## Introduction

The monarch butterfly, Danaus plexippus L., is perhaps the most widely recognized of all butterflies. The status in part reflects the fascination of the public with the unique biology of the species, namely the spectacular overwintering aggregations of adults in Mexico, the annual migration in North America to breed on milkweeds and then the fall migration back to Mexico1. The Eastern monarch butterfly population fluctuates greatly from year to year and has shown a consistent and significant decline2, causing growing concerns over its conservation status3. The causes of the decline and even the population decline in the breeding areas have been mired in some controversy4,5,6. Most previous studies have aimed at understanding the causes of the decline in population size5, while no study to our knowledge has looked at the potential drivers of the inter-annual variation in population growth rate7. From a population dynamics perspective the two aims are clearly distinct but complementary. The first assumes non-stationarity and tries to investigate whether carrying capacity is declining due to environmental changes (e.g. host plant, pesticides, climate change) or to find other demographic factors than can bring the population close to extinction. The second approach investigates the endogenous and exogenous factors that determine the change in population growth rate from one year to the following irrespective of any general trends in abundance8. Surprisingly, we know little about how population growth rate has fluctuated in the last two decades during the observed population decline.

As with most invertebrate species, monarch butterfly population growth rate is affected by environmental stochasticity. Large-scale climate fluctuations can influence breeding populations by affecting individual development time, voltinism9,10, reproduction11, migration and host plant quality12. Moreover, extreme weather can cause mass-mortality events in the overwintering sites in Mexico2. On the other hand, a variety of biotic factors are known to influence both larval and adult survival. Predators13, parasitoids14 and parasites15, in particular, are thought to strongly limit population growth rates. Besides the processes described above, the estimated decline in the host plant (i.e. milkweed) from the early 1990’s to now has been estimated to be c. 75%16,17,18. Potentially, this decline may cause increased competition for food among larvae leading to decreases in immature survival19,20. While most previous studies have measured and explained vital rates independent of population size, several processes described above could influence monarch population dynamics operating in a density-dependent manner. The fact that density-dependence can operate at different stages of the life cycle suggests that studying density processes is particularly challenging for migratory species21. However, in the case of the monarch butterfly, the monitoring of overwintering, breeding and migrating population offers one of the few cases where the whole population can be actually observed22.

Although several studies have analysed the monarch population dynamics and trends using intensive monitoring data from single and multiple locations5,7,20,23,24,25, no study has investigated the inter-annual fluctuations in population growth rate. First, we tested the presence of a negative density-dependence in the population dynamics of the overwintering population in Mexico26, of the adult population in North America5, and in the available time-series of egg density per host plant across the breeding range24 (Fig. 1). Second, we tested whether the population growth rate, after accounting for the density effect, varied over time and whether the potential density-dependence has became more pronounced in recent years. A direct (one-year lag) density-dependence would indicate the importance of a resource-driven, bottom-up regulation such as competition for host plants or top-down regulation through predation by generalists14 or disease attacks27. A delayed density-dependence (two-year lag) would indicate the presence of a top-down regulation by specialized natural enemies that can respond numerically to monarch population fluctuations8,28. Our results will provide new insights on the drivers of population dynamics of this endangered population that can be used to improve the conservation efforts currently in place.

## Results

### Overwintering population in Mexico

The multi-model inference analysis indicated relatively low model selection uncertainty with two best models (ΔAICc < 2). Both models were equally supported and included both a time and density effect (Table 1). The interaction Time × N t-1 was included only in the second best model, but the low model weight (0.252) and the low log-likelihood drop indicated low support for this interaction. We found a clear negative effect of population size in Mexico in the previous year on population growth rate (Fig. 2a). After accounting for the negative density effect, we found that the population growth rate declined over time (Fig. 2b). The standardized model estimates indicated that the density effect was stronger than the year effect (Table 2). The best model including both main effects explained c. 37% of the total variation in population growth rate.

