Hierarchical Bayesian modeling of random and residual variance–covariance matrices in bivariate mixed effects models

Bivariate mixed effects models are often used to jointly infer upon covariance matrices for both random effects ( u ) and residuals ( e ) between two different phenotypes in order to investigate the architecture of their relationship. However, these (co)variances themselves may additionally depend upon covariates as well as additional sets of exchangeable random effects that facilitate borrowing of strength across a large number of clusters. We propose a hierarchical Bayesian extension of the classical bivariate mixed effects model by embedding additional levels of mixed effects modeling of reparameterizations of u‐ level and e ‐level (co)variances between two traits. These parameters are based upon a recently popularized square‐root‐free Cholesky decomposition and are readily interpretable, each conveniently facilitating a generalized linear model characterization. Using Markov Chain Monte Carlo methods, we validate our model based on a simulation study and apply it to a joint analysis of milk yield and calving interval phenotypes in Michigan dairy cows. This analysis indicates that the e ‐level relationship between the two traits is highly heterogeneous across herds and depends upon systematic herd management factors.     

Forecasting intensifying disturbance effects on coral reefs

Anticipating future changes of an ecosystem's dynamics requires knowledge of how its key communities respond to current environmental regimes. The Great Barrier Reef (GBR) is under threat, with rapid changes of its reef‐building hard coral (HC) community structure already evident across broad spatial scales. While several underlying relationships between HC and multiple disturbances have been documented, responses of other benthic communities to disturbances are not well understood. Here we used statistical modelling to explore the effects of broad‐scale climate‐related disturbances on benthic communities to predict their structure under scenarios of increasing disturbance frequency. We parameterized a multivariate model using the composition of benthic communities estimated by 145,000 observations from the northern GBR between 2012 and 2017. During this time, surveyed reefs were variously impacted by two tropical cyclones and two heat stress events that resulted in extensive HC mortality. This unprecedented sequence of disturbances was used to estimate the effects of discrete versus interacting disturbances on the compositional structure of HC, soft corals (SC) and algae. Discrete disturbances increased the prevalence of algae relative to HC while the interaction between cyclones and heat stress was the main driver of the increase in SC relative to algae and HC. Predictions from disturbance scenarios included relative increases in algae versus SC that varied by the frequency and types of disturbance interactions. However, high uncertainty of compositional changes in the presence of several disturbances shows that responses of algae and SC to the decline in HC needs further research. Better understanding of the effects of multiple disturbances on benthic communities as a whole is essential for predicting the future status of coral reefs and managing them in the light of new environmental regimes. The approach we develop here opens new opportunities for reaching this goal.     

Multiple sources of evidence for density dependence in the endangered Hawaiian stilt (Himantopus mexicanus knudseni)

Hawaiian stilts (Himantopus mexicanus knudseni) are an endangered subspecies of the Black-necked stilt endemic to the Hawaiian Islands. Despite long-term study, the main drivers of Hawaiian stilt population dynamics are poorly understood. We tested for density dependence using two sources of evidence: a 30-year time series of annual estimated range-wide abundance, and two 15+ year time series of reproductive success. Using separate methods with independent data, sources allowed us to make up for the potentially positive bias of one approach with the more conservative nature of the second. We compared nonlinear density-dependent and density-independent population model fits to our time-series data, using both frequentist and Bayesian state-space approaches. Across both approaches, density-dependent models best fit observed population dynamics, with lower AICc and cross-validation statistics compared to density-independent models. Among density-dependent models, a conditional model in which density-independent dynamics occur below a population size threshold (~850–1,000 birds), and then density-dependent dynamics occur above that threshold, performed best across Bayesian and frequentist model comparisons, with the Ricker model ranked next or equivalently. Our analysis of reproduction data revealed a strong negative effect of local adult density on nest success (proportion of nests hatching at least one chick) at Kealia National Wildlife Refuge on Maui, where few alternative breeding habitats are available, but no such effect at another site where many nearby alternative wetlands are available. These congruent results across independent datasets and analytical approaches support the hypothesis that Hawaiian stilts exhibit density dependence across their range.     

Spatial synchrony in the response of a long range migratory species (Salmo salar) to climate change in the North Atlantic Ocean

A major challenge in understanding the response of populations to climate change is to separate the effects of local drivers acting independently on specific populations, from the effects of global drivers that impact multiple populations simultaneously and thereby synchronize their dynamics. We investigated the environmental drivers and the demographic mechanisms of the widespread decline in marine survival rates of Atlantic salmon (Salmo salar) over the last four decades. We developed a hierarchical Bayesian life cycle model to quantify the spatial synchrony in the marine survival of 13 large groups of populations (called stock units, SU) from two continental stock groups (CSG) in North America (NA) and Southern Europe (SE) over the period 1971–2014. We found strong coherence in the temporal variation in postsmolt marine survival among the 13 SU of NA and SE. A common North Atlantic trend explains 37% of the temporal variability of the survivals for the 13 SU and declines by a factor of 1.8 over the 1971–2014 time series. Synchrony in survival trends is stronger between SU within each CSG. The common trends at the scale of NA and SE capture 60% and 42% of the total variance of temporal variations, respectively. Temporal variations of the postsmolt survival are best explained by the temporal variations of sea surface temperature (SST, negative correlation) and net primary production indices (PP, positive correlation) encountered by salmon in common domains during their marine migration. Specifically, in the Labrador Sea/Grand Banks for populations from NA, 26% and 24% of variance is captured by SST and PP, respectively and in the Norwegian Sea for populations from SE, 21% and 12% of variance is captured by SST and PP, respectively. The findings support the hypothesis of a response of salmon populations to large climate‐induced changes in the North Atlantic simultaneously impacting populations from distant continental habitats.     

