Seasonal cycles of species diversity and similarity in a tropical butterfly community


  • Vidar Grøtan,

    1. Centre for Conservation Biology, Department of Biology, Norwegian University of Science and Technology, N-7491 Trondheim, Norway
    Search for more papers by this author
  • Russell Lande,

    1. Centre for Conservation Biology, Department of Biology, Norwegian University of Science and Technology, N-7491 Trondheim, Norway
    2. Division of Biology, Imperial College London, Silwood Park Campus, Ascot, Berkshire SL5 7PY, UK
    Search for more papers by this author
  • Steinar Engen,

    1. Centre for Conservation Biology, Department of Mathematical Sciences, Norwegian University of Science and Technology, N-7491 Trondheim, Norway
    Search for more papers by this author
  • Bernt-Erik Sæther,

    1. Centre for Conservation Biology, Department of Biology, Norwegian University of Science and Technology, N-7491 Trondheim, Norway
    Search for more papers by this author
  • Phil J. DeVries

    Corresponding author
    1. Department of Biology, University of New Orleans, New Orleans, LA 70148, USA
      Correspondence author. E-mail:
    Search for more papers by this author

Correspondence author. E-mail:


1. Studies of seasonality in ecological diversity rarely extend over more than a few years, and few studies of seasonal diversity have explicitly investigated the influence of environmental factors on seasonal community composition, especially in tropical communities.

2. Our 10 years of monthly sampling in Amazonian Ecuador yielded 20 996 individuals of 137 fruit-feeding butterfly species. Seasonal cycles of rainfall drive annual cycles in species diversity and community similarity. Undetermined processes operating most strongly during the dry season maintain species diversity and high community similarity across years.

3. Seasonal cycles in community diversity and similarity are superimposed on a gradual decline in similarity between community samples on a decadal time-scale because of long-term changes in species abundances.

4. Monitoring and analysis of changes in community composition over a range of time-scales can be used to refine models of community dynamics by incorporating environmental factors necessary to predict the ecological impact of future climate change.


Extreme seasonal cycles in temperature and rainfall at polar and temperate latitudes cause many species to evolve seasonal dormancy, diapause or hibernation, and seasonal reproduction. For example, in a rare long-term study of seasonal environmental effects on community dynamics, Guo et al. (2002) observed distinct non-overlapping summer and winter annual plant communities that coexisted in the desert of the south-western United States, despite many species having long-lived seed banks. Seasonality is greatly reduced in the tropics, but even in tropical rainforests, where many species remain active through the year and reproduce continuously, wet and dry seasons can differentially affect both species abundance and diversity. The high species diversity of tropical communities makes them important not only for biological conservation (Heywood 1995), but also for testing basic theories of species diversity (Williams 1964; Heywood 1995; Rosenzweig 1995; Lande et al. 2003).

Studies of environmental impacts on species diversity commonly compare ecological communities among spatial locations (Preston 1960, 1980; Williams 1964; Rosenzweig 1995; Magurran 2004; May et al. 2007; McGill et al. 2007), which differ in numerous, often unmeasured, environmental factors. In contrast, dynamic responses of species and communities to a changing environment are most appropriately investigated by observations through time. The dearth of temporal data on species diversity was emphasized by Preston (1960), Rosenzweig (1995) and Magurran (2007, 2011). But the difficulty of conducting long-term studies has limited most investigations of impacts of seasonal change on community dynamics to a few years, especially in the tropics (e.g. Leigh et al. 1996; Bonebrake et al. 2010; Ribeiro et al. 2010).

For species with multiple generations per year, seasonal cycles provide a natural experiment replicated in time to assess the ecological impact of changing environments. Because of their short generations, insects are ideal for the study of seasonal impacts on species abundance and diversity, and among tropical insects, butterflies are taxonomically the best known (DeVries 1987, 1997). We sampled monthly for 10 years a community of more than 100 species of fruit-feeding butterflies from a neotropical rainforest. Here, we analyse the dynamics of species diversity and abundance of this community in relation to time series of precipitation and temperature. The few previous long-term studies of seasonality in tropical insects (Wolda 1988, 1992, 1996; Smythe 1996; Wolda & Chandler 1996) did not analyse environmental impacts on community abundance or diversity and instead focused on the most abundant species or pooled species into higher taxa.

