Colonization and extinction rates estimated from temporal dynamics of ecological communities: The island r package

Abstract

en

1. The temporal dynamics of ecological communities are inherently complex, as dispersal processes, interspecific biotic interactions and environmental fluctuations interact to shape species assemblages. We developed an r package, island—a community ecology tool to analyse temporal patterns and explore potential drivers of community dynamics.
2. The r package island is inspired by the simplicity of the Theory of Island Biogeography. Our package includes a suite of functions to easily confront models of increasing complexity to community data from the simplest stochastic model underlying Island Biogeography Theory to more elaborate models that include species responses to environmental variables and imperfect detectability, obtained at regular or irregular sampling times, using maximum‐likelihood and AIC‐based model selection.
3. Models implemented in island should be regarded as simple approximations of true temporal community dynamics. In this sense, we call them effective models which we use to estimate effective parameters. These models are simple, but dynamic, as opposed to purely statistical. We illustrate the concept of dynamic effective models by using an immigration–birth–death stochastic model of population dynamics. We generated simulated community data to demonstrate the correspondence between the underlying true model parameters values and our effective parameter estimates.
4. We present three examples showcasing the uses of our package: detectability estimation and model selection, influence of environmental covariates on community dynamics and estimation of co‐occurrence networks. Three detailed vignettes with a full set of examples accompany the r Package island available on CRAN.

Foreign Language Abstract Resumen

es

1. La din′amica temporal de las comunidades ecol′ogicas es intr′ınsecamente compleja, ya que procesos como la dispersi′on, interacciones entre especies y fluctuaciones ambientales interactu′an determinando su composici′on. Hemos desarrollado el paquete de R island, una herramienta de ecolog′ıa de comunidades para analizar patrones temporales y estudiar los mecanismos que determinan la din′amica de las comunidades.
2. El paquete island est′a inspirado en la simplicidad de la Teor′ıa de Biogeograf′ıa de Islas. Nuestro paquete contiene funciones que, con datos temporales de comunidad, permiten evaluar f′acilmente modelos de complejidad creciente desde el modelo estoc′astico m′as sencillo de la Teor′ıa de Biogeograf′ıa de Islas hasta modelos m′as elaborados que incluyen respuestas de las especies al ambiente o detectabilidad imperfecta, obtenidos mediante esquemas de muestreo regulares o irregulares, utilizando m′axima verosimilitud y selecci′on de modelos basada en AIC.
3. Los modelos implementados en island deben ser considerados como aproximaciones sencillas a la din′amica temporal real de la comunidad. En este sentido, los denominamos modelos efectivos que utilizamos para estimar par′ametros efectivos. Estos modelos son sencillos, pero din′amicos, en oposici′on a modelos puramente estad′ısticos. Hemos ilustrado el concepto de modelos efectivos din′amicos utilizando un modelo estoc′astico de din′amica poblacional basado en los procesos de inmigraci′on, nacimiento y muerte, mediante el que generamos datos de comunidad simulados para demostrar la correspondencia entre los par′ametros reales subyacentes y nuestras estimas efectivas.
4. Presentamos tres ejemplos mostrando los usos del paquete: estimas de detectabilidad y selecci′on de modelos, influencia del ambiente en la din′amica de la comunidad e identificaci′on de redes de coocurrencia. El paquete island, disponible en CRAN, est′a acompan˜ado con un muestrario de ejemplos en tres detalladas vin˜etas.

