When mechanism matters: Bayesian forecasting using models of ecological diffusion

Ecological diffusion is a theory that can be used to understand and forecast spatio‐temporal processes such as dispersal, invasion, and the spread of disease. Hierarchical Bayesian modelling provides a framework to make statistical inference and probabilistic forecasts, using mechanistic ecological models. To illustrate, we show how hierarchical Bayesian models of ecological diffusion can be implemented for large data sets that are distributed densely across space and time. The hierarchical Bayesian approach is used to understand and forecast the growth and geographic spread in the prevalence of chronic wasting disease in white‐tailed deer (Odocoileus virginianus). We compare statistical inference and forecasts from our hierarchical Bayesian model to phenomenological regression‐based methods that are commonly used to analyse spatial occurrence data. The mechanistic statistical model based on ecological diffusion led to important ecological insights, obviated a commonly ignored type of collinearity, and was the most accurate method for forecasting.     

Forecasting species ranges by statistical estimation of ecological niches and spatial population dynamics

Aim The study and prediction of species–environment relationships is currently mainly based on species distribution models. These purely correlative models neglect spatial population dynamics and assume that species distributions are in equilibrium with their environment. This causes biased estimates of species niches and handicaps forecasts of range dynamics under environmental change. Here we aim to develop an approach that statistically estimates process‐based models of range dynamics from data on species distributions and permits a more comprehensive quantification of forecast uncertainties. Innovation We present an approach for the statistical estimation of process‐based dynamic range models (DRMs) that integrate Hutchinson's niche concept with spatial population dynamics. In a hierarchical Bayesian framework the environmental response of demographic rates, local population dynamics and dispersal are estimated conditional upon each other while accounting for various sources of uncertainty. The method thus: (1) jointly infers species niches and spatiotemporal population dynamics from occurrence and abundance data, and (2) provides fully probabilistic forecasts of future range dynamics under environmental change. In a simulation study, we investigate the performance of DRMs for a variety of scenarios that differ in both ecological dynamics and the data used for model estimation. Main conclusions Our results demonstrate the importance of considering dynamic aspects in the collection and analysis of biodiversity data. In combination with informative data, the presented framework has the potential to markedly improve the quantification of ecological niches, the process‐based understanding of range dynamics and the forecasting of species responses to environmental change. It thereby strengthens links between biogeography, population biology and theoretical and applied ecology.     

A Hierarchical Bayesian Model to Quantify Uncertainty of Stream Water Temperature Forecasts

Providing generic and cost effective modelling approaches to reconstruct and forecast freshwater temperature using predictors as air temperature and water discharge is a prerequisite to understanding ecological processes underlying the impact of water temperature and of global warming on continental aquatic ecosystems. Using air temperature as a simple linear predictor of water temperature can lead to significant bias in forecasts as it does not disentangle seasonality and long term trends in the signal. Here, we develop an alternative approach based on hierarchical Bayesian statistical time series modelling of water temperature, air temperature and water discharge using seasonal sinusoidal periodic signals and time varying means and amplitudes. Fitting and forecasting performances of this approach are compared with that of simple linear regression between water and air temperatures using i) an emotive simulated example, ii) application to three French coastal streams with contrasting bio-geographical conditions and sizes. The time series modelling approach better fit data and does not exhibit forecasting bias in long term trends contrary to the linear regression. This new model also allows for more accurate forecasts of water temperature than linear regression together with a fair assessment of the uncertainty around forecasting. Warming of water temperature forecast by our hierarchical Bayesian model was slower and more uncertain than that expected with the classical regression approach. These new forecasts are in a form that is readily usable in further ecological analyses and will allow weighting of outcomes from different scenarios to manage climate change impacts on freshwater wildlife.     

Progress and opportunities in advancing near-term forecasting of freshwater quality