A major challenge in analyses of species diversity in ecological communities is that the number of species recorded increases with sampling intensity (Preston 1960; Pielou 1975; Lande 1996). The presence of a rare species in a random sample is a stochastic event that must be accounted for when comparing species diversity among different samples (Pielou 1975; Engen et al. 2002, 2008; Connolly & Dornelas 2011). This problem becomes severe for highly diverse communities containing many rare species, which typifies tropical communities. Among replicate random samples of a given size from a community, the number and identity of species varies substantially. Species richness is therefore statistically less reliable than other measures of diversity that weight species more evenly as a function of their frequency in the community; this also applies to the corresponding measures of community similarity (Lande 1996; Lande et al. 2003).

To account for sampling effects on species diversity, we use a parametric approach assuming a lognormal distribution of actual species abundances, and Poisson sampling within species (Fisher et al. 1943). The distribution of observed number of individuals among species follows the Poisson–lognormal distribution (Bulmer 1974; O'Hara 2005), whereas joint samples from two communities follow the corresponding bivariate distribution (Engen et al. 2002, 2008; Engen et al. 2011). The lognormal species abundance distribution often provides a good fit to data from species-rich communities (Preston 1948, 1960, 1980; Williams 1964; Magurran 2004, 2007; May et al. 2007; Ulrich et al. 2010), especially when sampling effects are included (McGill et al. 2007; Connolly & Dornelas 2011). Another important property of the lognormal species abundance model is that it can be derived from the population dynamics of simple multi-species community models (Engen & Lande 1996).

A desirable property of a measure of species diversity is that for a given number of species, S, diversity is maximized when all species are equally abundant, and diversity decreases with increasing unevenness in species abundances (Lewontin 1972; Lande 1996). Thus for a given number of species, diversity should decrease with increasing σ2. For example, the commonly used Shannon information measure of species diversity is inline image where pi represents the frequency of the ith species in the community. We assume that the actual number of species in the community, S, remained constant during the study. This is reasonable for our data, because it is unlikely that any butterfly species in lowland Amazonia became extinct during the decade of our sampling. Bulmer's (1974) approximation for the lognormal species abundance distribution, H ≈ ln Sσ2/2, thus shows explicitly that σ2 is a negative indicator of Shannon diversity. Thus, like Shannon diversity, σ2 is most sensitive to changes in frequencies of species of intermediate abundance, in comparison to species richness and Simpson diversity measures that respectively depend most on the rare and common species (Lande 1996, Lande et al. 2003). The estimated correlation, ρ, of the natural log of actual species abundances between two samples was used as a measure of community similarity between each pair of months (Engen et al. 2002, 2008, 2011; Lande et al. 2003).

Our long-term intensive sampling study was conducted to provide a baseline for comparing changes in species diversity at different temporal scales for a rainforest fruit-feeding Nymphalid butterfly community in Amazonian Ecuador that is relatively undisturbed by human activities. In the present paper, we develop and apply statistical methods for analysing the temporal dynamics of a community including seasonal weather data. We detect distinct seasonal cycles in species diversity and similarity and investigate whether they are influenced by temporal variation in current and past rainfall and temperature with time-lags up to 3 months to encompass the typical generation time of species in this community. We also examine how the gradual decline in interannual community similarity over a decade relates to long-term changes in species abundances.

Materials and methods

Study site and data collection

Data were collected from August 1994 to July 2004 at the La Selva Lodge, Sucumbios Province, eastern Ecuador in the upper Amazon Basin 75 km E.S.E. of the town of Coca. The study area consisted of approximately 2 km2 of undisturbed forest bounded by the Rio Napo, and the oxbow lakes Garza Cocha and Mandi Cocha (0 29’ 50·3“S; 76 22’28·9”W) near the settlement of Anyañgu (DeVries & Walla 2001). The study site is situated within approximately 30 000 hectares of intact floodplain forest.

