Forecasting species range dynamics with process‐explicit models: matching methods to applications

Knowing where species occur is fundamental to many ecological and environmental applications. Species distribution models (SDMs) are typically based on correlations between species occurrence data and environmental predictors, with ecological processes captured only implicitly. However, there is a growing interest in approaches that explicitly model processes such as physiology, dispersal, demography and biotic interactions. These models are believed to offer more robust predictions, particularly when extrapolating to novel conditions. Many process–explicit approaches are now available, but it is not clear how we can best draw on this expanded modelling toolbox to address ecological problems and inform management decisions. Here, we review a range of process–explicit models to determine their strengths and limitations, as well as their current use. Focusing on four common applications of SDMs – regulatory planning, extinction risk, climate refugia and invasive species – we then explore which models best meet management needs. We identify barriers to more widespread and effective use of process‐explicit models and outline how these might be overcome. As well as technical and data challenges, there is a pressing need for more thorough evaluation of model predictions to guide investment in method development and ensure the promise of these new approaches is fully realised.     

Colonization and persistence ability explain the extent to which plant species fill their potential range

Aim How species traits and environmental conditions affect biogeographical dynamics is poorly understood. Here we test whether estimates of a species’ evolutionary age, colonization and persistence ability can explain its current ‘range filling’ (the ratio between realized and potential range size). Location Fynbos biome (Cape Floristic Region, South Africa). Methods For 37 species of woody plants (Proteaceae), we estimate range filling using atlas data and distribution models, evolutionary age using molecular phylogenies, and persistence ability using estimates of individual longevity (which determines the probability of extinction of local populations). Colonization ability is estimated from validated process‐based seed dispersal models, the arrangement of potential habitat, and data on local abundance. To relate interspecific variation in range filling to evolutionary age, colonization and persistence ability, we use two complementary model types: phenomenological linear models and the process‐based metapopulation model of Levins. Results Linear model analyses show that range filling increases with a species’ colonization and persistence ability but is not affected by species age. Moreover, colonization ability is a better predictor of range filling than its component variables (local abundance and dispersal ability). The phylogenetically independent interaction between colonization and persistence ability is significant (P < 0.05) for 97% of 180 alternative phylogenies. While the selected linear model explains 42% of the variance in arcsine transformed range filling, the Levins model performs more poorly. It overestimates range filling for realistic parameter values and produces unrealistic parameter estimates when fitted statistically. Main conclusions Colonization and local extinction seem to shape Proteaceae range dynamics on ecological rather than macroevolutionary time‐scales. Our results suggest that the positive abundance–range size relationship in this group is due primarily to the effect of abundance on colonization. In summary, this study contributes to a process‐based understanding of range dynamics and highlights the importance of colonization for the future survival of Fynbos Proteaceae.     

Benchmarking novel approaches for modelling species range dynamics

Increasing biodiversity loss due to climate change is one of the most vital challenges of the 21st century. To anticipate and mitigate biodiversity loss, models are needed that reliably project species’ range dynamics and extinction risks. Recently, several new approaches to model range dynamics have been developed to supplement correlative species distribution models (SDMs), but applications clearly lag behind model development. Indeed, no comparative analysis has been performed to evaluate their performance. Here, we build on process‐based, simulated data for benchmarking five range (dynamic) models of varying complexity including classical SDMs, SDMs coupled with simple dispersal or more complex population dynamic models (SDM hybrids), and a hierarchical Bayesian process‐based dynamic range model (DRM). We specifically test the effects of demographic and community processes on model predictive performance. Under current climate, DRMs performed best, although only marginally. Under climate change, predictive performance varied considerably, with no clear winners. Yet, all range dynamic models improved predictions under climate change substantially compared to purely correlative SDMs, and the population dynamic models also predicted reasonable extinction risks for most scenarios. When benchmarking data were simulated with more complex demographic and community processes, simple SDM hybrids including only dispersal often proved most reliable. Finally, we found that structural decisions during model building can have great impact on model accuracy, but prior system knowledge on important processes can reduce these uncertainties considerably. Our results reassure the clear merit in using dynamic approaches for modelling species’ response to climate change but also emphasize several needs for further model and data improvement. We propose and discuss perspectives for improving range projections through combination of multiple models and for making these approaches operational for large numbers of species.     