Near-term freshwater forecasts, defined as sub-daily to decadal future predictions of a freshwater variable with quantified uncertainty, are urgently needed to improve water quality management as freshwater ecosystems exhibit greater variability due to global change. Shifting baselines in freshwater ecosystems due to land use and climate change prevent managers from relying on historical averages for predicting future conditions, necessitating near-term forecasts to mitigate freshwater risks to human health and safety (e.g., flash floods, harmful algal blooms) and ecosystem services (e.g., water-related recreation and tourism). To assess the current state of freshwater forecasting and identify opportunities for future progress, we synthesized freshwater forecasting papers published in the past 5 years. We found that freshwater forecasting is currently dominated by near-term forecasts of water quantity and that near-term water quality forecasts are fewer in number and in the early stages of development (i.e., non-operational) despite their potential as important preemptive decision support tools. We contend that more freshwater quality forecasts are critically needed and that near-term water quality forecasting is poised to make substantial advances based on examples of recent progress in forecasting methodology, workflows, and end-user engagement. For example, current water quality forecasting systems can predict water temperature, dissolved oxygen, and algal bloom/toxin events 5 days ahead with reasonable accuracy. Continued progress in freshwater quality forecasting will be greatly accelerated by adapting tools and approaches from freshwater quantity forecasting (e.g., machine learning modeling methods). In addition, future development of effective operational freshwater quality forecasts will require substantive engagement of end users throughout the forecast process, funding, and training opportunities. Looking ahead, near-term forecasting provides a hopeful future for freshwater management in the face of increased variability and risk due to global change, and we encourage the freshwater scientific community to incorporate forecasting approaches in water quality research and management.     

A Bayesian forecasting model: predicting U.S. male mortality

This article presents a Bayesian approach to forecast mortality rates. This approach formalizes the Lee-Carter method as a statistical model accounting for all sources of variability. Markov chain Monte Carlo methods are used to fit the model and to sample from the posterior predictive distribution. This paper also shows how multiple imputations can be readily incorporated into the model to handle missing data and presents some possible extensions to the model. The methodology is applied to U.S. male mortality data. Mortality rate forecasts are formed for the period 1990-1999 based on data from 1959-1989. These forecasts are compared to the actual observed values. Results from the forecasts show the Bayesian prediction intervals to be appropriately wider than those obtained from the Lee-Carter method, correctly incorporating all known sources of variability. An extension to the model is also presented and the resulting forecast variability appears better suited to the observed data.     

An ensemble data assimilation modeling system for operational outdoor microalgae growth forecasting

Microalgae have received increasing attention as a potential feedstock for biofuel or biobased products. Forecasting the microalgae growth is beneficial for managers in planning pond operations and harvesting decisions. This study proposed a biomass forecasting system comprised of the Huesemann Algae Biomass Growth Model (BGM), the Modular Aquatic Simulation System in Two Dimensions (MASS2), ensemble data assimilation (DA), and numerical weather prediction Global Ensemble Forecast System (GEFS) ensemble meteorological forecasts. The novelty of this study is to seek the use of ensemble DA to improve both BGM and MASS2 model initial conditions with the assimilation of biomass and water temperature measurements and consequently improve short-term biomass forecasting skills. This study introduces the theory behind the proposed integrated biomass forecasting system, with an application undertaken in pseudo-real-time in three outdoor ponds cultured with Chlorella sorokiniana in Delhi, California, United States. Results from all three case studies demonstrate that the biomass forecasting system improved the short-term (i.e., 7-day) biomass forecasting skills by about 60% on average, comparing to forecasts without using the ensemble DA method. Given the satisfactory performances achieved in this study, it is probable that the integrated BGM-MASS2-DA forecasting system can be used operationally to inform managers in making pond operation and harvesting planning decisions.     

Complexity is costly: a meta‐analysis of parametric and non‐parametric methods for short‐term population forecasting

Short‐term forecasts based on time series of counts or survey data are widely used in population biology to provide advice concerning the management, harvest and conservation of natural populations. A common approach to produce these forecasts uses time‐series models, of different types, fit to time series of counts. Similar time‐series models are used in many other disciplines, however relative to the data available in these other disciplines, population data are often unusually short and noisy and models that perform well for data from other disciplines may not be appropriate for population data. In order to study the performance of time‐series forecasting models for natural animal population data, we assembled 2379 time series of vertebrate population indices from actual surveys. Our data were comprised of three vastly different types: highly variable (marine fish productivity), strongly cyclic (adult salmon counts), and small variance but long‐memory (bird and mammal counts). We tested the predictive performance of 49 different forecasting models grouped into three broad classes: autoregressive time‐series models, non‐linear regression‐type models and non‐parametric time‐series models. Low‐dimensional parametric autoregressive models gave the most accurate forecasts across a wide range of taxa; the most accurate model was one that simply treated the most recent observation as the forecast. More complex parametric and non‐parametric models performed worse, except when applied to highly cyclic species. Across taxa, certain life history characteristics were correlated with lower forecast error; specifically, we found that better forecasts were correlated with attributes of slow growing species: large maximum age and size for fishes and high trophic level for birds. Synthesis Evaluating the data support for multiple plausible models has been an integral focus of many ecological analyses. However, the most commonly used tools to quantify support have weighted models’ hindcasting and forecasting abilities. For many applications, predicting the past may be of little interest. Concentrating only on the future predictive performance of time series models, we performed a forecasting competition among many different kinds of statistical models, applying each to many different kinds of vertebrate time series of population abundance. Low‐dimensional (simple) models performed well overall, but more complex models did slightly better when applied to time series of cyclic species (e.g. salmon).     