Nonlinearity in interspecific interactions in response to climate change: Cod and haddock as an example

Climate change has profound ecological effects, yet our understanding of how trophic interactions among species are affected by climate change is still patchy. The sympatric Atlantic haddock and cod are co‐occurring across the North Atlantic. They compete for food at younger stages and thereafter the former is preyed by the latter. Climate change might affect the interaction and coexistence of these two species. Particularly, the increase in sea temperature (ST) has been shown to affect distribution, population growth and trophic interactions in marine systems. We used 33‐year long time series of haddock and cod abundances estimates from two data sources (acoustic and trawl survey) to analyse the dynamic effect of climate on the coexistence of these two sympatric species in the Arcto‐Boreal Barents Sea. Using a Bayesian state‐space threshold model, we demonstrated that long‐term climate variation, as expressed by changes of ST, affected species demography through different influences on density‐independent processes. The interaction between cod and haddock has shifted in the last two decades due to an increase in ST, altering the equilibrium abundances and the dynamics of the system. During warm years (ST over ca. 4°C), the increase in the cod abundance negatively affected haddock abundance while it did not during cold years. This change in interactions therefore changed the equilibrium population size with a higher population size during warm years. Our analyses show that long‐term climate change in the Arcto‐Boreal system can generate differences in the equilibrium conditions of species assemblages.     

Colonization history of Galapagos giant tortoises: Insights from mitogenomes support the progression rule

Galapagos giant tortoises (Chelonoidis spp.) are a group of large, long-lived reptiles that includes 14 species, 11 of which are extant and threatened by human activities and introductions of non-native species. Here, we evaluated the phylogenetic relationships of all extant and two extinct species (Chelonoidis abingdonii from the island of Pinta and Chelonoidis niger from the island of Floreana) using Bayesian and maximum likelihood analysis of complete or nearly complete mitochondrial genomes. We also provide an updated phylogeographic scenario of their colonization of the Galapagos Islands using chrono-phylogenetic and biogeographic approaches. The resulting phylogenetic trees show three major groups of species: one from the southern, central, and western Galapagos Islands; the second from the northwestern islands; and the third group from the northern, central, and eastern Galapagos Islands. The time-calibrated phylogenetic and ancestral area reconstructions generally align with the geologic ages of the islands. The divergence of the Galapagos giant tortoises from their South American ancestor likely occurred in the upper Miocene. Their diversification on the Galapagos adheres to the island progression rule, starting in the Pleistocene with the dispersal of the ancestral form from the two oldest islands (San Cristóbal and Española) to Santa Cruz, Santiago, and Pinta, followed by multiple colonizations from different sources within the archipelago. Our work provides an example of how to reconstruct the history of endangered taxa in spite of extinctions and human-mediated dispersal events and provides a framework for evaluating the contribution of colonization and in situ speciation to the diversity of other Galapagos lineages.     

Congruent population genetic structures and divergence histories in anther‐smut fungi and their host plants Silene italica and the Silene nutans species complex

Study of the congruence of population genetic structure between hosts and pathogens gives important insights into their shared phylogeographical and coevolutionary histories. We studied the population genetic structure of castrating anther‐smut fungi (genus Microbotryum) and of their host plants, the Silene nutans species complex, and the morphologically and genetically closely related Silene italica, which can be found in sympatry. Phylogeographical population genetic structure related to persistence in separate glacial refugia has been recently revealed in the S. nutans plant species complex across Western Europe, identifying several distinct lineages. We genotyped 171 associated plant–pathogen pairs of anther‐smut fungi and their host plant individuals using microsatellite markers and plant chloroplastic single nucleotide polymorphisms. We found clear differentiation between fungal populations parasitizing S. nutans and S. italica plants. The population genetic structure of fungal strains parasitizing the S. nutans plant species complex mirrored the host plant genetic structure, suggesting that the pathogen was isolated in glacial refugia together with its host and/or that it has specialized on the plant genetic lineages. Using random forest approximate Bayesian computation (ABC‐RF), we found that the divergence history of the fungal lineages on S. nutans was congruent with that previously inferred for the host plant and probably occurred with ancient but no recent gene flow. Genome sequences confirmed the genetic structure and the absence of recent gene flow between fungal genetic lineages. Our analyses of individual host–pathogen pairs contribute to a better understanding of co‐evolutionary histories between hosts and pathogens in natural ecosystems, in which such studies remain scarce.