Adult butterflies in the family Nymphalidae that feed primarily on the juices of rotting fruit compose a feeding guild known as fruit-feeding nymphalids (DeVries 1987, 1997). In neotropical forests, this guild accounts for 40–50% of nymphalid species, and these butterflies are readily sampled using traps baited with rotting fruits (DeVries 1987; DeVries et al. 1997; DeVries & Walla 2001). Sampling protocol and trap locations are described in detail in DeVries et al. (1997) and DeVries & Walla (2001). Traps were situated at 25 locations each fitted with one understory trap and one canopy trap. All trap sites were at least 100 m from an aquatic boundary. Traps were baited with bananas obtained locally, mashed and fermented for 48 h in a large container prior to use each month. Sampling was conducted for five consecutive days during the first 10 days of each month, except for a gap of eight consecutive months illustrated in Fig. 1. Each month, traps were baited on the day prior to the first day of sampling, and new bait was added on the third day of sampling. Except for nine common, readily identified species involved in a mark–release–recapture study (Tufto et al. 2012), individuals of all other species were sampled, placed in glassine envelopes marked with date of capture and preserved for subsequent identification by PJD. For the nine species involved in the mark–release–recapture study, only the date of first capture was used in the present analysis. Data obtained during the five sampling days on a given month were pooled for all 25 understory and 25 canopy traps to constitute a single monthly sample. Despite the large total sample size in our study, analysis of temporal changes in the community over a broad range of time-scales requires pooling the data across geographic locations and in canopy and understory, to maintain an average sample size per month not much less than the total number of species estimated in the community. Otherwise statistical uncertainty in estimates of monthly species diversity swamps any temporal signals in the data. For similar reasons, our previous analyses of interannual spatiotemporal dynamics of this community (Engen et al. 2002; Lande et al. 2003) pooled data across months within years and across canopy and understory, and our analysis of vertical stratification within and among species in the community (Walla et al. 2004) pooled all temporal and horizontal spatial data.

Figure 1.

 Time series of (a) total community abundance and (b–k) the 10 most common species of fruit-feeding Nymphalid butterflies. Samples were captured over 10 years (August 1994 to July 2004) at paired understory and canopy traps at 25 locations in a 2 km2 area at La Selva Lodge, Ecuador.

Weather data

Monthly data on net precipitation and average temperature at the study site were interpolated from gridded spatial data archives. We were unable to find station-based weather data covering the study period near our study site and therefore resorted to gridded data to interpolate the local weather. The gridded weather data were obtained from under Global precipitation monthly grids for 1900–2008, version 2.01 and Global surface air temperature monthly grids for 1900–2008, version 2.01. The resolution of the data was a 0·5 by 0·5 of latitude/longitude grid centred on 0·25 , and we extracted data for the grid cell covering the study area.

Statistical methods

Poisson–lognormal distribution

The lognormal species abundance distribution has been widely applied in analyses of how community structure varies in space and time (Williams 1964; Magurran 2004). However, the lognormal distribution is continuous. To describe integer numbers of individuals in a sample from a community, we follow Fisher et al. (1943) and Bulmer (1974) by assuming that the number of individuals of a given species observed in a sample is Poisson distributed with mean proportional to the abundance of the species in the community. The number of individuals, N, sampled for a given species with log abundance in the community x is then Poisson distributed with mean νex= ex+ ln ν , where the parameter ν expresses the sampling intensity. Assuming that abundances of different species in the community are lognormally distributed, x is then normally distributed among species with mean μ and variance σ2, whereas the log of the Poisson mean, x+ ln ν, is normal with mean μ+ ln ν and the same variance σ2 . The number of individuals N sampled from a random species in the community then constitutes a sample from the Poisson–lognormal distribution with parameters (μ+ ln ν, σ2). The parameter μ in the underlying abundance distribution cannot be estimated unless the sampling intensity is known or can be estimated in some way. The sampling intensity itself depends on the trapping effort. As our study involved a constant trapping effort per month, the sampling intensity was constant but unknown. The sampling intensity affects the expected number of individuals in the sample, but has no influence on the form of the distribution as the variance parameter σ2 is unaffected by changing sampling intensities (Engen et al. 2008; Connolly et al. 2009).

The total number of species in the community, S, is generally unknown and may be difficult to estimate. Following Fisher et al. (1943) and Bulmer (1974), we only consider the numbers of individuals of species that are represented in the sample. Thus, there is an unknown number of species that are present in the community but are absent from a sample from the community. The observed numbers of individuals of the different species therefore follow a zero-truncated distribution because the number of species with a count of zero is unknown. The expected fraction of unobserved species given a set of parameters in the Poisson–lognormal distribution and a certain sampling intensity is q(0; μ+ ln ν, σ2), and the zero-truncated Poisson–lognormal distribution is therefore

image(eqn 1)

defined for n=1,2,…. The maximum likelihood estimation of the parameters of this distribution was first derived by Bulmer (1974).