Application of Statistical Classification Technique to the Forecasting of Outcomes of Diseases

A probabilistic statistical model based on statistical classification is proposed for disease outcome forecasting. In particular, cardiac infarction outcome is forecasted and a table of the forecasting results is given. A conclusion of theoretical character is made about the preferable use of a non-uniform band width in the construction of a general histogram for unknown distribution density estimation.     

物候模式识别在生态动力预报中的应用

以物候资料和数值天气预报模式输出图为基础,应用模式识别和数理逻辑判断的自动化技术,阐述制作生态动力预报的原理、方法和步骤.生态动力预报技术使传统的物候学在气象学和自动化技术支持下,扩展应用到生态预报业务领域,使物候预报从单站预报阶段发展到区域预报阶段,同时促进了农业气象预报方法从定性、统计阶段向动力预报阶段发展.该方法在农作物播种、长势、灌溉与施肥、病虫害防治等方面具有广阔的应用前景.     

How will climate novelty influence ecological forecasts? Using the Quaternary to assess future reliability

Future climates are projected to be highly novel relative to recent climates. Climate novelty challenges models that correlate ecological patterns to climate variables and then use these relationships to forecast ecological responses to future climate change. Here, we quantify the magnitude and ecological significance of future climate novelty by comparing it to novel climates over the past 21,000 years in North America. We then use relationships between model performance and climate novelty derived from the fossil pollen record from eastern North America to estimate the expected decrease in predictive skill of ecological forecasting models as future climate novelty increases. We show that, in the high emissions scenario (RCP 8.5) and by late 21st century, future climate novelty is similar to or higher than peak levels of climate novelty over the last 21,000 years. The accuracy of ecological forecasting models is projected to decline steadily over the coming decades in response to increasing climate novelty, although models that incorporate co‐occurrences among species may retain somewhat higher predictive skill. In addition to quantifying future climate novelty in the context of late Quaternary climate change, this work underscores the challenges of making reliable forecasts to an increasingly novel future, while highlighting the need to assess potential avenues for improvement, such as increased reliance on geological analogs for future novel climates and improving existing models by pooling data through time and incorporating assemblage‐level information.     

Long-term and short-term forecast models for Poaceae (grass) pollen in Poznań, Poland,constructed using regression analysis

Airborne concentrations of Poaceae pollen have been monitored in Poznań for more than 10 years and the length of the dataset is now considered sufficient for statistical analysis. The objective of this paper is to produce long-range forecasts that predict certain characteristics of the grass pollen season (such as the start, peak and end dates of the grass pollen season) as well as short-term forecasts that predict daily variations in grass pollen counts for the next day or next few days throughout the main grass pollen season. The method of forecasting was regression analysis. Correlation analysis was used to examine the relationship between grass pollen counts and the factors that affect its production, release and dispersal. The models were constructed with data from 1994 to 2004 and tested on data from 2005 and 2006. The forecast models predicted the start of the grass pollen season to within two days and achieved 61% and 70% accuracy on a scale of 1–4 when forecasting variations in daily average grass pollen counts in 2005 and 2006, respectively. This study has emphasised how important the weather during the few weeks or months preceding pollination is to grass pollen production, and draws attention to the importance of considering large-scale patterns of climate variability (indices of the North Atlantic Oscillation) when constructing forecast models for allergenic pollen.     

Phenology predicts the native and invasive range limits of common ragweed

Accurate models for species' distributions are needed to forecast the progress and impacts of alien invasive species and assess potential range‐shifting driven by global change. Although this has traditionally been achieved through data‐driven correlative modelling, robustly extrapolating these models into novel climatic conditions is challenging. Recently, a small number of process‐based or mechanistic distribution models have been developed to complement the correlative approaches. However, tests of these models are lacking, and there are very few process‐based models for invasive species. We develop a method for estimating the range of a globally invasive species, common ragweed (Ambrosia artemisiifolia L.), from a temperature‐ and photoperiod‐driven phenology model. The model predicts the region in which ragweed can reach reproductive maturity before frost kills the adult plants in autumn. This aligns well with the poleward and high‐elevation range limits in its native North America and in invaded Europe, clearly showing that phenological constraints determine the cold range margins of the species. Importantly, this is a ‘forward’ prediction made entirely independently of the distribution data. Therefore, it allows a confident and biologically informed forecasting of further invasion and range shifting driven by climate change. For ragweed, such forecasts are extremely important as the species is a serious crop weed and its airborne pollen is a major cause of allergy and asthma in humans. Our results show that phenology can be a key determinant of species' range margins, so integrating phenology into species distribution models offers great potential for the mechanistic modelling of range dynamics.     

