proportion of run, riffle, and pool habitats within each study reach was calculated from the Froude numbers. The GRD’s seasonal hydro-physical habitats were characterized using basic descriptive statistics (mean and 95% CI). The variation in these hydraulic parameters among seasons, habitat types, and segments was examined by an analysis of variance (ANOVA), and post hoc pairwise comparisons were performed using Tukey’s honestly significant difference (HSD) test. A two-way ANOVA test was used to investigate any interactive effects of season and habitat on hydraulic variations. The level of significance was set at p one and zero to those categories for which w ≤ one. By assigning one and zero to each group, we developed an HSC to calculate the area weighted suitability (AWS) at each measured point. Hydraulic habitat suitability is expressed as AWS in terms of usable area in metres of width or square metres per metre of reach (m2/m).
To obtain the AWS value for the reach, we multiplied the combined suitability index (CSI, which is the product of the suitability of depth and velocity at a point) and the proportion of the reach area represented by that point. Using a 39-year average base flow of 536.11 m3/s (90% exceedance flow) in May, we predicted the fluctuation (decrease by 10%) in the currently available maximum AWS (i.e., 22.718 m2/m, AWS of May) in the range of flows from 200–900 m3/s. We simulated the AWS in this particular range because this range represents the 39-year low and maximum values of the 90% exceedance flow for the low-water season (November–May). Covering this variation over a broader scale increases the applicability of our ecological thresholds across time. Using the same base flow and range, we also estimated the minimum flows that retain various standards (%) of habitat protection. Further, we also determined the minimum flow that provides the maximum AWS for the low-water season.
Ecological thresholds using flow-ecology relationships
As water depth and velocity are the result of instream habitat features, such as pools, riffles, and runs, we only incorporated depth and velocity when estimating the hydraulic habitat suitability. Additionally, GRD habitat selection is strongly guided by the depth and velocity of a river section24,51. Generalized linear models (GLMs) using logit functions were used to examine the relationship between GRD presence and hydraulic properties (depth and velocity). Four different GLMs (depth, velocity, depth*velocity, and depth + velocity) were developed, and the Akaike information criterion (AIC) was used to select the best models. The additive effect of depth and velocity on the GRD presence was found in the model with the best performance; therefore, we further used a generalized additive model (GAM) to capture the possible non-linear influence of depth and velocity on GRD presence. Because of the possibility of both linear and non-linear relationships11, we again used a GAM to capture the functional relationships between ecology (AWS) and flow. The degree of smoothness for all the GAMs identified by the iterative approach (up to 25 smoothing factors were checked) and the selected smoothing parameter (i.e., 20 for all the GAM models) that yielded a significant covariate (at the 0.005 level of significance) explained the maximum deviance and adjusted R2. Both the GLM and GAM models were fitted using the lm and mgcv packages in R Studio. More188 Shares109 Views
in EcologySkin microbiome correlates with bioclimate and Batrachochytrium dendrobatidis infection intensity in Brazil’s Atlantic Forest treefrogs
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