Population Time Series Research Articles

Revisiting Fishery Sustainability Targets

Density-dependent population dynamic models strongly influence many of the world’s most important harvest policies. Nearly all classic models (e.g. Beverton-Holt and Ricker) recommend that managers maintain a population size of roughly 40–50 percent of carrying capacity to maximize sustainable harvest, no matter the species’ population growth rate. Such insights are the foundational logic behind most sustainability targets and biomass reference points for fisheries. However, a simple, less-commonly used model, called the Hockey-Stick model, yields very different recommendations. We show that the optimal population size to maintain in this model, as a proportion of carrying capacity, is one over the population growth rate. This leads to more conservative optimal harvest policies for slow-growing species, compared to other models, if all models use the same growth rate and carrying capacity values. However, parameters typically are not fixed; they are estimated after model-fitting. If the Hockey-Stick model leads to lower estimates of carrying capacity than other models, then the Hockey-Stick policy could yield lower absolute population size targets in practice. Therefore, to better understand the population size targets that may be recommended across real fisheries, we fit the Hockey-Stick, Ricker and Beverton-Holt models to population time series data across 284 fished species from the RAM Stock Assessment database. We found that the Hockey-Stick model usually recommended fisheries maintain population sizes higher than all other models (in 69–81% of the data sets). Furthermore, in 77% of the datasets, the Hockey-Stick model recommended an optimal population target even higher than 60% of carrying capacity (a widely used target, thought to be conservative). However, there was considerable uncertainty in the model fitting. While Beverton-Holt fit several of the data sets best, Hockey-Stick also frequently fit similarly well. In general, the best-fitting model rarely had overwhelming support (a model probability of greater than 95% was achieved in less than five percent of the datasets). A computational experiment, where time series data were simulated from all three models, revealed that Beverton-Holt often fit best even when it was not the true model, suggesting that fisheries data are likely too small and too noisy to resolve uncertainties in the functional forms of density-dependent growth. Therefore, sustainability targets may warrant revisiting, especially for slow-growing species.

Accounting for observation noise in equation‐free forecasting: The hidden‐Markov S‐map

Abstract Ecosystems contain numerous species interacting with each other and the environment. However, data on all relevant state variables is rarely available, hampering inference and prediction. Empirical dynamic modelling (EDM) is a valuable tool for prediction, inference and control in such partially observed systems. However, EDM typically assumes that the available time series are observed without error. Failing to account for observation noise strongly biases estimates of Lyapunov exponents and reduces forecast accuracy. To address this limitation, we propose incorporating EDM into a hidden Markov framework and using an iterative scheme based on the expectation maximization (EM) algorithm to obtain filtered state and parameter estimates. We evaluate the performance of this approach on several simulated dynamical systems with a range of additive noise levels, as well as on insect population time series. Accounting for observation noise improved accuracy of population forecasts and estimates of Lyapunov exponents (LE) over a wide range of noise levels relevant to ecological time series.

Mathematical biases in the calculation of the Living Planet Index lead to overestimation of vertebrate population decline

The Living Planet Index (LPI) measures the average change in population size of vertebrate species over recent decades and has been repeatedly used to assess the changing state of nature. The LPI indicates that vertebrate populations have decreased by almost 70% over the last 50 years. This is in striking contrast with current studies based on the same population time series data that show that increasing and decreasing populations are balanced on average. Here, we examine the methodological pipeline of calculating the LPI to search for the source of this discrepancy. We find that the calculation of the LPI is biased by several mathematical issues which impose an imbalance between detected increasing and decreasing trends and overestimate population declines. Rather than indicating that vertebrate populations do not substantially change, our findings imply that we need better measures for providing a balanced picture of current biodiversity changes. We also show some modifications to improve the reliability of the LPI.

Multi-scale population analysis unit construction method considering scene feature variability and long/short-term patterns in spatiotemporal population activities

ABSTRACT Differences in the spatial scale and component elements of urban scenes affect the analysis of spatiotemporal changes in population distribution (PD) patterns. Fixed scales and geometric forms constrained previous analyses of PD and spatiotemporal changes, which neglected the realistic characteristics of urban scenarios. These limitations hinder the ability to capture the diversity and spatiotemporal representation of PD patterns across multiple spatial scales. This study developed a multi-spatial scale population analysis unit (PAU) construction method considering the scenario heterogeneity and long/short-term patterns of spatiotemporal population changes (PC). Initially, we decompose the multi-scale changes in population time series patterns and their relationships with scene features along the temporal dimension to analyze the primary and secondary factors. Starting from the temporal characteristics of the PD and PC, we established a validation and correction method for the factors. Finally, combined with a multi-feature clustering method, a multi-scale PAU construction method driven by scene feature factors is proposed. Experiments were conducted at different spatial scales in both routine and emergent scenarios. The results indicated that this method can help to obtain more homogeneous analysis regions and enhance the stability and phase pattern representations of changes in PDs, thereby improving the interpretability of analytical results.

Resilience assessment in complex natural systems.

Ecological resilience is the capability of an ecosystem to maintain the same structure and function and avoid crossing catastrophic tipping points (i.e. undergoing irreversible regime shifts). While fundamental for management, concrete ways to estimate and interpret resilience in real ecosystems are still lacking. Here, we develop an empirical approach to estimate resilience based on the stochastic cusp model derived from catastrophe theory. The cusp model models tipping points derived from a cusp bifurcation. We extend cusp in order to identify the presence of stable and unstable states in complex natural systems. Our Cusp Resilience Assessment (CUSPRA) has three characteristics: (i) it provides estimates on how likely a system is to cross a tipping point (in the form of a cusp bifurcation) characterized by hysteresis, (ii) it assesses resilience in relation to multiple external drivers and (iii) it produces straightforward results for ecosystem-based management. We validate our approach using simulated data and demonstrate its application using empirical time series of an Atlantic cod population and marine ecosystems in the North Sea and the Mediterranean Sea. We show that Cusp Resilience Assessment is a powerful method to empirically estimate resilience in support of a sustainable management of our constantly adapting ecosystems under global climate change.