The cost of complexity in forecasts of population abundances is reduced but not eliminated by borrowing information across space using a hierarchical approach

Anticipating ecological changes is paramount if we are to manage biodiversity and the services they provide to humanity. When forecasting population abundances, studies have shown that simple statistical models often have better forecast performance than complex models. These studies have evaluated forecasts of models fitted separately to data from single sites (single-site approach). Here, we aim to contrast the forecast performance and forecast horizon between a single-site approach and a hierarchical multi-site approach where a single model is fitted to data from multiple-sites, and to investigate how they vary with model complexity. We used 5273 population time series on 84 species from the Swedish breeding bird survey program, and found that simple models on average had better forecast performance and forecast horizon than complex models for both the single- and the multi-site approach. However, the cost of complexity was considerably reduced under the multi-site approach, while the proportion of species for which complex models had better forecast performance than simple models was also much larger than under the single-site approach. This suggests that the multi-site approach is useful for inclusion of more detailed processes which may benefit forecasts for some species and which are of importance for managers. Still, our results are in line with some previous studies suggesting that it is surprisingly difficult to construct complex models that, on average, beat trivial baseline forecasts.     

A Simulation Optimization Approach to Epidemic Forecasting

Reliable forecasts of influenza can aid in the control of both seasonal and pandemic outbreaks. We introduce a simulation optimization (SIMOP) approach for forecasting the influenza epidemic curve. This study represents the final step of a project aimed at using a combination of simulation, classification, statistical and optimization techniques to forecast the epidemic curve and infer underlying model parameters during an influenza outbreak. The SIMOP procedure combines an individual-based model and the Nelder-Mead simplex optimization method. The method is used to forecast epidemics simulated over synthetic social networks representing Montgomery County in Virginia, Miami, Seattle and surrounding metropolitan regions. The results are presented for the first four weeks. Depending on the synthetic network, the peak time could be predicted within a 95% CI as early as seven weeks before the actual peak. The peak infected and total infected were also accurately forecasted for Montgomery County in Virginia within the forecasting period. Forecasting of the epidemic curve for both seasonal and pandemic influenza outbreaks is a complex problem, however this is a preliminary step and the results suggest that more can be achieved in this area.     

Time series predictions with neural nets: Application to airborne pollen forecasting

Pollen allergy is a common disease causing rhinoconjunctivitis (hay fever) in 5–10% of the population. Medical studies have indicated that pollen related diseases could be highly reduced if future pollen contents in the air could be predicted. In this work we have developed a new forecasting method that applies the ability of neural nets to predict the future behaviour of chaotic systems in order to make accurate predictions of the airborne pollen concentration. The method requires that the neural net be fed with non-zero values, which restricts the method predictions to the period following the start of pollen flight. The operational method outlined here constitutes a different point of view with respect to the more generally used forecasts of time series analysis, which require input of many meteorological parameters. Excellent forecasts were obtained training a neural net by using only the time series pollen concentration values.     

Ecological forecasting under climate change: the case of Baltic cod

Good decision making for fisheries and marine ecosystems requires a capacity to anticipate the consequences of management under different scenarios of climate change. The necessary ecological forecasting calls for ecosystem-based models capable of integrating multiple drivers across trophic levels and properly including uncertainty. The methodology presented here assesses the combined impacts of climate and fishing on marine food-web dynamics and provides estimates of the confidence envelope of the forecasts. It is applied to cod (Gadus morhua) in the Baltic Sea, which is vulnerable to climate-related decline in salinity owing to both direct and indirect effects (i.e. through species interactions) on early-life survival. A stochastic food web-model driven by regional climate scenarios is used to produce quantitative forecasts of cod dynamics in the twenty-first century. The forecasts show how exploitation would have to be adjusted in order to achieve sustainable management under different climate scenarios.     