Predicting changes in the distribution and abundance of species under environmental change

Environmental changes are expected to alter both the distribution and the abundance of organisms. A disproportionate amount of past work has focused on distribution only, either documenting historical range shifts or predicting future occurrence patterns. However, simultaneous predictions of abundance and distribution across landscapes would be far more useful. To critically assess which approaches represent advances towards the goal of joint predictions of abundance and distribution, we review recent work on changing distributions and on effects of environmental drivers on single populations. Several methods have been used to predict changing distributions. Some of these can be easily modified to also predict abundance, but others cannot. In parallel, demographers have developed a much better understanding of how changing abiotic and biotic drivers will influence growth rate and abundance in single populations. However, this demographic work has rarely taken a landscape perspective and has largely ignored the effects of intraspecific density. We advocate a synthetic approach in which population models accounting for both density dependence and effects of environmental drivers are used to make integrated predictions of equilibrium abundance and distribution across entire landscapes. Such predictions would constitute an important step forward in assessing the ecological consequences of environmental changes.     

Estimating indices of range shifts in birds using dynamic models when detection is imperfect

There is intense interest in basic and applied ecology about the effect of global change on current and future species distributions. Projections based on widely used static modeling methods implicitly assume that species are in equilibrium with the environment and that detection during surveys is perfect. We used multiseason correlated detection occupancy models, which avoid these assumptions, to relate climate data to distributional shifts of Louisiana Waterthrush in the North American Breeding Bird Survey (BBS) data. We summarized these shifts with indices of range size and position and compared them to the same indices obtained using more basic modeling approaches. Detection rates during point counts in BBS surveys were low, and models that ignored imperfect detection severely underestimated the proportion of area occupied and slightly overestimated mean latitude. Static models indicated Louisiana Waterthrush distribution was most closely associated with moderate temperatures, while dynamic occupancy models indicated that initial occupancy was associated with diurnal temperature ranges and colonization of sites was associated with moderate precipitation. Overall, the proportion of area occupied and mean latitude changed little during the 1997–2013 study period. Near‐term forecasts of species distribution generated by dynamic models were more similar to subsequently observed distributions than forecasts from static models. Occupancy models incorporating a finite mixture model on detection – a new extension to correlated detection occupancy models – were better supported and may reduce bias associated with detection heterogeneity. We argue that replacing phenomenological static models with more mechanistic dynamic models can improve projections of future species distributions. In turn, better projections can improve biodiversity forecasts, management decisions, and understanding of global change biology.     

Integral projection models perform better for small demographic data sets than matrix population models: a case study of two perennial herbs

1. Matrix population models are widely used to describe population dynamics, conduct population viability analyses and derive management recommendations for plant populations. For endangered or invasive species, management decisions are often based on small demographic data sets. Hence, there is a need for population models which accurately assess population performance from such small data sets.
2. We used demographic data on two perennial herbs with different life histories to compare the accuracy and precision of the traditional matrix population model and the recently developed integral projection model (IPM) in relation to the amount of data.
3. For large data sets both matrix models and IPMs produced identical estimates of population growth rate (λ). However, for small data sets containing fewer than 300 individuals, IPMs often produced smaller bias and variance for λ than matrix models despite different matrix structures and sampling techniques used to construct the matrix population models.
4. Synthesis and applications . Our results suggest that the smaller bias and variance of λ estimates make IPMs preferable to matrix population models for small demographic data sets with a few hundred individuals. These results are likely to be applicable to a wide range of herbaceous, perennial plant species where demographic fate can be modelled as a function of a continuous state variable such as size. We recommend the use of IPMs to assess population performance and management strategies particularly for endangered or invasive perennial herbs where little demographic data are available.     

Pushed beyond the brink: Allee effects,environmental stochasticity,and extinction

To understand the interplay between environmental stochasticity and Allee effects, we analyse persistence, asymptotic extinction, and conditional persistence for stochastic difference equations. Our analysis reveals that persistence requires that the geometric mean of fitness at low densities is greater than one. When this geometric mean is less than one, asymptotic extinction occurs with high probability for low initial population densities. Additionally, if the population only experiences positive density-dependent feedbacks, conditional persistence occurs provided the geometric mean of fitness at high population densities is greater than one. However, if the population experiences both positive and negative density-dependent feedbacks, conditional persistence only occurs if environmental fluctuations are sufficiently small. We illustrate counter-intuitively that environmental fluctuations can increase the probability of persistence when populations are initially at low densities, and can cause asymptotic extinction of populations experiencing intermediate predation rates despite conditional persistence occurring at higher predation rates.     