If we jointly consider two communities (sampled from different locations and/or times), each species will be represented by a realization of a bivariate random variable expressing its abundance in the two communities (Engen et al. 2002, 2008). Still assuming a lognormal species abundance distribution as the marginal distribution in each community, the log abundances in two communities will follow a bivariate normal distribution with parameters inline image. The parameters inline image and inline image represent the marginal lognormal distributions in the two communities while the parameter ρ is the correlation in log abundances among the two communities. A high positive correlation means that a given species that is relatively common (or rare) in the first community will tend to have similar relative abundance also in the second community. Assuming Poisson sampling leads to a bivariate distribution of the number of individuals of a species in the two samples (N1,N2), conditional on presence in at least one of them. Species that are present in both communities but absent in both samples need to be accounted for by using a truncated distribution. The zero-truncated bivariate Poisson–lognormal distribution takes the form

image(eqn 2)

where the function q here is redefined for the two dimensional case. The parameters inline image and ρ can be estimated without any knowledge about the unknown sampling intensities ν1 and ν2 that may differ among different samples. Estimates of μ1 and μ2 can only be found if sampling intensities are known.

The R-package poilog (Grøtan & Engen 2009) was used for estimating the parameters in the univariate and the bivariate Poisson–lognormal distribution.

Species abundance distribution for pooled data

The data were pooled by summing all monthly abundances for each species. The parameter estimates from the fit of the pooled data to the lognormal species abundance distribution are described in the Results. Goodness-of-fit statistics can be obtained by comparing the log likelihood when fitting the observed data with the bootstrap distribution of log likelihoods produced by simulating data and refitting the parameters. If the log likelihood of the data occurs towards one of the tails in the bootstrap distribution of log likelihoods, this will indicate lack of fit. However, Fig. S1 (Supporting information) shows that the data log likelihood is nearly at the 50th percentile (0·469) of the bootstrap distribution of log likelihoods. Connolly et al. (2009) proposed another (but related) goodness-of-fit test statistic for the Poisson–lognormal distribution. Using this method did not indicate any lack of fit (inline image). Graphs of species abundance distributions from data and from simulated Poisson–lognormal sampling are displayed in Fig. 2 in discrete bins on a log base 3 scale, with edges at 3j/2 for j=0,1,2,3,…, containing 1,2−4,5−13,14−40,… individuals per species (Williams 1964; Lande et al. 2003).

Figure 2.

 Species abundance distributions for the pooled data. Histogram bars: observed distribution. Smooth curve: lognormal distribution fitted using poilog (Grøtan & Engen 2008). Large dots: expected Poisson–lognormal distribution, simulated by first sampling species expected abundances from the fitted lognormal and then Poisson sampling numbers of individuals within species; error bars are 95% confidence intervals from repeated simulations.

Bias correction of estimated parameters

Point estimates of parameters of the lognormal species abundance distribution in a community may be biased to a degree that depends on the parameters and on the observed number of species in a sample. Parameter estimation is based on the idea of Fisher et al. (1943), fitting the distribution of observed abundances of the species present in the sample. Hence, what is commonly considered as the number of observations in statistical inference is here the observed number of species, rather than the total number of individuals in the sample. The total individuals in the sample only have two minor effects compared to the observed number of species. First, if the number of individuals is large, the stochastic effects of the Poisson sampling of each species are reduced. This mainly only affects common species. As the sample size increases, additional species will be represented in the sample with small numbers of individuals and still large effects of the Poisson sampling. Secondly, the number of individuals has an effect on the values of the parameters in the distribution of observed abundances. Altogether, the importance of total individual number in estimation and testing is much less than that of observed species number. This has been illustrated by Engen et al. (2008 Fig. 2, 2011 Fig. 2) in graphs showing that variation in individual numbers has little effect on sampling variance of parameter estimates. In standard statistical theory, the bias of an estimator is often proportional to the inverse of the number of observations. When modelling the bias in parameter estimates for species abundance distributions, we therefore obtain the most accurate bias correction by using the observed species number rather than the observed total number of individuals in the sample as an independent variable in the model. Commonly used methods for bias correction based on bootstrap procedures (Efron & Tibshirani 1993) assume that the bias is constant with changing parameters. We here choose instead to use a fixed point method that allows us to estimate bias as a function of the set of parameters as well as the observed number of species.