### Adult population density in North America

The analyses of the population density in North America indicated relatively low model selection uncertainty with two best models presenting ΔAICc < 2 (Table 1). Both models explained over half of the total variation in growth rate and both included a negative density effect in the previous year (Fig. 3a). Contrary to the overwintering population, the Time effect was not supported since its inclusion in the second model caused a very small log-likelihood drop. The main effect of the density in the previous year was comparable to that found in the overwintering population (Table 2). We found no support for the Time × N t-1 interaction.

### Egg density per host plant in North America

We found low model uncertainty with only one best model (model weight: 0.685) (Table 1). The multi-model inference analysis indicated only support for a negative effect of the density of eggs per stem in the previous year (Fig. 3b). The model explained over 40% of the total variation. We found no support for a Time effect or for the interaction between Egg t-1 and Time (Table 2).

## Discussion

The Eastern population of the monarch butterfly has strongly declined over the last two decades in the overwintering sites. Our study found a strong and consistent negative density dependence in the population dynamics of the monarch butterfly using three independent datasets. The signal was present in the overwintering population in Mexico and in the time series of both adult population density and egg density per host plant in North America. In the overwintering population, after accounting for the density-dependence effect, the population growth rate linearly declined over time. This time effect is particularly worrying as it suggests a population decline where stochastic events can assume prominence to drive the population close to extinction22,29. The temporal stability of the slope of the density effect (i.e. no support for a density x time interaction) indicated that the negative density-dependence and the decline of the population are likely independent phenomena. The density effect explained c. 37-50% of the total variation in population growth rate indicating that several density-related mechanisms that had been tested only locally can actually be important to explain population dynamics. Our results provide new insights on the drivers of population dynamics of this endangered population that can be used to improve both current and future conservation efforts.

Multiple non-exclusive mechanisms can be offered to explain a direct negative density-dependence in the population dynamics of the monarch butterfly. First, disease spread is expected to work in a density-dependent manner. Both field observational30 and experimental studies27,31 found that monarch infection probability by Ophryocystis elektroscirrha, an obligate protozoan parasite, increased significantly with increasing larval densities and aggregation of monarchs around milkweed. At high butterfly density O. elektroscirrha loads can decrease larval survival, and cause smaller adult size, resulting in shorter adult lifespans and fewer eggs laid15. Moreover, parasite infection can affect migration success so that infected butterflies will travel shorter distances than uninfected individuals32,33. A second reason could be linked to higher mortality rates by opportunistic, generalist predators and parasitoids such as tachinid flies, that have been demonstrated to be important mortality factors for the immature stages14,28. A third explanation is linked to host plant limitation20. After leaving the overwintering site, monarchs fly north and start breeding in Texas in spring. Here, observed larval and egg density are usually higher than in the summer breeding areas27. Experimental work testing field-realistic larval density found small density-dependent reduction in vital rates, suggesting that intraspecific competition may occur early in the breeding season in the southern portion of the breeding range19. Accordingly to this mechanism, we found a negative density effect in the time-series of egg density per host plant. This effect is consistent with the negative relationship previously found between local egg density and larval survival in sites with low milkweed availability20.

One of the most common conclusions of previous research on the monarch butterfly decline is that environmental stochasticity is the key compounded driver of population decline9,12,25,40,42,43. Large-scale climate fluctuations can affect host plant distribution, individual reproductive success, and population growth7,40,43. Similarly, extreme weather events have been implicated in mass-mortality events of adult butterflies in the overwintering sites2,42. Besides these drivers, our analysis clearly points to the importance of density-dependent processes that had been empirically tested only at the local scale13,19,27 or with modelling exercises38,39,44. Our study suggests that more effort should be placed into incorporating density effects in future population models not just between generations but also between years7,45. This approach will help in deciphering the drivers of change that are leading to the rapid decline of this population. Finally, the observed negative time effect on growth rate in the overwintering population is particularly worrying as it may indicate a decline in the carrying capacity in the breeding areas22,29,46, where mutual reinforcement among biotic and abiotic processes may drive population size to a rapid decline.