外来入侵物种的风险评估定量模型及应用

预防生物入侵的一个重要手段是对外来物种进行风险评估,应用模型则是定量评估的必备方法。本文简述了常用的适生性风险评估模型,概述了诸如遗传算法、模糊包络模型、自组织特征映射网络等较新的理论方法,它们使用环境变量和物种实际分布数据,利用不同的机理模型预测物种潜在分布区。本文还综述了适用于研究物种扩散性的模型,积分差分方程模型可以模拟物种扩散行为,元胞自动机模型可以揭示种间竞争关系,景观中性模型大多用于种群动态等生态过程的研究。     

Population dynamics can be more important than physiological limits for determining range shifts under climate change

Evidence is accumulating that species' responses to climate changes are best predicted by modelling the interaction of physiological limits, biotic processes and the effects of dispersal‐limitation. Using commercially harvested blacklip (Haliotis rubra) and greenlip abalone (Haliotis laevigata) as case studies, we determine the relative importance of accounting for interactions among physiology, metapopulation dynamics and exploitation in predictions of range (geographical occupancy) and abundance (spatially explicit density) under various climate change scenarios. Traditional correlative ecological niche models (ENM) predict that climate change will benefit the commercial exploitation of abalone by promoting increased abundances without any reduction in range size. However, models that account simultaneously for demographic processes and physiological responses to climate‐related factors result in future (and present) estimates of area of occupancy (AOO) and abundance that differ from those generated by ENMs alone. Range expansion and population growth are unlikely for blacklip abalone because of important interactions between climate‐dependent mortality and metapopulation processes; in contrast, greenlip abalone should increase in abundance despite a contraction in AOO. The strongly non‐linear relationship between abalone population size and AOO has important ramifications for the use of ENM predictions that rely on metrics describing change in habitat area as proxies for extinction risk. These results show that predicting species' responses to climate change often require physiological information to understand climatic range determinants, and a metapopulation model that can make full use of this data to more realistically account for processes such as local extirpation, demographic rescue, source‐sink dynamics and dispersal‐limitation.     

Autumn larval cold tolerance does not predict the northern range limit of a widespread butterfly species

Climate change is driving range shifts, and a lack of cold tolerance is hypothesized to constrain insect range expansion at poleward latitudes. However, few, if any, studies have tested this hypothesis during autumn when organisms are subjected to sporadic low‐temperature exposure but may not have become cold‐tolerant yet. In this study, we integrated organismal thermal tolerance measures into species distribution models for larvae of the Giant Swallowtail butterfly, Papilio cresphontes (Lepidoptera: Papilionidae), living at the northern edge of its actively expanding range. Cold hardiness of field‐collected larvae was determined using three common metrics of cold‐induced physiological thresholds: the supercooling point, critical thermal minimum, and survival following cold exposure. P. cresphontes larvae were determined to be tolerant of chilling but generally die at temperatures below their SCP, suggesting they are chill‐tolerant or modestly freeze‐avoidant. Using this information, we examined the importance of low temperatures at a broad scale, by comparing species distribution models of P. cresphontes based only on environmental data derived from other sources to models that also included the cold tolerance parameters generated experimentally. Our modeling revealed that growing degree‐days and precipitation best predicted the distribution of P. cresphontes, while the cold tolerance variables did not explain much variation in habitat suitability. As such, the modeling results were consistent with our experimental results: Low temperatures in autumn are unlikely to limit the distribution of P. cresphontes. Understanding the factors that limit species distributions is key to predicting how climate change will drive species range shifts.     

Spatial variation in the magnitude and functional form of density‐dependent processes on the large skipper butterfly Ochlodes sylvanus

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Past and future demographic dynamics of alpine species: limited genetic consequences despite dramatic range contraction in a plant from the Spanish Sierra Nevada

Anthropogenic global climate change is expected to cause severe range contractions among alpine plants. Alpine areas in the Mediterranean region are of special concern because of the high abundance of endemic species with narrow ranges. This study combined species distribution models, population structure analyses and Bayesian skyline plots to trace the past and future distribution and diversity of Linaria glacialis, an endangered narrow endemic species that inhabits summits of Sierra Nevada (Spain). The results showed that: (i) the habitat of this alpine‐Mediterranean species in Sierra Nevada suffered little changes during glacial and interglacial stages of late Quaternary; (ii) climatic oscillations in the last millennium (Medieval Warm Period and Little Ice Age) moderately affected the demographic trends of L. glacialis; (iii) future warming conditions will cause severe range contractions; and (iv) genetic diversity will not diminish at the same pace as the distribution range. As a consequence of the low population structure of this species, genetic impoverishment in the alpine zones of Sierra Nevada should be limited during range contraction. We conclude that maintenance of large effective population sizes via high mutation rates and high levels of gene flow may promote the resilience of alpine plant species when confronted with global warming.     