1 INTRODUCTION

The dynamics of community assembly play out over ecological time‐scales. Its central unresolved problems require datasets that span these temporal scales. Long‐term data hold the key to unravelling the respective roles that ecological interactions and environmental factors play in community assembly over space and time. Our understanding of how species diversity and community structure change with time has been influenced by opposing theories emphasizing either dispersal and individual species adaptations to local environments (Gleason, 1926) or biotic interactions (Clements, 1916). Earlier approaches in studying the relative importance of community assembly drivers have largely been based on randomization procedures of species within the assembly (package stepcam, van der Plas et al. (2015), Chase, Kraft, Smith, Vellend, and Inouye (2011)). Related approaches use several community‐level patterns, such as the species–abundance distribution and the aggregation of conspecific individuals, to constrain community assembly, and study the behaviour of different biodiversity metrics across scales (package mobsim, May, Gerstner, McGlinn, Xiao, and Chase (2018)). Although these approaches are useful for some purposes, we need models incorporating assumptions at the individual and/or species level since community‐level patterns truly emerge from bottom‐up ecological processes affecting the fate of individuals and species (Allouche & Kadmon, 2009; Hortal, Triantis, Meiri, Thébault, & Sfenthourakis, 2009; Hubbell, 2001; May, Huth, & Wiegand, 2015; Vellend, 2015). The range of possible mechanistic simulation models for community dynamics is infinite (Cabral, Valente, & Hartig, 2017; Hortal, De Marco Jr, Santos, & Diniz‐Filho, 2012), and such models are usually difficult to decipher (May et al., 2015), often clouding rather than enlightening our understanding of community assembly processes. It is our contention that there is still considerable power in the dynamic simplicity of Island Biogeography Theory (MacArthur & Wilson, 1963, 1967) that is yet unexplored and largely overlooked. Here, we work with the stochastic model underlying this theory and develop a dynamic framework to analyse the relative importance of competing processes in structuring real‐world communities.

The ultimate test of ecological theory lies in confronting it with real‐world data over ecologically relevant time‐scales to see if its basic assumptions still hold. Ecological monitoring programmes are only now beginning to generate rich long temporal datasets (Hortal et al., 2015), for a variety of taxa around the world (see, for instance, Condit (1998) and Hubbell, Condit, and Foster (2005)), and developing robust methods to deal with their complexities is often a challenge. For many systems, the speed of data accumulation far outstrips our ability to explore and generate new conceptual ideas emerging from these data (Barberán, 2014). This is perhaps unsurprising given the lack of common conceptual frameworks providing simple effective models to confront new theoretical ideas with community data.

We present an r package, island, that helps analyse temporal patterns in community assembly. Inspired by Island Biogeography Theory (IBT), we focus on estimating colonization and extinction rates from species presence data over time and space. Functions in island implement a number of methods to characterize communities and guilds within communities, and test conceptual ideas of the drivers of community assembly through AIC‐based model selection. While other r packages exist that are geared to estimate colonization and extinction dynamics, such as r package unmarked (function colext()), they typically focus on single populations in space and time rather than a community‐level approach. In addition, using existing packages for sparse data or irregular sampling schemes is not straightforward. Although recent community‐level approaches that expand IBT to include biological interactions are of great value (Cazelles, Mouquet, Mouillot, & Gravel, 2016b; Gravel, Massol, Canard, Mouillot, & Mouquet, 2011), they do not provide robust maximum‐likelihood methods for the analysis of community time‐series data. Instead, they are centred on the distribution of species presences at stationarity, under different interaction structures, across scales, and over environmental gradients (Cazelles et al., 2016b).

A detailed description of the theoretical underpinnings of the package is provided in the Supplementary Material S0. Our basic model is the simplest stochastic formulation of the theory of island biogeography (Alonso, Pinyol‐Gallemí, Alcoverro, & Arthur, 2015). Since temporal dynamics of real‐world communities are influenced by an entangled web of factors, we emphasize that the colonization–extinction models of r package island should only be regarded as a simple way to effectively approximate community dynamics under certain assumptions. Colonization and extinction pairs (c, e) represent effective parameters characterizing communities as if population changes were driven by independent species dynamics. These parameters should be regarded as coarse‐grained approximations of the intrinsic, species‐specific parameters driving population processes and species interactions. In Box 1, we illustrate the correspondence between effective (c, e) rates and the underlying parameters driving community dynamics. Species population dynamics can be modelled as a stochastic process driven by elemental events such as immigration of new species to local communities, local births and deaths, and interactions between individuals of the same or different species (Capitán, Cuenda, & Alonso, 2015; Capitán, Cuenda, & Alonso, 2017; Haegeman & Loreau, 2011; Solé, Alonso, & McKane, 2002; Vellend, 2010, 2015). In Box 1, abundances were generated from a species immigration–birth–death (IBD) model (Haegeman & Loreau, 2011), and then transformed into presence–absence data in order to estimate colonization–extinction probabilities. Other stochastic community models can be also used (for detailed information see help (“ibd_models”) and vignette (“IBDmodels”)).