## Methods

### Dynamics of the overwintering population

The Eastern North American monarch population exhibits a migratory behaviour from the breeding areas located in northern and central United States and southern Canada to overwintering sites in Mexico. Overwintering monarchs arriving in Mexico coalesce predominately on oyamel fir forests at densities ranging from 6.9 to 60.9 million monarchs per ha47. By measuring the forest area occupied by the overwintering butterflies it is possible to estimate the total population size and this has been done in a consistent fashion since 199426. We used the latest time-series provided by WWF (available at http://www.wwf.org.mx, access 8th May 2016) (see supplementary material Table S1). As forest area used by the overwintering population is expected to be related to population size, we used this variable as a proxy for population size (N). Although a certain degree of methodological inconsistencies can be present, this is the sole total population size estimate available2,22. Then, we built a discrete model of population dynamics as the baseline for developing and comparing competing models to explain the inter-annual variation of the population growth rate. The population growth rate (dependent variable) was defined as:

$$R=ln({N}_{t}/{N}_{t-1}),$$

where N t is the forest area occupied or population size in the current year while N t-1 is the population size in the previous year. We hypothesized that R would exhibit endogenous direct negative feedback (density dependence) where:

$$R=f({N}_{t-1})+\varepsilon ,$$
(Model 1)

where ε represents sampling error in the estimation of the population density plus exogenous (i.e., density independent) effects on R.

We also tested delayed (two-year lag) density dependent feedback with the effect of the population density two years before.

$$R=f({N}_{t-1}+{N}_{t-2})+\varepsilon$$
(Model 2)

As we found no support for a delayed density dependence (general linear model R~N t-1  + N t-2), we proceeded to test only direct density dependence in the following models. Finally, we fitted Model 1 with Time (year in the time series) and the interaction between N t-1 and Time:

$$R=f({N}_{t-1}+Time+{N}_{t-1}\times Time)+\varepsilon$$
(Model 3)

We hypothesized that the slope of the population size effect should be more negative in the later part of the time series compared to the beginning. If supported, this interaction would indicate an exacerbation of the negative feedback even if the total population size is declining. Beside population size, we did not test any exogenous variables such as climate variables because migrating species have intricate and complex relationships with climate that can vary geographically48 and cannot easily be described by simple weather variables40.

### Dynamics of the adult population in North America

To test for density-dependence we also used available population density (Density) data from the breeding area in North America. This data was recently compiled using the data provided by the North American Butterfly Association (NABA) that has collected citizen science data on population density over the last decades5. Inamine et al. (2016) clustered the data into three spatially distinct regions: South (south of 34.5°N and west of 79°W), the closest to the overwintering sites, Northeast (north of 34.5°N and east of 79°W), and Midwest (north of 34.5°N and west of 79°W) (Fig. 1) (see supplementary material Table S2). Northeast and Midwest included observations on the entire summer breeding season and corresponded to the core of the breeding areas. South was temporally subdivided into two seasons: Spring south (1st March through 30th June, corresponding to breeding individuals migrated from Mexico), and Fall south (1st September to 30th November, corresponding to non-breeding migrants moving south). We also added two additional time-series: Cape May and Peninsula Point. Cape May (New Jersey), is a major funnelling point for monarchs migrating south from the Northeast, while Peninsula Point (Michigan), is a funnelling point for monarchs migrating south from both eastern and midwestern Canadian populations5.

Similarly to the overwintering population, we first fitted Model 1 and Model 2. As we found no support for a delayed density dependence (general linear mixed model R~ Density t-1  + Density t-2 , random = Site), we proceeded to test only direct density dependence in the following models. Compared to the overwintering population time series, the NABA point data did not provide an optimal estimate of the total population size, but each time-series should provide a good estimate of local density34. Similarly to the overwintering population, we fitted a model testing whether the potential density-dependence varied over time:

$$R=f(Densit{y}_{t-1}+Time+Densit{y}_{t-1}\times Time)+\varepsilon$$
(Model 4)

### Dynamics of egg density per host plant in North America

Finally, we also retrieved recently compiled data on egg density per host plant across the breeding range by extracting the information from published figures24. We retrieved five time series spanning from 1997 to 2014 coming from the Monarch Larva Monitoring Project (see supplementary material Table S3). We grouped the time series in three regions (Midwest, Northeast and South). The authors associated each time series to the prevalent monarch generation (supplementary material Table S3)24. For each time-series, we computed a growth rate based on egg density (REGG) as:

$${R}_{EGG}=ln(Eg{g}_{t}/Eg{g}_{t-1}),$$

where Egg t is the density per host plant in year t and Egg t-1 is the density per host plant in the previous year t-1.