A parameter estimate, say inline image, may contain some bias. Writing inline image for the unbiased parameter, we have inline image, where inline image is the expected bias given inline image. This implies that inline image may vary with inline image. However, inline image may also be affected by, for example sample size, thus inline image may be a complicated function. If we are able to obtain a model for inline image, we can rearrange the above equation to inline image, implying that we can obtain a bias-corrected estimate inline image given inline image and inline image. The bias-corrected estimate inline image can be found by an iterative method inline image, which after a few iterations converges to inline image. This method for bias correction can easily be extended to cases where several parameters are estimated jointly. As an example, in the univariate Poisson–lognormal distribution, there are two estimated parameters, inline image and inline image. In addition, the number of species in the sample, inline image, may affect the bias. By simulating a large number of samples with known parameter values and estimating the parameters, we can as the next step model the expected bias of the parameters when inline image and the observed number of species in the sample is S. Thus, we obtain models inline image and inline image that predict the bias in parameter estimates of inline image and inline image, respectively. Using the univariate Poisson–lognormal distribution as an example, the same iterative method as shown above can be extended to several parameters,

image(eqn 3a)
image(eqn 3b)

and convergence usually is achieved within a few iterations.

Bias correction for the univariate model

Estimates of parameters of the univariate Poisson–lognormal distribution were bias corrected as follows. First, for each set of parameter estimates obtained from fitting the univariate Poisson distribution to each of the 112 months included in the study, we simulated 1000 new data sets and refitted the parameters. All simulations were conditioned on the number of observed species in the samples. The next step was to model the bias based on the constructed set of known parameter values (the parameter estimates fitted to the butterfly data) and the stochastic realizations of bias (given by parameter estimates obtained based on simulating data with known parameter values). Using standard linear regressions, simulated realizations of bias in inline image and inline image were entered as response variables with linear effects as well as 2-way and 3-way interactions of inline image, inline image and S used as explanatory variables. Thus, the linear regressions can be written in the general form

image(eqn 4)

where inline image can be replaced with inline image and inline image in the two independent linear regressions and α is an intercept term.

Model simplification was performed using a stepwise algorithm, the step function in the stats package (R Development Core Team 2010) which selects models based on the AIC (Burnham & Anderson 2002) of candidate models. Because the 3-way interaction was highly significant, none of the models were simplified by the stepwise algorithm (Tables S1 and S2, Supporting information). The estimated models of bias were used in the iterative procedure to obtain bias-corrected estimates of the parameters.

Bias correction for the bivariate model

Bias correction for the bivariate Poisson–lognormal model was performed similarly to that for the univariate case. For each of the 6216 pairs of samples in different months, we simulated a bivariate sample using the estimated parameters of the bivariate lognormal distribution and conditioning on the observed numbers of species in the two samples, S1 and S2. After estimating the parameters based on simulated samples, we then fitted standard linear regressions of the form

image(eqn 5)

where inline image can be replaced with inline image and inline image respectively in the five independent linear regressions and α is an intercept term. After model simplification using the same procedures as outlined in the univariate case, the selected models for expected bias given parameters and sample sizes (Tables S3, S4 and S5, Supporting information) were thereafter used in the iterative procedure to obtain bias-corrected estimates of parameters.

Autoregression and density dependence of N

The best model explaining temporal fluctuations in community size, N, is a linear autoregression of N with two time-lags and environmental noise (Table S8, Supporting information). This conforms to the theory for estimating total density dependence in an age-structured population (Lande et al. 2002a eqns 9a, 10b), according to which the total density dependence in the life history, D, equals the sum of the autocorrelation coefficients minus 1. Here, we apply this theory to estimate the total density dependence in community size and the time-scale for return to equilibrium community size in the absence of environmental fluctuations. This is only a rough approximation because this butterfly community is composed of many species with interspecific variation in life history, and reproduction occurs continuously rather than at discrete time intervals. From Table 2, we find D = 0·3837 per generation. The magnitude of this estimate is comparable to that of D estimated for several vertebrate species (Lande et al. 2002a,b). According to the theory, the rate of return to equilibrium in the absence of environmental stochasticity is γ=D/T where T is the generation time or average age of mothers at reproduction at stable age distribution. The mean generation time of species in the butterfly community is roughly 2·5 months per generation, so the rate of return to equilibrium community size is approximately γ = 1·54, corresponding to a time-scale of 1/γ = 6·5 months, which agrees well with our previous estimate of the time-scale 0·51 years obtained from analysis of spatiotemporal fluctuations in annual changes in average log abundance of species in this community during the first 5 years of the data (Lande et al. 2003, p. 178).

Table 2.   Estimated partial regression coefficients for the best model explaining variation in total community abundance N (Table S8, Supporting information). Possible independent variables were community abundance at time-lags 1–3 months (Nt−1Nt−2Nt−3), and temperature and precipitation at time-lags 0–3 months (TTt−1Tt−2Tt−3 and PPt−1Pt−2Pt−3)
 Std. estimateEstimateStd. errort valuePr(>|t|)
  1. Possible quadratic terms were also included for precipitation variables. Units as in Table 1. R2 = 0·5121.