Box 1. The colonization–extinction model and community dynamics

Here we generated synthetic, simulated communities using an IBD stochastic model (Haegeman & Loreau, 2011). Births occur with probability r⁺ a_i per unit time (a_i is the i‐th species abundance), and immigrations at rate μ. Species abundances decrease at rate r⁻ a_i (intrinsic mortality) or (intraspecific competition), where K represents a carrying capacity, and r = |r⁺−r⁻|. These assumptions result in a deterministic logistic population model with immigration (da_i/dt = ra_i (1−a_i/K) + μ for i = 1, 2,…, S). In Figure B1, we show the correspondence between the population carrying capacity, K, and the colonization probability, T₁₀, and the extinction probability, T₀₁ (see Eq. S0–6), in panel a and b respectively. In panels c and d, we show how an empirically derived functional dependence between colonization and extinction probabilities, estimated from community time‐series data, would constrain the scaled rates of the IBD that are compatible with it. Simulation averages over 3,000 stochastic replicates of the IBD community model yield two probability surfaces, T₀₁ (μ/r^+, r⁻/r⁺⁾ and T₁₀ (μ/r^+, r⁻/r⁺⁾, as functions of scaled immigration and mortality rates (c). The intersection T₀₁ = f (T₁₀) provided an estimation of the region in parameter space where the intrinsic IBD species rates are compatible with the observed, macroscopic rates (d).

Figure B1

All curves in panel a are shown for the same scaled mortality (r⁻/r⁺ = 0.8), while all curves in panel b share the same value for the scaled immigration (μ/r⁺ = 0.5). In all cases, simulation was done for S = 20 species. The assumed functional dependence between colonization and extinction probabilities is T₀₁ = f (T₁₀) = 0.6−0.5T₁₀ (panels c and d).

Without exhausting the numerous possibilities of the package (Table 1 summarizes its functions and vignettes), we discuss three worked examples showcasing the capabilities of island. In the first, we explore how imperfect detectability influences model parameter estimates, and show how our package functions identify species groups or guilds and help investigate the extent to which species ecological equivalence underlies temporal community dynamics (Alonso et al., 2015). We then extend the basic model to analyse the influence of environmental variability on community dynamics. Finally, we show how functions in island can help unveil the potential interaction structure of species assemblages using a novel way of assigning significance to empirical species co‐occurrences.

Table 1. Vignettes and main functions of r package island

Main functions	Description
regular_sampling_scheme()	Estimates colonization and extinction rates under regular (temporally equispaced) sampling schemes
irregular_single_dataset()	Estimates colonization and extinction rates under irregular
irregular_multiple_datasets()	sampling schemes for single or multiple datasets
sss_cepd(), mss_cepd()	Estimates colonization and extinction rates, as well as detectability and initial occupancy probabilities, with data in single or multiple replicated datasets
upgma_model_selection()	Conducts a model selection procedure that searches for an optimal partition of the data (based on a categorical variable) for its colonization and extinction parameters (or, alternatively, for detectability and initial occupancy)
greedy_environmental_fit()	Estimates the best model for colonization and extinction rates and their dependency on environmental variables using a greedy algorithm that sequentially adds the variables with most influence in the data
cetotrans()	Transforms colonization and extinction rates to transition probabilities after a specified interval of time
PA_simulation(), data_generation() r_squared(), simulated_model()	Simulates species richness dynamics or presence–absence matrices according to specified transition probabilities. Returns the value of R^2 or the average squared error of the predictions of model simulations
ibd_models()	Simulates stochastic population dynamics under immigration, birth and death processes under three different models (Alonso & McKane, 2002; Haegeman & Loreau, 2011; Kendall, 1948)

Vignette	Description
vignette(“island”)	Introduces the main concepts applied in the package, details data preparation, and illustrates the use of the functions that estimate colonization and extinction rates, as well as the influence of environmental variables, and simulation of the associated dynamics
vignette(“detectability”)	Explains how colonization and extinction rates are estimated under imperfect detectability, and details data entry and use of functions under this scenario. Also explains model selection to detect groups of species of equivalent colonization–extinction dynamics
vignette(“IBDmodels”)	Shows the correspondence between parameters driving deaths, births and immigrations at the individual level and colonization–extinction rates at the population level

