How ecosystem productivity and species richness are interrelated is one of the most debated subjects in the history of ecology1. Decades of intensive study have yet to discern the actual mechanisms behind observed global patterns2, 3. Here, by integrating the predictions from multiple theories into a single model and using data from 1,126 grassland plots spanning five continents, we detect the clear signals of numerous underlying mechanisms linking productivity and richness. We find that an integrative model has substantially higher explanatory power than traditional bivariate analyses. In addition, the specific results unveil several surprising findings that conflict with classical models4, 5, 6, 7. These include the isolation of a strong and consistent enhancement of productivity by richness, an effect in striking contrast with superficial data patterns. Also revealed is a consistent importance of competition across the full range of productivity values, in direct conflict with some (but not all) proposed models. The promotion of local richness by macroecological gradients in climatic favourability, generally seen as a competing hypothesis8, is also found to be important in our analysis. The results demonstrate that an integrative modelling approach leads to a major advance in our ability to discern the underlying processes operating in ecological systems.

Integrative modelling reveals mechanisms linking productivity and plant species richness

Bayesian statistics is an approach to data analysis based on Bayes’ theorem, where available knowledge about parameters in a statistical model is updated with the information in observed data. The background knowledge is expressed as a prior distribution and combined with observational data in the form of a likelihood function to determine the posterior distribution. The posterior can also be used for making predictions about future events. This Primer describes the stages involved in Bayesian analysis, from specifying the prior and data models to deriving inference, model checking and refinement. We discuss the importance of prior and posterior predictive checking, selecting a proper technique for sampling from a posterior distribution, variational inference and variable selection. Examples of successful applications of Bayesian analysis across various research fields are provided, including in social sciences, ecology, genetics, medicine and more. We propose strategies for reproducibility and reporting standards, outlining an updated WAMBS (when to Worry and how to Avoid the Misuse of Bayesian Statistics) checklist. Finally, we outline the impact of Bayesian analysis on artificial intelligence, a major goal in the next decade. This Primer on Bayesian statistics summarizes the most important aspects of determining prior distributions, likelihood functions and posterior distributions, in addition to discussing different applications of the method across disciplines.

Bayesian statistics and modelling

1.	Many insect species are under threat from the anthropogenic drivers of global change. There have been numerous well‐documented examples of insect population declines and extinctions in the scientific literature, but recent weaker studies making extreme claims of a global crisis have drawn widespread media coverage and brought unprecedented public attention. This spotlight might be a double‐edged sword if the veracity of alarmist insect decline statements do not stand up to close scrutiny.

2.	We identify seven key challenges in drawing robust inference about insect population declines: establishment of the historical baseline, representativeness of site selection, robustness of time series trend estimation, mitigation of detection bias effects, and ability to account for potential artefacts of density dependence, phenological shifts and scale‐dependence in extrapolation from sample abundance to population‐level inference.

3.	Insect population fluctuations are complex. Greater care is needed when evaluating evidence for population trends and in identifying drivers of those trends. We present guidelines for best‐practise approaches that avoid methodological errors, mitigate potential biases and produce more robust analyses of time series trends.

4.	Despite many existing challenges and pitfalls, we present a forward‐looking prospectus for the future of insect population monitoring, highlighting opportunities for more creative exploitation of existing baseline data, technological advances in sampling and novel computational approaches. Entomologists cannot tackle these challenges alone, and it is only through collaboration with citizen scientists, other research scientists in many disciplines, and data analysts that the next generation of researchers will bridge the gap between little bugs and big data.

/pdf/interpreting-insect-declines-seven-challenges-and-a-way-2uns64wf7x.pdf

Interpreting insect declines: seven challenges and a way forward

Dispersal is a process of central importance for the ecological and evolutionary dynamics of populations and communities, because of its diverse consequences for gene flow and demography. It is subject to evolutionary change, which begs the question, what is the genetic basis of this potentially complex trait? To address this question, we (i) review the empirical literature on the genetic basis of dispersal, (ii) explore how theoretical investigations of the evolution of dispersal have represented the genetics of dispersal, and (iii) discuss how the genetic basis of dispersal influences theoretical predictions of the evolution of dispersal and potential consequences. Dispersal has a detectable genetic basis in many organisms, from bacteria to plants and animals. Generally, there is evidence for significant genetic variation for dispersal or dispersal-related phenotypes or evidence for the micro-evolution of dispersal in natural populations. Dispersal is typically the outcome of several interacting traits, and this complexity is reflected in its genetic architecture: while some genes of moderate to large effect can influence certain aspects of dispersal, dispersal traits are typically polygenic. Correlations among dispersal traits as well as between dispersal traits and other traits under selection are common, and the genetic basis of dispersal can be highly environment-dependent. By contrast, models have historically considered a highly simplified genetic architecture of dispersal. It is only recently that models have started to consider multiple loci influencing dispersal, as well as non-additive effects such as dominance and epistasis, showing that the genetic basis of dispersal can influence evolutionary rates and outcomes, especially under non-equilibrium conditions. For example, the number of loci controlling dispersal can influence projected rates of dispersal evolution during range shifts and corresponding demographic impacts. Incorporating more realism in the genetic architecture of dispersal is thus necessary to enable models to move beyond the purely theoretical towards making more useful predictions of evolutionary and ecological dynamics under current and future environmental conditions. To inform these advances, empirical studies need to answer outstanding questions concerning whether specific genes underlie dispersal variation, the genetic architecture of context-dependent dispersal phenotypes and behaviours, and correlations among dispersal and other traits.