Correcting R2 for the effect of Poisson sampling

Let y be lognormally distributed, so that x = ln y is N(μ, σ2) with distribution g(x). If x is the log abundance of a species, then the distribution of x given that the observed number of individuals of that species is n is

image(eqn 6)

where A is a normalization constant such that ∫g(x|n)dx=1. If the observed counts in a given month are n1,n2,…,ns, with underlying unknown abundances y1,y2,…,ys, the abundances are estimated as the expected values of the conditional distributions,

image(eqn 7)

where μ and σ2 [used in g(x|ni)] are those estimated from the sample. This is also carried out for the estimated number of zero observations. The number of zeros must first be estimated as the closest integer to s/[1 − q(0; μσ2)]−s = sq(0; μσ2)/[1 − q(0; μσ2)] where q(·) is defined in eqn (1). Bootstrap resampling reflecting the Poisson stochasticity is now performed by simulating, say 1000 times, the nbi = Poissoninline image. For each resampling, the standard deviation of σ is estimated, giving a bootstrap variance vt for each monthly sample.

Variation in σ among months can after fitting a linear model be decomposed in the following way. For the explained part of σt, we write st=α+βZt where α is an intercept, β is a vector of k regression coefficients and Z is a T × k matrix of covariates, where T is the number of observations through time. Then σt = st + rt, where rt is a residual with zero mean and variance, say τ2, assumed constant. The estimate of σt is inline image where et is the sampling error with known variance vt calculated by resampling as shown above. Then


and summing over time produces


which gives the estimator

image(eqn 8)

Finally, let Vs be the mean sum of squares of the st. Then the fraction of the variance in σ explained by the covariates is estimated as inline image.


Our statistical analysis assumes a lognormal distribution of actual species abundances (Preston 1948, 1960, 1980; Williams 1964; Magurran 2004, 2007) and Poisson sampling within species (Bulmer 1974; Engen et al. 2002; Lande et al. 2003). The observed species abundance distribution for the pooled sample of 20 996 individuals contained 137 species of fruit-feeding Nymphalids, including 10 species observed only once. Figure 2 illustrates the good fit of the pooled data to the Poisson–lognormal sampling distribution (see also Fig. S1, Supporting information).

Parameter estimates for the lognormal species abundance distribution [and their 95% parametric bootstrap confidence intervals] were inline image and inline image. The estimate of the number of species observed in the sample relative to the actual number of species in the community was 0·889[0·805,0·941]. Thus, as 137 species were observed, the estimate of the actual number of species in the community was inline image.

Time series of abundances for the total community and the 10 most common species show no obvious annual periodicity, although several of the species display irregular outbreaks that sometimes are synchronized among species (Fig. 1). The means of community abundance by calendar month (Fig. 3a) suggest an annual cycle with a twofold range between wet and dry seasons, but the large standard deviation of monthly community abundance among years obscures any evidence of an annual periodicity in the full time series for community abundance (Fig. 1a).

Figure 3.

 Mean ± one standard deviation of community and physical data by calendar month: (a) total community abundance, (b) standard deviation of species log abundances σ (a negative measure of species diversity), (c) precipitation, (d) temperature.

Most species’ abundances in the monthly samples are too rare for robust statistical analysis of their time series, because they are absent from the samples in many or most months, and occasionally even some of the 10 most common species were not trapped (Fig. 1b–k). We therefore focused on the seasonal dynamics of community composition, using the estimated standard deviation, σ, of log species abundances each month as an inverse measure of species diversity, and the estimated correlation, ρ, of log species abundances between 2 months as a measure of community similarity.

The average annual cycle of species diversity (Fig. 3b) displays a highly repeatable twofold difference in σ, with the highest diversity (smallest σ) during the dry season and the lowest diversity during the wet season. Local weather data, reconstructed by spatial interpolation of monthly records from nearby weather stations, also show annual cycles with a more than threefold difference in mean precipitation between wet and dry seasons, but a nearly uniform temperature with only 2 C mean range between dry and wet seasons (Fig. 3c,d). Using the full time series, the best regression model of monthly species diversity on monthly weather data, σt = 0·53 + 1·48Pt + 3·27Pt−2, involved only current precipitation, Pt, and 2-month lagged precipitation, Pt−2, with no contribution from temperature or community abundance (Table 1). Coefficients of these two terms were highly significant, and additional nonlinear terms did not significantly improve the fit. This simple linear model explained 28% of the observed temporal variance in σ, a substantial fraction considering the statistical noise involved in monthly samples from the community (averaging 187 individuals per month) and the use of gridded weather data. Reducing the unexplained residual variance in σ by subtracting the expected Poisson sampling variance, as suggested by Fisher et al. (1943), increased the proportion of variance explained to 38%. The 2-month lagged precipitation produces a much larger positive impact on σ than does the current precipitation, explaining why the minimum and maximum σ occur 2 months after those for mean precipitation (Fig. 3b,c).