2 DETECTABILITY AND MODEL SELECTION

When working with presence datasets, we often make the simplifying assumption of perfect detectability, assuming that sufficient replication at the site level accounts for genuine absences. In reality, it is difficult to discard interspecies differences in detectability, which could have profound consequences when interpreting assemblage patterns. MacKenzie developed a likelihood approach for parameter estimation when species detectability is not perfect. Mackenzie's seminal idea can be used to obtain better estimates of site occupancies (MacKenzie et al., 2002) as well as non‐biased estimates of colonization–extinction model parameters (MacKenzie, Nichols, Hines, Knutson, & Franklin, 2003). Package island provides a new implementation of MacKenzie's likelihood for uneven time intervals and sparse sampling schemes.

Figure 1 shows parameter estimation, using function regular_sampling_scheme, compared to estimates obtained with imperfect detectability (function sss_cedp). We generated a set of data matrices based on stochastic iterations of a colonization–extinction model, whose parameters are known, drawn randomly from a uniform distribution between 0 and 1. From these data, we compared true parameter values with parameter estimates, both with perfect and imperfect detectability, as detectability increases. We show that detectability should be above 0.9 per site to yield parameter estimates close to true parameter values. By contrast, detectability per transect above 0.25 seems to be enough to obtain reliable parameter estimates for models including imperfect detectability (see function mss_cepd and vignette(“detectability”)).

Figure 1

Effect of imperfect detectability on estimated colonization and extinction rates. We generated colonization–extinction dynamics for communities of 100 species (S = 100) for known colonization–extinction (true) values. In (a), model parameters were estimated assuming perfect detectability from model‐generated S × T data matrices, where the number of rows (S = 100) is interpreted as the number of species in a community undergoing independent colonization–extinction dynamics (or, alternatively, as the number of sites that have been monitored over T = 100 sampling times for just one species). True presences were then filtered according to detectability levels to generate the observed data matrices. Ten thousand different colonization–extinction pairs are represented. In (b), parameters were estimated assuming imperfect detectability from S × N data matrices, with S = 100 and T = 10, but four different transects per sampling time, so that N = 40. Again true presences were filtered according to detectability levels to generate the observed data matrices. One thousand different colonization–extinction pairs are represented.

In addition, we used data (“lakshadweepPLUS”) on coral reef fishes (Alonso et al., 2015) to investigate whether trophic guilds are effectively equivalent in terms of their effective colonization–extinction dynamics across the sampling period so they can be characterized by the same colonization–extinction–detectability–Φ0 model parameters across all groups, or if they need to be grouped differently to optimize the trade‐off between model simplicity and prediction ability according to Akaike information criterion. The function upgma_model_selection performs this analysis, with the input argument PerfectDetectability = FALSE (see vignette(“detectability”) for more details), yielding, as an output, Table 2.

Table 2. Seven models are compared

Model	k	AIC c	AIC dif	AIC weights
{Alg Cor Mac Mic Omn Pis Zoo}	2	12,800	127.57	1.8 10^−28
{Cor Zoo Mac Omn Pis Mic} {Alg}	4	12,713	40.641	1.4 10^−09
{Pis Mic Zoo Mac Cor} {Alg} {Omn}	6	12,715	42.61	5.1 10^−10
{Mic Zoo Mac Cor} {Pis} {Alg} {Omn}	8	12,680	7.9	1.7 10^−2
{Mic Mac Cor} {Zoo} {Pis} {Alg} {Omn}	10	12,672	0	0.91
{Mic Mac} {Cor} {Zoo} {Pis} {Alg} {Omn}	12	12,678	5.4	0.06
{Mic} {Mac} {Cor} {Zoo} {Pis} {Alg} {Omn}	14	12,681	8.8	0.01

• The column k represents the number of model parameters. The first model, with only two parameters (1st row, k = 2), considers all species described by the same colonization and extinction rates. In this sense, they are all equivalent, and, therefore, this is the most neutral one. The second model considers two groups (2nd row, k = 4), where algal feeders are characterized by a different colonization–extinction pair, and the remaining trophic guilds share the same colonization–extinction rates, and so on, until the last model (7th row, k = 14), where every guild is described by a different colonization–extinction pair.