Matching the forecast horizon with the relevant spatial and temporal processes and data sources

Most phenomenological, statistical models used to generate ecological forecasts take either a time-series approach, based on long-term data from one location, or a space-for-time approach, based on data describing spatial patterns across environmental gradients. However, the magnitude and even the sign of environment–response relationships detected using these two approaches often differs, leading to contrasting predictions about responses to future environmental change. Here we consider how the forecast horizon determines whether more accurate predictions come from the time-series approach, the space-for-time approach or a combination of the two. As proof of concept, we use simulated case studies to show that forecasts for short and long forecast horizons need to focus on different ecological processes, which are reflected in different kinds of data. First, we simulated population or community dynamics under stationary temperature using two simple, mechanistic models. Second, we fit statistical models to the simulated data using a time-series approach, a space-for-time approach or a weighted average. We then forecast the response to a temperature increase using the statistical models, and compared these forecasts to temperature effects simulated by the mechanistic models. We found that the time-series approach made accurate short-term predictions because it captured initial conditions and effects of fast processes such as birth and death. The space-for-time approach made more accurate long-term predictions because it better captured the influence of slower processes such as evolutionary and ecological selection. The weighted average made accurate predictions at all time scales, including intermediate time-scales where the other two approaches performed poorly. A weighted average of time-series and space-for-time approaches shows promise, but making this weighted model operational will require new research to predict the rate at which slow processes begin to influence dynamics.     

Winter weather and waterfowl surveys in north-western Ontario, Canada

Abstract Aim An analysis is presented to examine whether variation in breeding waterfowl estimates can be explained by weather patterns prior to annual surveys. Location The location of the study is north‐western Ontario, Canada. Methods Annual, systematic survey data for breeding waterfowl are available from the 1950s to the present for north‐western Ontario. Regional monthly climate data for this area were compiled using weather data derived from interpolated annual climate surfaces. These data were analysed using stepwise multiple linear regression for each species and for waterfowl functional groups to assess whether monthly climate data accounted for some of the variation in waterfowl numbers. Results For all dabbling ducks pooled, 12% of the variation in annual abundance was explained by April temperatures, with more dabbling ducks observed in years when April was relatively cool. For diving ducks, 23% of the variation in pooled abundance was explained by April temperatures and February precipitation, where more diving ducks were observed in years when February had relatively less precipitation and April was cool. Patterns for individual species varied. Main conclusions Mean monthly weather data for months prior to surveys explained some of the variation in numbers of waterfowl observed in annual surveys. This suggests that future incorporation of weather data into waterfowl population models may help refine population estimates.     

Can the past predict the future? Experimental tests of historically based population models

A frequently advocated approach for forecasting the population‐level impacts of climate change is to project models based on historical, observational relationships between climate and demographic rates. Despite the potential pitfalls of this approach, few historically based population models have been experimentally validated. We conducted a precipitation manipulation experiment to test population models fit to observational data collected from the 1930s to the 1970s for six prairie forb species. We used the historical population models to predict experimental responses to the precipitation manipulations, and compared these predictions to ones generated by a statistical model fit directly to the experimental data. For three species, a sensitivity analysis of the effects of precipitation and grass cover on forb population growth showed consistent results for the historical population models and the contemporary statistical models. Furthermore, the historical population models predicted population growth rates in the experimental plots as well or better than the statistical models, ignoring variation explained by spatial random effects and local density‐dependence. However, for the remaining three species, the sensitivity analyses showed that the historical and statistical models predicted opposite effects of precipitation on population growth, and the historical models were very poor predictors of experimental responses. For these species, historical observations were not well replicated in space, and for two of them the historical precipitation‐demography correlations were weak. Our results highlight the strengths and weaknesses of observational and experimental approaches, and increase our confidence in extrapolating historical relationships to predict population responses to climate change, at least when the historical correlations are strong and based on well‐replicated observations.     

Partitioning and mapping uncertainties in ensembles of forecasts of species turnover under climate change

Forecasts of species range shifts under climate change are fraught with uncertainties and ensemble forecasting may provide a framework to deal with such uncertainties. Here, a novel approach to partition the variance among modeled attributes, such as richness or turnover, and map sources of uncertainty in ensembles of forecasts is presented. We model the distributions of 3837 New World birds and project them into 2080. We then quantify and map the relative contribution of different sources of uncertainty from alternative methods for niche modeling, general circulation models (AOGCM), and emission scenarios. The greatest source of uncertainty in forecasts of species range shifts arises from using alternative methods for niche modeling, followed by AOGCM, and their interaction. Our results concur with previous studies that discovered that projections from alternative models can be extremely varied, but we provide a new analytical framework to examine uncertainties in models by quantifying their importance and mapping their patterns.