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Structured demographic models are among the most common and useful tools in population biology. However, the introduction of integral projection models (IPMs) has caused a profound shift in the way many demographic models are conceptualized. Some researchers have argued that IPMs, by explicitly representing demographic processes as continuous functions of state variables such as size, are more statistically efficient, biologically realistic, and accurate than classic matrix projection models, calling into question the usefulness of the many studies based on matrix models. Here, we evaluate how IPMs and matrix models differ, as well as the extent to which these differences matter for estimation of key model outputs, including population growth rates, sensitivity patterns, and life spans. First, we detail the steps in constructing and using each type of model. Second, we present a review of published demographic models, concentrating on size-based studies, which shows significant overlap in the way IPMs and matrix models are constructed and analyzed. Third, to assess the impact of various modeling decisions on demographic predictions, we ran a series of simulations based on size-based demographic data sets for five biologically diverse species. We found little evidence that discrete vital rate estimation is less accurate than continuous functions across a wide range of sample sizes or size classes (equivalently bin numbers or mesh points). Most model outputs quickly converged with modest class numbers (≥10), regardless of most other modeling decisions. Another surprising result was that the most commonly used method to discretize growth rates for IPM analyses can introduce substantial error into model outputs. Finally, we show that empirical sample sizes generally matter more than modeling approach for the accuracy of demographic outputs. Based on these results, we provide specific recommendations to those constructing and evaluating structured population models. Both our literature review and simulations question the treatment of IPMs as a clearly distinct modeling approach or one that is inherently more accurate than classic matrix models. Importantly, this suggests that matrix models, representing the vast majority of past demographic analyses available for comparative and conservation work, continue to be useful and important sources of demographic information.

Species’ geographic ranges and climatic niches are likely to be increasingly mismatched due to rapid climate change. If a species’ range and niche are out of equilibrium, then population performance should decrease from high-latitude “leading” range edges, where populations are expanding into recently ameliorated habitats, to low-latitude “trailing” range edges, where populations are contracting from newly unsuitable areas. Demographic compensation is a phenomenon whereby declines in some vital rates are offset by increases in others across time or space. In theory, demographic compensation could increase the range of environments over which populations can succeed and forestall range contraction at trailing edges. An outstanding question is whether range limits and range contractions reflect inadequate demographic compensation across environmental gradients, causing population declines at range edges. We collected demographic data from 32 populations of the scarlet monkeyflower (Erythranthe cardinalis) spanning 11° of latitude in western North America and used integral projection models to evaluate population dynamics and assess demographic compensation across the species’ range. During the 5-y study period, which included multiple years of severe drought and warming, population growth rates decreased from north to south, consistent with leading-trailing dynamics. Southern populations at the trailing range edge declined due to reduced survival, growth, and recruitment, despite compensatory increases in reproduction and faster life-history characteristics. These results suggest that demographic compensation may only delay population collapse without the return of more favorable conditions or the contribution of other buffering mechanisms such as evolutionary rescue.

1. Conservation science can be most effective in its decision-support role when seeking answers to clearly formulated questions of direct management relevance. Emerging wildlife diseases, a driver of global biodiversity loss, illustrate the challenges of performing this role: in spite of considerable research, successful disease mitigation is uncommon. Decision analysis is increasingly advocated to guide mitigation planning, but its application remains rare. 2. Using an integral projection model, we explored potential mitigation actions for avoiding population declines and the ongoing spatial spread of the fungus Batrachochytrium salamandrivorans (Bsal). This fungus has recently caused severe amphibian declines in north-western Europe and currently threatens Palearctic salamander diversity. 3. Available evidence suggests that a Bsal outbreak in a fire salamander (Salamandra salamandra) population will lead to its rapid extirpation. Treatments such as antifungals or probiotics would need to effectively interrupt transmission (reduce probability of infection by nearly 90%) in order to reduce the risk of host extirpation and successfully eradicate the pathogen. 4. Improving the survival of infected hosts is most likely to be detrimental as it increases the potential for pathogen transmission and spread. Active removal of a large proportion of the host population has some potential to locally eradicate Bsal and interrupt its spread, depending on the presence of Bsal reservoirs and on the host's spatial dynamics, which should therefore represent research priorities. 5. Synthesis and applications. Mitigation of Batrachochytrium salamandrivorans epidemics in susceptible host species is highly challenging, requiring effective interruption of transmission and radical removal of host individuals. More generally, our study illustrates the advantages of framing conservation science directly in the management decision context, rather than adapting to it a posteriori.