Similarly to the adult population models, we first fitted both a direct (Egg t-1 ) and a delayed density dependence term (Egg t-2 ). As we found no support for a delayed density dependence (general linear mixed model R EGG ~Egg t-1   + Egg t-2 , random = Site), we proceeded to test only direct density dependence. Then, we fitted a model testing whether the potential density-dependence varied over time:

$${R}_{EGG}=f(Eg{g}_{t-1}+Time+Time\times Eg{g}_{t-1})+\varepsilon$$
(Model 5)

### Statistical analyses

For overwintering population, Model 3 was fitted using general linear models. For adult population in North America, Model 4 was fitted using linear mixed-effects models including Density t-1 , Time, and Density t-1 x Time as fixed effects and site as a random factor. In Model 4, Density t-1 was ln-transformed to improve linearity. For egg density per host plant, Model 5 was fitted using linear mixed-effects models including Egg t-1 , Time, and Egg t-1 x Time as fixed effects and site as a random factor. Egg t-1 was ln-transformed to improve linearity. Before fitting all models, we standardized the explanatory variables to mean 0 and SD 1 to make slope estimates comparable. The assumptions of the models were tested by inspecting diagnostic plots of model residuals. Residuals approximated a normal distribution and exhibited homoscedasticity. Model selection was performed using an information theoretic approach to evaluate alternative competing models involving the variables included in Models 3-549. Our information-theoretic approach compared the fit of all the possible candidate models nested within the full models. Models were fitted using the maximum likelihood method. The fit of each model in the set was then evaluated using second-order Akaike’s information criterion (AICc). The best fit is indicated by AICcMIN, the lowest value of AICc. In a set of n models each model i can be ranked using its difference in AICc score with the best-fitting model (ΔAICc i  = AICc i  − AICcMIN). A model in a set can be considered plausible if its ΔAICc is below 2. We also computed the model weight (wi) as the weight of evidence in favour of each model. The weights wi represent the relative likelihood of a model. For each model, we first calculated its likelihood as exp(−0.5*∆AICci). The weight wi for a model is its likelihood divided by the sum of the likelihoods across all models. For each variable, we also provided model-averaged coefficients and intervals of confidence (CI 95%)50,51. The multi-model inference analyses were performed using the ‘MuMIn’ package52 implemented in R version 2.13.053 using the functions dredge(), model.avg() and confint().

Before fitting the models described above, we retrieved published data for severe storm occurrence in Mexico during the period 1993-2016, because a major storm causing mass-mortality can strongly affect population size irrespective of any density effect. Two major storms in early 2002 and 2004 caused recorded mass-mortality26. Hence, two population growth rate estimates (2001-2002 and 2003-2004) were certainly affected by these events. We therefore ran all models excluding these two years. Another major winter storm occurred in the area between the 31st of January and the 2nd of February 2010 but no data on observed mass-mortality events are available. The only available document reports that climatic data indicates that this major storm very likely did not cause major butterfly mortality (L. Brower, L. Fink, I. Ramirez, R. Zubieta and D. Slayback, http://monarchwatch.org). Similarly between the 8th and the 9th of March 2016 another storm struck the overwintering sites, heavily damaging the forest but no clear published data of mass butterfly mortality is available. We therefore did not exclude data for the years 2010 and 2016 in the models presented in the main text. However, we also ran a conservative test excluding the four years potentially affected by storms. All the results remained qualitatively similar compared to those presented in the main text (see supplementary material Tables S46)54.

### Data availability

All data analysed during this study are included in this published article and its Supplementary Information files.