Table 1.   Estimated partial regression coefficients for the best model explaining variation in σ (Table S6, Supporting information). Possible independent variables were current and past temperature and precipitation at time-lags 0–3 months (TTt−1Tt−2Tt−3 and PPt−1Pt−2Pt−3) and community abundance at time-lags 1–3 months (Nt−1Nt−2 and Nt−3)
 Std. estimateEstimateStd. errort valuePr(>|t|)
  1. Units for community size, temperature and precipitation are individuals, C and metres respectively. Standardized estimates are dimensionless, after transforming all variables to zero mean and unit variance. R2 =  0·2842. Corrected R2 = 0·3835 after removing the variance because of Poisson sampling (Table S7, Supporting information).


The annual cycle of species diversity is also evident in the autocorrelation diagram for σ (Fig. 4a). In contrast to point estimates of species diversity within months, community correlations between months, ρ, are bivariate estimates that preclude standard time series analysis. Nevertheless, this statistic facilitates a description of community similarity as a function of the time-lag between months (Fig. 4b), which also clearly displays an annual cycle. Community similarity remains quite high for the duration of the study, but the annual cycle in community similarity is superimposed on a gradual decline in similarity with increasing time-lag on a time-scale of decades. This gradual decline in community similarity is evidently caused by long-term changes in species frequencies in the community, as can be seen in the time series for some of the most common species in the community, such as Historis acheronta, Panacea prola, and P. divalis (Fig. 1b,c,h).

Figure 4.

 Temporal correlation patterns for community and physical data: (a) autocorrelation of σ, (b) mean community correlation. In both panels, the increasing amplitude and irregularity at longer time-lags is because of smaller numbers of pairs of months at longer lags, which increases the noise.

Host plant abundance is considered a major factor influencing butterfly density and geographical range (Yamamoto et al. 2007), but its effect on individual species frequencies in our study is unclear. For example, consider two abundant species in our samples. Historis acheronta occurs in forests from Mexico to Brazil and Bolivia (and the Greater Antilles), and its host plant (Cecropia spp, Urticaceae) is a common pioneer tree throughout lowland and montane forests (DeVries 1987; Berg et al. 2005). Nessaea hewitsoni occurs in a wide range of forest habitats from Colombia across the Amazon basin to Peru and Boliva, and its host plants (Plukenetia spp, Euphorbiaceae) are common vines throughout lowland forests (PJD, pers. obs., Gillespie 1993). Given their host plant ranges and abundance we might expect H. acheronta and N. hewitsoni to show relatively constant frequencies, but they do not (Fig. 1). Such contrasting frequencies indicate that other, unknown or unmeasured factors have influenced individual species densities (e.g. DeVries & Walla 2001; DeVries et al. 2012).

The annual cycle in community similarity vs. the time-lag from the standard (aseasonal) time series analysis (Fig. 4b) does not distinguish whether particular seasons contribute disproportionately to this pattern. To investigate this, we analysed community similarity, and weather, as functions of both time-lag and calendar month (Fig. 5). As expected from the nearly homoscedastic annual cycles in weather (Fig. 3c,d), the coloured contours for precipitation and temperature (Fig.  5b,c) each show two peaks of autocorrelation per year, corresponding to their mean annual maximum and minimum, with the wet season peak autocorrelation occurring earlier for precipitation than for temperature. The autocorrelation cycles for weather persist with almost the same amplitude across the entire range of time-lags (Fig. 5b,c). By comparison, the community correlation (Fig. 5a) has only one peak per year during the dry season, corresponding to the maximum mean species diversity (minimum mean σ, Fig. 3b). The intensity of the dry season peak in community correlation decreases with increasing time-lag across the years (Fig. 5a) consistent with the gradual decline in similarity across years in the standard (aseasonal) time series analysis (Fig. 4b).

Figure 5.