3 ENVIRONMENTAL VARIABILITY AND COMMUNITY DYNAMICS

The influence of environmental variability on community dynamics has been explored using a variety of approaches (Cazelles et al., 2016b; Legendre, Dallot, & Legendre, 1985; Parmesan, 2006). Colonization and extinction rates may depend, in general, on a number of relevant environmental covariates (understanding covariate as an independently measured variable with a potential influence on the dynamics). The simplest form incorporating environmental factors reduces to assume a linear dependency,

(1)

Y_it being the value of the i‐th environmental covariate (i = 1,…, F) at time t. Note that colonization and extinction rates are once again considered as effective parameters since they encompass the mean‐field response of the community to the environment, regardless of species identity.

We include in island a subset of a historical dataset, idaho, consisting of a series of permanent 1 m² quadrats located on the sagebrush steppe in eastern Idaho, USA, sampled annually from 1923 to 1973 (Zachmann, Moffet, & Adler, 2010). It also contains records of covariates such as monthly precipitation, mean temperature and snowfall, for which we estimated annual summaries.

We evaluated the influence of the environmental covariates on the colonization and extinction rate of the whole community, between 1932 and 1956, using function greedy_environmental_fit, that sequentially selects the environmental covariate that better improves the AIC of the model in each iteration. The model selected included the influence over colonization of snow in November and March and the influence over extinction of snow in May and June and temperature in May, December and April. We simulated the dynamics of the accumulated species richness in the quadrats using these rates. Figure 2 shows that the model with environmental variables better approximates observed species richness over time than a single pair of colonization and extinction rates.

Figure 2

Simulations of a sagebrush steppe plant community in Idaho, USA. The black line represents the local richness aggregated to all quadrats every sampled year. The blue line stands for the median overall richness averaged over 1,000 simulations, and the 95% confidence lines are depicted in red. (a) These simulations have been calculated with the maximum‐likelihood estimated pair of colonization and extinction rates for this dataset. (b) Here we considered colonization and extinction rates as functions of the environmental covariates selected sequentially maximizing its AIC at each step. The use of the environmental covariates improved substantially the performance of our simulations

We estimated the goodness‐of‐fit of the environmental‐based model in relation to the null expectation yielded by the model driven solely by averaged colonization and extinction rates using the quantity , where (, respectively) is the (null) model quadratic error, estimated with simulated_model. We get R² = 0.673 for the model based on environmental covariates relative to the null model. Calculations and model are detailed in the r script environmental.R (see Supplementary Materials S1), and more information can be found in vignette (“island”).

4 SPECIES CO‐OCCURRENCE NETWORKS

The inference of interactions from patterns of presence/absence goes back at least to Diamond's ‘checkerboard’ pattern to infer competitive exclusion (Diamond, 1975). These research efforts continue today (Barberán, Bates, Casamayor, & Fierer, 2012; Cazelles, Araújo, Mouquet, & Gravel, 2016a; Chase et al., 2011). Here we developed a procedure to test the species independence assumption. Our method highlights species pairs that co‐occur more or less than expected under independent colonization–extinction dynamics—the null hypothesis. These significant pair‐wise associations can then be used to build a network.

We used the dataset alonso15, which describes community reassembly after a coral mass mortality event in the relatively unfished Lakshadweep Archipelago (Alonso et al., 2015). For simplicity, we only show results for the guild of corallivores. To obtain co‐occurrence networks, we first calculated empirical colonization and extinction rates for each island and guild. Second, we simulated presence/absence matrices for the species in the guild based on previously calculated rates. Third, we obtained the distribution of expected co‐occurrences given the stochastic colonization–extinction dynamics (computed after a number of model realizations). Finally, we compared actual co‐occurrences with the distribution of occurrences across replicates under the null model to determine if observed co‐occurrence values were significantly lower or higher (confidence level 2.5% or 97.5%) than null model predictions respectively. The results show that some species of corallivores are much more likely to be found together, while others (like Chaetodon plebius) tend to exclude others in the guild (Figure 3). The file corallivores. r provides the code necessary to conduct this analysis (see Suplementary Materials S2).