Positive density dependence (i.e., Allee effects) can create a threshold of population states below which extinction of the population occurs. The existence of this threshold, which can often be a complex, multi-dimensional surface, rather than a single point, is of particular importance in degraded populations for which there is a desire for successful restoration. Here, we incorporated positive density dependence into a closed, size- and age-structured integral projection model parameterized with empirical data from an eastern oyster, Crassostrea virginica, population in Pamlico Sound, North Carolina, USA. To understand the properties of the threshold surface, and implications for restoration, we introduced a general method based on a linearization of the threshold surface at its unique, unstable equilibrium. We estimated the number of oysters of a particular age (i.e., stock enhancement), or the surface area of dead shell substrate required (i.e., habitat enhancement) to move a population from an extinction trajectory to a persistence trajectory. The location of the threshold surface was strongly affected by changes in the amount of local larval retention. Traditional stock enhancement with oysters <1 yr old (i.e., spat) required three times as many oysters relative to stock enhancement with oysters between ages 3 and 7 yr old, while the success of habitat enhancement depended upon the initial size distribution of the population. The methodology described here demonstrates the importance of considering positive density dependence in oyster populations, and also provides insights into effective management and restoration strategies when dealing with a high dimensional threshold separating extinction and persistence.

Dynamic population models typically aim to predict demography and the resulting population dynamics in relation to environmental variation. However, they rarely include the diversity of individual responses to environmental changes, thus hampering our understanding of demographic mechanisms. We develop an integrated integral projection model (IPM2) that is a combination of an integrated population model (IPMpop) and an integral projection model (IPMind). IPM2 includes interactions between environmental and individual effects on demographic rates and can forecast both population size and individual trait distributions. First, we study the performance of this model using eight simulated scenarios with variable reproductive selective pressures on an individual trait. When the individual trait interacts with the environmental variable and the selective pressure on the individual trait is nonlinear, only IPM2 produces adequate predictions, because IPMind does not link predictions between the population level and observed data and because IPMpop does not include the individual trait. Second, we apply IPM2 to a population of barn swallows. The model accurately predicts trends of the barn swallow population while also providing mechanistic insights. High precipitation negatively influenced population dynamics through delaying laying dates, which lowered reproductive and survival rates. To predict the future of populations, we need to understand their individual drivers and thus include individual responses to their environment while following the entire population. As a consequence, IPM2 will improve our ability to test ecological and evolutionary hypotheses and improve the accuracy of population forecasting to aid management programs.

Extended-range (10–30 days) forecast, lying between well-developed short-range weather and long-range (monthly and seasonal) climate predictions, is one of the most challenging forecast currently faced by operational meteorological centers around the world. In this study, a set of spatial–temporal projection (STP) models was developed to predict low-frequency rainfall events at lead times of 5–30 days. We focused on early monsoon rainy season (mid April–mid July) in South China. To ensure that the model developed can be used for real-time forecast, a non-filtering method was developed to extract the low-frequency atmospheric signals of 10–60 days without using a band-pass filter. The empirical models were built based on 12-year (1996–2007) data, and independent forecast was then conducted for a 5 year (2008–2012) period. The assessment of the 5-year forecast of rainfall over South China indicates that the ensemble prediction of the STP models achieved a useful skill (with a temporal correlation coefficient exceeding 95 % confidence level) at a lead time of 20 days. The amplitude error was generally less than one standard deviation at all lead times of 5–30 days. Furthermore, the STP models provided useful probabilistic forecasts with the ranked probability skill score between 0.3–0.5 up to 30-day forecast in advance. The evaluation demonstrated that the STP models exhibited useful 10–30 days forecast skills for real-time extended-range rainfall prediction in South China.

Understanding which factors cause populations to decline begins with identifying which parts of the life cycle, and which vital rates, have changed over time. However, in a world where humans are altering the environment both rapidly and in different ways, the demographic causes of decline likely vary over time. Identifying temporal variation in demographic causes of decline is crucial to assure that conservation actions target current and not past threats. However, this has rarely been studied as it requires long time series. Here we investigate how the demography of a long-lived shorebird (the Eurasian Oystercatcher Haematopus ostralegus) has changed in the past four decades, resulting in a shift from stable dynamics to strong declines (−9% per year), and recently back to a modest decline. Since individuals of this species are likely to respond differently to environmental change, we captured individual heterogeneity through three state variables: age, breeding status, and lay date (using integral projection models). Timing of egg-laying explained significant levels of variation in reproduction, with a parabolic relationship of maximal productivity near the average lay date. Reproduction explained most variation in population growth rates, largely due to poor nest success and hatchling survival. However, the demographic causes of decline have also been in flux over the last three decades: hatchling survival was low in the 2000s but improved in the 2010s, while adult survival declined in the 2000s and remains low today. Overall, the joint action of several key demographic variables explain the decline of the oystercatcher, and improvements in a single vital rate cannot halt the decline. Conservations actions will thus need to address threats occurring at different stages of the oystercatcher’s life cycle. The dynamic nature of the threat landscape is further supported by the finding that the average individual no longer has the highest performance in the population, and emphasizes how individual heterogeneity in vital rates can play an important role in modulating population growth rates. Our results indicatethat understanding population decline in the current era requires disentangling demographic mechanisms, individual variability, and their changes over time.