Modelling the local dynamics of the zebra mussel (Dreissena polymorpha)

1. The bivalve Dreissena polymorpha has invaded many freshwater ecosystems worldwide in recent decades. Because of their high fecundity and ability to settle on almost any solid substratum, zebra mussels usually outcompete the resident species and cause severe damage to waterworks. Time series of D. polymorpha densities display a variety of dynamical patterns, including very irregular behaviours. Unfortunately, there is a lack of mathematical modelling that could explain these patterns. 2. Here, we propose a very simple discrete‐time population model with age structure and density dependence that can generate realistic dynamics. Most of the model parameters can be derived from existing data on D. polymorpha. Some of them are quite variable: with respect to these we perform a sensitivity analysis of the model behaviour and verify that non‐equilibrial regimes (either periodic or chaotic) are the rule rather than the exception. 3. Even in circumstances where the model dynamics are aperiodic it is possible to predict total density peaks from previous peaks. This turns out to be true also in the presence of environmental stochasticity. 4. Using the stochastic model we explore the effects of age‐selective predation. Quite surprisingly, larger removal rates of adults do not always result in smaller population densities and mussel biomasses. Moreover, non‐selective predation can result in skewed size‐frequency distributions which, therefore, are not necessarily the footprint of predators’ preference for larger or smaller zebra mussels.     

Ecological memory at millennial time-scales: the importance of data constraints,species longevity and niche features

Ecological memory describes how antecedent conditions drive the dynamics of an ecological system. Palaeoecological records are paramount to understand ecological memory at millennial time-scales, but the concept is widely neglected in the literature, and a formal approach is lacking. Here, we fill such a gap by introducing a quantitative framework for ecological memory in palaeoecology, and assessing how data constraints and taxa traits shape ecological memory patterns. We simulate the population dynamics and pollen abundance of 16 virtual taxa with different life and niche traits as a response to an environmental driver. The data is processed to mimic a realistic sediment deposition and sampled at increasing depth intervals. We quantify ecological memory with Random Forests, and assess how data properties and taxa traits shape ecological memory. We find that life-span and niche features modulate the relative importance of the antecedent values of the driver and the pollen abundance over periods of 240 yr and longer. Additionally, we find that accumulation rate and decreasing pollen-sampling resolution inflate the importance of antecedent pollen abundance. Our results suggest that: 1) ecological memory patterns are sensitive to varying accumulation rates. A better understanding on the numerical basis of this effect may enable the assimilation of ecological memory concepts and methods in palaeoecology; 2) incorporating niche theory and models is essential to better understand the nature of ecological memory patterns at millennial time-scales. 3) Long-lived generalist taxa are highly decoupled from the environmental signal. This finding has implications on how we interpret the abundance-environment relationship of real taxa with similar traits, and how we use such knowledge to forecast their distribution or reconstruct past climate.     

Quantifying patch‐specific seed dispersal and local population dynamics to estimate population spread of an endangered plant species

AimHabitat loss and fragmentation impose high extinction risk upon endangered plant species globally. For many endangered plant species, as the remnant habitats become smaller and more fragmented, it is vital to estimate the population spread rate of small patches in order to effectively manage and preserve them for potential future range expansion. However, population spread rate has rarely been quantified at the patch level to inform conservation strategies and management decisions. To close this gap, we quantify the patch‐specific seed dispersal and local population dynamics of Minuartia smejkalii, which is a critically endangered plant species endemic in the Czech Republic and is of urgent conservation concern.LocationŽelivka and Hrnčíře, Czechia.MethodsWe conducted demographic analyses using population projection matrices with long‐term demographic data and used an analytic mechanistic dispersal model to simulate seed dispersal. We then used information on local population dynamics and seed dispersal to estimate the population spread rate and compared the relative contributions of seed dispersal and population growth rate to the population spread rate.ResultsWe found that although both seed dispersal and population growth rate in M. smejkalii were critically limited, the population spread rate depended more strongly on the maximal dispersal distance than on the population growth rate.Main conclusionsWe recommend conservationists to largely increase the dispersal distance of M. smejkalii. Generally, efforts made to increase seed dispersal ability could largely raise efficiency and effectiveness of conservation actions for critically endangered plant species.     

Backward bifurcations and strong Allee effects in matrix models for the dynamics of structured populations

In nonlinear matrix models, strong Allee effects typically arise when the fundamental bifurcation of positive equilibria from the extinction equilibrium at r=1 (or R₀=1) is backward. This occurs when positive feedback (component Allee) effects are dominant at low densities and negative feedback effects are dominant at high densities. This scenario allows population survival when r (or equivalently R₀) is less than 1, provided population densities are sufficiently high. For r>1 (or equivalently R₀>1) the extinction equilibrium is unstable and a strong Allee effect cannot occur. We give criteria sufficient for a strong Allee effect to occur in a general nonlinear matrix model. A juvenile–adult example model illustrates the criteria as well as some other possible phenomena concerning strong Allee effects (such as positive cycles instead of equilibria).