https://onlinelibrary.wiley.com/doi/pdf/10.1111/brv.12356

Genetics of Dispersal

Synthesizing multiple data types for biological conservation using integrated population models

https://besjournals.onlinelibrary.wiley.com/doi/epdf/10.1111/1365-2664.13080

Evaluating population viability and efficacy of conservation management using integrated population models

/pdf/addressing-data-integration-challenges-to-link-ecological-2m8jrfm6jq.pdf

Addressing data integration challenges to link ecological processes across scales

Quantifying how climate and land use factors drive population dynamics at regional scales is complex because it depends on the extent of spatial and temporal synchrony among local populations, and the integration of population processes throughout a species’ annual cycle. We modeled weekly, site-specific summer abundance (1994–2013) of monarch butterflies Danaus plexippus at sites across Illinois, USA to assess relative associations of monarch abundance with climate and land use variables during the winter, spring, and summer stages of their annual cycle. We developed negative binomial regression models to estimate monarch abundance during recruitment in Illinois as a function of local climate, site-specific crop cover, and county-level herbicide (glyphosate) application. We also incorporated cross-seasonal covariates, including annual abundance of wintering monarchs in Mexico and climate conditions during spring migration and breeding in Texas, USA. We provide the first empirical evidence of a negative association between county-level glyphosate application and local abundance of adult monarchs, particularly in areas of concentrated agriculture. However, this association was only evident during the initial years of the adoption of herbicide-resistant crops (1994–2003). We also found that wetter and, to a lesser degree, cooler springs in Texas were associated with higher summer abundances in Illinois, as were relatively cool local summer temperatures in Illinois. Site-specific abundance of monarchs averaged approximately one fewer per site from 2004–2013 than during the previous decade, suggesting a recent decline in local abundance of monarch butterflies on their summer breeding grounds in Illinois. Our results demonstrate that seasonal climate and land use are associated with trends in adult monarch abundance, and our approach highlights the value of considering fine-resolution temporal fluctuations in population-level responses to environmental conditions when inferring the dynamics of migratory species.

Local and cross-seasonal associations of climate and land use with abundance of monarch butterflies Danaus plexippus

Occupancy modeling is a widely used analytical technique for assessing species distributions and range dynamics. However, occupancy analyses ignore variation in abundances of occupied sites, even though site abundances affect many of the parameters being estimated (e.g., extinction, colonization, detection probability). We introduce a new model (“dynamic N-occupancy”) capable of providing accurate estimates of local abundance, population gains (reproduction/immigration), and apparent survival probabilities while accounting for imperfect detection using only detection/nondetection data. Our model utilizes heterogeneity in detection based on variations in site abundances to estimate latent demographic rates via a dynamic N-mixture modeling framework. We validate our model using simulations across a wide range of values and examine the data requirements, including the number of years and survey sites needed, for unbiased and precise estimation of parameters. We apply our model to estimate spatio-temporal heterogeneity in abundances of barred owls (Strix varia) within a recently invaded region in Oregon (USA). Estimates of apparent survival and population gains are consistent with those from a nearby radio-tracking study and elucidate how barred owl abundances have increased dramatically over time. The dynamic N-occupancy model greatly improves inferences on individual-level population processes from occupancy data by explicitly modeling the latent population structure.

This article is protected by copyright. All rights reserved.

https://www.fs.fed.us/pnw/pubs/journals/pnw_2016_rossman001.pdf

Sarah P. Saunders

Papers

Synthesizing multiple data types for biological conservation using integrated population models

Evaluating population viability and efficacy of conservation management using integrated population models

Addressing data integration challenges to link ecological processes across scales

Local and cross-seasonal associations of climate and land use with abundance of monarch butterflies Danaus plexippus

Dynamic N-occupancy models: estimating demographic rates and local abundance from detection-nondetection data