Figure 3

Network of significant co‐occurrences of corallivorous fishes at the Lakshadweep Archipelago. Pairs of species linked with a red line co‐occurred less than expected, while the green line indicates species that co‐occurred more than expected according to the null expectation provided by the IBT stochastic model‐based colonization and extinction rates characterizing each trophic guild. All species belong to genus Chaetodon, except Cantherhines dumerilii and Amanses scopas

5 DISCUSSION

Long time‐series data on multispecies assemblages are rich in information but notoriously complex to analyse. Having tools that can robustly explore these rich datasets is critical to testing and advancing theories of community dynamics. In this contribution, we present an r package that implements models and maximum‐likelihood methods to analyse community dynamics based on the simplest stochastic model underlying IBT. The functions developed in island allow for implementation of colonization–extinction models with and without perfect detectability.

Most r packages to analyse community data provide metrics based on statistical approaches, such as diversity indices and ordination techniques (Oksanen, Blanchet, Kindt, Legendre, & O'Hara, 2016), or indices of functional diversity (Laliberté, Legendre, & Shipley, 2014) that can be applied over time (May et al., 2018). Many packages develop methods to specifically deal with and describe temporal community dynamics (Hallett et al., 2016), but few of these methods focus on the potential dynamic processes underlying community assembly over time. Promising recent approaches provide a clear link between models and basic dynamic ecological theory, which also use IBT as a point of departure (Gravel et al., 2011; Cazelles et al., 2016b,a; Massol et al., 2017)—as we have done in island package. However, they do not develop maximum‐likelihood methods for community time‐series data analysis in practical settings. More work is needed in this direction.

Our package complements some of the capabilities of the otherwise comprehensive unmarked r package (Fiske & Chandler, 2011), which implements MacKenzie et al.'s (2003) colonization–extinction dynamic model (see colext function). However, unlike the unmarked r package, our basic model parameter estimates are rates (in T–1 units) rather than dimensionless probabilities (Fiske & Chandler, 2011, 2015; MacKenzie et al., 2003). As a consequence, methods of island r package work well with irregular sampling times, helping address the problem of missing data, which so often constrains the analysis of long‐term data series.

The three case studies showcase the use of our methods and functions to analyse whole community dynamics monitored for a period of time across a range of sampling locations (see package vignettes for other applications and alternative examples). Colonization–extinction models to analyse single species over a range of sites—a metapopulation—have been widely used (Hanski, 1994, 1999, 2001; Hanski & Ovaskainen, 2000). By contrast, comprehensive community temporal datasets have been and still are expensive to obtain and, consequently, methods to analyse community dynamics have received much less attention. Such methods are still scarce in spite of an entire body of theory devoted to the study of metacommunmities (Holyoak, Leibold, & Holt, 2005). Our examples analyse data frames that include at least three factors (“species”, “sampling location” and “species guild”) that can be studied separately with standard model selection techniques, and “sampling time”, which is our model dynamic variable. Our model estimates can be considered effective parameters that provide aggregated information reflecting true community dynamics. The idea of an effective model has important theoretical and ecological implications. While all models implemented in the packages rely on “the species independence assumption”, merely finding good agreement between them and community data does not imply that between‐species interactions are unimportant. The success of fit implies instead that all the biotic interactions influencing a focal species can be effectively represented by its average model parameters. Species dynamics are only effectively decoupled to achieve a mean‐field description of true community dynamics (Solé et al., 2002). Even if the overall performance of a given model assuming species independence is good, our approach can be used to unveil significant pair‐wise species interdependencies or associations, as we show in our third case study.

By using a process‐based stochastic immigration–birth–death model to generate synthetic data, we show how effective colonization and extinction rates can be compared with intrinsic immigration and death rates (Box 1). In this sense, the parameters calculated by our island r package provide effective coarse‐grain measures of the intrinsic quantities driving processes affecting individuals and their interactions to end up determining community dynamics over time.