 Coloured contours (a–c) are functions of both time-lag and calendar month; data were pooled by time-lag ranges of 1, 2–4, and 5–9 years (± up to 6 months) to provide comparable statistical accuracy at different time-lags. In each coloured panel, the horizontal midline at k = 0 gives the (auto)correlation for each calendar month at different (multi)annual intervals. Colours are standardized across each row of panels.


Our analyses revealed obvious annual cycles in species diversity and community similarity in this tropical rainforest butterfly community (Figs 3–5). Large seasonal fluctuations occurred in community composition, with the standard deviation of log species abundances, σ (a negative measure of species diversity), displaying a twofold average change between wet and dry seasons (Fig. 3b). Smaller but highly repeatable annual cycles in community similarity were superimposed on a gradual decline in community similarity on a decadal time-scale because of long-term changes in species abundances (Figs 4 and 1b,c,h). Maximum species diversity (minimum σ) and maximum community similarity across years both occurred during the dry season. A decrease in σ increases species evenness in the community, which can only occur by rare species increasing and common species decreasing in frequency, a hallmark of frequency-dependent factors acting to maintain species diversity (Chesson 2000). This interpretation of annual cycles in σ depends on the mean generation time of species in the community being sufficiently short for community composition to respond significantly to seasonal cycles.

Assuming that fecundity is roughly independent of adult age, the mean generation time can be approximated as the mean egg-to-adult development time plus mean adult life span (Lande et al. 2002a, Lande et al. 2003). The development time of neotropical butterflies ranges from 2 to 3 weeks for small species, and up to about 3 months for large species (DeVries 1987, 1997). Among nine species from this community in a mark–recapture study, the mean adult life span ranged from a few weeks for large species with high dispersal rate to 2 months for small species with low dispersal rate (Tufto et al. 2012). These data imply a mean generation time of 2–3 months, which is sufficiently short for community composition to respond to seasonal environmental fluctuations. The best model for temporal fluctuations in σ, after removing the Poisson sampling variance, explained 38% of the variance as driven by current and especially 2-month lagged precipitation (Table 1), reflecting the average generation time of species in the community.

The short mean generation time also allows total community abundance, N, to fluctuate rapidly (Fig. 1a). Changes in community abundance do not display annual cycles and so cannot explain the seasonality in species diversity (Fig. 4). However, bounded fluctuations in N indicate that it must be subject to some overall density regulation. This is confirmed by the best model of community abundance as an autoregressive process, with half the variance in N explained by 1- and 2-month lagged N, current and 2-month lagged precipitation, and 2-month lagged temperature (Table 2). Coefficients of the autoregression terms give the expected time-scale for return to the average or equilibrium N of about 6 months, indicating strong overall density dependence (Lande et al. 2002, Lande et al. 2003).

Larval host plants typically respond to increased precipitation by producing new leaves and shoots (Aide 1993), the preferred oviposition site for many neotropical butterflies (DeVries 1987, 1997). Fruit production also peaks during the wet season (Foster 1996). These resources are therefore relatively scarce during the dry season, but the relative importance of resource competition, avian predation, parasitoids and pathogens in limiting abundance is not known for any tropical butterfly species or community. These results and our previous analysis of annual changes of species relative abundances in space and time in this community (Lande et al. 2003) support the view that species-specific responses to environmental fluctuations and interspecific variation in life history both contribute to the maintenance of species diversity and community similarity through time.

The seasonal impact of precipitation on species diversity we detected (Figs 4 and 5) reflects the prevalent operation of non-neutral mechanisms in natural communities where most changes in species relative abundances are environmentally driven (Chesson 2000; Lande et al. 2003). This is confirmed by long-term dynamics of fossil communities and observations on newly created islands (Lande et al. 2003; Ricklefs 2003; Leigh et al. 2004), where the extinction rate of common species far exceeds that expected from neutrality (Hubbell 2001).

Our long-term intensive sampling of a tropical rainforest butterfly community provides a baseline for comparing temporal variation in species diversity of butterflies at different temporal scales in a tropical rainforest relatively undisturbed by human activities. Long-term sampling of community dynamics in relation to changing environments also can be used to test and refine non-neutral models predicting the ecological impacts of future climate change.


We thank C. Dunn, C. Funk, R. Guerra, H. Greeney, R. Hill, E. Schwartz, and T. Walla for assistance with field work and data entry, and F.A. Jones for discussion. This study was supported by the Royal Society of London (R.L.), MacArthur Foundation (P.J.D., R.L), National Geographic Society (P.J.D.), and Norwegian University of Science and Technology through the Centre for Conservation Biology (V.G., S.E. and B.-E.S.).