Disturbances elicit both positive and negative effects on organisms; these effects vary in their strength and their timing. Effects of disturbance interval (i.e., the length of time between disturbances) on population growth will depend on both the timing and strength of positive and negative effects of disturbances. Climate change can modify the relative strengths of these positive and negative effects, leading to altered optimal disturbance intervals (the disturbance interval at which population growth rate is highest) and changes in the sensitivity of population growth rate to disturbance interval. While we know that climate may alter impacts of disturbance in some systems, we have a poor understanding of which effects of disturbance and which vital rates might drive an altered response to disturbance interval in a changing climate. We use demographic monitoring of natural populations of Dionaea muscipula, the Venus flytrap, that have experienced natural and managed fires, combined with realistic past and future climate projections, to construct climate- and fire-driven integral projection models (IPMs). We use these IPMs to compare the effect of fire return interval (FRI) on population growth rate in past and future climates. To dissect the mechanisms driving FRI response, we then construct IPMs with demographic data from an experimental manipulation of fire effects (ash addition, neighbor removal) and an accidental fire. Our results show that an FRI of 10 years is optimal for D. muscipula in past climate conditions, but a longer FRI (12 years) is optimal in future climate conditions. Further, deviations from optimal FRI reduce population growth rate dramatically in the past climate, but this reduction is muted in a future climate (future minus past sensitivity = 0.006, 95% CI [0.002, 0.011]). Finally, our experimental work suggests that fire effects are driven in part by positive, additive effects of competitor removal and ash addition immediately following a fire; for one population, both these treatments significantly increased population growth rate. Our work suggests that climate change can alter the response of populations to disturbance, highlighting the need to consider the interacting effects of multiple abiotic drivers when projecting future population growth and geographical distributions.

As the major form of coral reef regime shift, stony coral to macroalgal transitions have received considerable attention. In the Caribbean, however, regime shifts in which scleractinian corals are replaced by octocoral assemblages hold potential for maintaining reef associated communities. Accordingly, forecasting the resilience of octocoral assemblages to future disturbance regimes is necessary to understand these assemblages' capacity to maintain reef biodiversity. We parameterised integral projection models quantifying the survival, growth, and recruitment of the octocorals, Antillogorgia americana , Gorgonia ventalina , and Eunicea flexuosa, in St John, US Virgin Islands, before, during, and after severe hurricane disturbance. Using these models, we forecast the density of populations of each species under varying future hurricane regimes. We demonstrate that although hurricanes reduce population growth, A. americana , G. ventalina , and E. flexuosa each display a capacity for quick recovery following storm disturbance. Despite this recovery potential, we illustrate how the population dynamics of each species correspond with a longer-term decline in their population densities. Despite their resilience to periodic physical disturbance events, ongoing global change jeopardises the future viability of octocoral assemblages.

PurposeThis study caries a survey approach using the expert's interview and literature to select the important criteria to select and evaluate the third-party reverse logistics providers (3PRLPs) in manufacturing companies. In total, 16 criteria are selected to evaluate 3PRLPs, and these criteria are classified on the basis of three main elements of sustainable growth, including economic, social and environmental development. Therefore, a hybrid decision-making approach is utilized to evaluate and rank the 3PRLPs in manufacturing companies.Design/methodology/approachThis paper proposes a new decision-making approach using the projection model and entropy method under the interval-valued intuitionistic fuzzy set to assess 3PRLPs based on sustainability perspectives. A survey approach using the literature review and experts' interview is conducted to select the important criteria to select and evaluate 3PRLPs in manufacturing companies. To assess the criteria weight, the entropy method is used. Further, the projection model is applied to prioritize the 3PRLPs option. Sensitivity analysis and comparison process are performed in order to test and validate the developed method.FindingsThe presented methodology uses the benefits to determine the former for measuring the parameters considered and the latter for rating the 3PRLPs alternatives. A case study is taken to 3PRLPs in the manufacturing industry to illustrate the efficiency of the introduced hybrid method. The findings of this study indicate that when facing uncertainties of input and qualitative data, the proposed solution delivers more viable performance and therefore is suitable for wider uses.Originality/valueThe conception of the circular economy (CE) comes from the last 4 decades, and in recent years, tremendous attention has been carried out on this concept, partially because of the availability of natural resources in the world and changes in consumption behaviour of developed and developing nations. Remarkably, the sustainable supply chain management concepts are established parallel to the CE foundations, grown in industrial practice and ecology literature for a long time. In fact, to reduce the environmental concerns, sustainable supply chain management seeks to diminish the materials' flow and minimize the unintentional harmful consequences of consumption and production processes. Customers and governments are becoming increasingly aware of the environmental sustainability in the CE era, which allows businesses to concentrate more resources on reverse logistics (RLs). However, most manufacturing enterprises have been inspired to outsource their RL operations to competent 3PRLPs due to limited resources and technological limitations. In RL outsourcing practices, the selection of the best 3PRLP is helpfully valuable due to its potential to increase the economic viability of enterprises and boost their long-term growth.