Our first worked example highlights the importance of accounting for imperfect detectability in community datasets. We clearly show that maximum‐likelihood estimation based on perfect detectability can yield highly biased estimates unless we work with detectability per sampling time higher than 0.9. By contrast, models that explicitly account for imperfect detectability produce reliable estimates when detectability per transect is just over 0.25. Ideally, we recommend models that account for imperfect detectability, while recognizing that we often do not have the luxury of sufficient replicated datasets, limiting us to simpler approaches. In these situations, the potential biases of imperfect detectability should be clearly acknowledged while interpreting model results. As a rule of thumb, with at least four replicates per sampling time and a detectability over 0.5, it is possible to use the simpler, more straightforward methods from island to estimate almost unbiased colonization–extinction parameters.

Our second worked example shows how environmental variables can be taken into account to better explain community dynamics through effective colonization and extinction rates. Notice that rates were simply written as linear combinations of environmental covariates. Since our methods estimate rates rather than probabilities, we do not need to make use of the logit link to consider covariates (Fiske & Chandler, 2011, 2015). In addition, our methods can cope with highly flexible sampling schemes including non‐evenly spaced sampling time intervals. Simple model selection techniques can be used to emphasize the relatively stronger influence of a small set of environmental covariates on the dynamics of community‐level species richness.

Finally, our third case study uses the community colonization–extinction model, which is based on species independence, as a null working hypothesis to assign a level of significance to species pairwise co‐occurrence. Most robust methods to find when species co‐occurrence is significantly higher or lower than random expectations are based on static probabilistic models (Barberán et al. (2012); Veech (2013); Griffith, Veech, and Marsh (2016), cooccur r package, but see also Cazelles et al. (2016a) and Cirtwill and Stouffer (2015)). Instead we used a dynamic community assembly model as a null model, where independent species extinctions and colonizations occur at the rates previously estimated from community data. In addition, because we can generate stochastic replicates with the same sampling structure as the given dataset, we do not require the stationarity assumption. As a result, as shown in the resulting co‐occurrence network (see Figure 3), where links represent only significant co‐occurrences, we identified a group of species that tend to occur together, and a species, Chaetodon plebeius, that occurred less than expected with most species in the guild under the null assumption of species‐independent colonization–extinction dynamics. This clearly warrants further ecological investigation. This example highlights a novel procedure to investigate species interactions from community data over time, which can go easily unnoticed or biased if only static probabilistic methods are used.

Our understanding of what shapes ecological communities requires a constant conversation between empirical observations and theory. Some of the most basic questions of community assembly such as the stationarity or temporal dynamism of communities have yet to be resolved (Warren et al., 2015). Questions such as these require real‐world data to test assumptions and predictions of ecological theory. As valuable multispecies temporal datasets are becoming increasingly available, having adequate tools to explore them is vital. We hope that the methods developed in our island r package allow for more detailed analyses of ecological community temporal datasets and an advancement of basic ecological theory.

ACKNOWLEDGEMENTS

This work was funded by the Spanish “Ministerio de Economía y Competitividad” under the projects SITES (CGL2012‐39964, D.A.V.J.O.) and BRIDGES (CGL2015‐69043‐P, D.A., E.O.C., J.A.C.), the FPI predoctoral Fellowship programme (BES‐2013‐066798, V.J.O.) and the Ramón y Cajal Fellowship programme (D.A.). R.A. was supported by Rohini Nilekani Philanthropies and the Spanish National Research Council (Memorandum of understanding between CEAB‐IMEDEA‐NCF).

DATA ACCESSIBILITY

All data used in this article are available in the r package island, which can be downloaded from the Comprehensive R Archive Network at https://cran.r-project.org/web/packages/island/index.html.

AUTHORS’ CONTRIBUTIONS

V.J.O., E.O.C. and D.A. conceived the initial ideas; D.A. wrote a preliminary draft. R.A. collected Lakshadweep data; V.J.O., J.A.C. and D.A. designed the methodology, analysed the data and led the writing of the manuscript; V.J.O. prepared the vignettes and documented the package. All authors contributed critically to the drafts and gave final approval for publication.