Anticipating a risky future: long short-term memory (LSTM) models for spatiotemporal extrapolation of population data in areas prone to earthquakes and tsunamis in Lima, Peru

Abstract. In this paper, we anticipate geospatial population distributions to quantify the future number of people living in earthquake-prone and tsunami-prone areas of Lima and Callao, Peru. We capitalize upon existing gridded population time series data sets, which are provided on an open-source basis globally, and implement machine learning models tailored for time series analysis, i.e., based on long short-term memory (LSTM) networks, for prediction of future time steps. Specifically, we harvest WorldPop population data and teach LSTM and convolutional LSTM models equipped with both unidirectional and bidirectional learning mechanisms, which are derived from different feature sets, i.e., driving factors. To gain insights regarding the competitive performance of LSTM-based models in this application context, we also implement multilinear regression and random forest models for comparison. The results clearly underline the value of the LSTM-based models for forecasting gridded population data; the most accurate prediction obtained with an LSTM equipped with a bidirectional learning scheme features a root-mean-squared error of 3.63 people per 100 × 100 m grid cell while maintaining an excellent model fit (R2= 0.995). We deploy this model for anticipation of population along a 3-year interval until the year 2035. Especially in areas of high peak ground acceleration of 207–210 cm s−2, the population is anticipated to experience growth of almost 30 % over the forecasted time span, which simultaneously corresponds to 70 % of the predicted additional inhabitants of Lima. The population in the tsunami inundation area is anticipated to grow by 61 % until 2035, which is substantially more than the average growth of 35 % for the city. Uncovering those relations can help urban planners and policymakers to develop effective risk mitigation strategies.

Time series prediction of insect pests in tea gardens.

Tea-garden pest control is crucial to ensure tea quality. In this context, the time-series prediction of insect pests in tea gardens is very important. Deep-learning-based time-series prediction techniques are advancing rapidly but research into their use in tea-garden pest prediction is limited. The current study investigates the time-series prediction of whitefly populations in the Tea Expo Garden, Jurong City, Jiangsu Province, China, employing three deep-learning algorithms, namely Informer, the Long Short-Term Memory (LSTM) network, and LSTM-Attention. The comparative analysis of the three deep-learning algorithms revealed optimal results for LSTM-Attention, with an average root mean square error (RMSE) of 2.84 and average mean absolute error (MAE) of 2.52 for 7 days' prediction length, respectively. For a prediction length of 3 days, LSTM achieved the best performance, with an average RMSE of 2.60 and an average MAE of 2.24. These findings suggest that different prediction lengths influence model performance in tea garden pest time series prediction. Deep learning could be applied satisfactorily to predict time series of insect pests in tea gardens based on LSTM-Attention. Thus, this study provides a theoretical basis for the research on the time series of pest and disease infestations in tea plants. © 2024 Society of Chemical Industry.

Analyzing demand reduction and recovery of major rail stations in Japan during COVID-19 using mobile spatial statistics

Mobile spatial statistics from across Japan are used to analyze the vitality of stations over the COVID period. Time series population information of 500m × 500m meshes that include major stations are extracted. We analyze the demand loss patterns of 69 train stations during the first COVID wave. We firstly discuss the correlation of this data with annual ridership information. We then conduct a clustering analysis of the time series data and distinguish five impact patterns which we try to explain with a multinomial logistic regression. Stations in large cities had higher ridership but were also more affected than smaller cities. We also find that cities with less dense populations and more local population frequenting the station appear to be more robust to the pandemic. Our results can be used to help cities forecasting the impact of future pandemics on the local economy.

Inverse relationships between coyote and wild turkey population time series: Implications for future studies of predator–prey interactions

AbstractChanges in predator communities such as the emergence of new predators alter predator–prey interactions profoundly. Coyotes (Canis latrans) have expanded their geographic distributions from the western United States (US) to the Eastern US, potentially suppressing some prey populations as their relative abundance has increased. To assess the relationship between coyotes and one of their prey, the eastern wild turkey (Meleagris gallopavo silvestris), we employed time series analysis and multivariate autoregressive state‐space models (MARSSMs) to a 23‐year capture per unit effort data set from both species in the state of Mississippi, US. The best MARSSM model indicated density dependence in each species. The competing MARSSM indicated that increases in coyote relative abundance reduced the population growth rate of wild turkeys. We recommend that future studies use long‐term time series of multiple coexisting predators and their alternative prey to assess the effects of the predator guild on the dynamics of prey populations.

Feature-based and shape-match classifications of animal population time series

Estimation of long-term population trends can help population ecologists and conservation biologists assess the status and conditions of wildlife populations to inform the decision making of wildlife management and conservation. Machine learning methods such as time series clustering classify population time series into different clusters that have different trends and dynamic patterns as an alternative to statistical models. We used dynamic time warping (DTW) clustering and feature-based clustering to classify 15 rabbit population times in Mississippi, the United States from 1985 to 2005. Our feature-based method used the parameters of the order-2 Gompertz population models (or autoregressive time series models) as the features of population dynamics. We also estimated the long-term trends of the rabbit populations with the Theil-Sen analysis (TSA). The DTW clustering identified two clusters as optimal classification having the highest Silhouette score. Dynamic time warping clustering had 80% consistency in time series memberships with the TSA, whereas feature-based clustering had 87% consistency. Shape-match DTW clustering not only matches the shapes of trajectories, but also trends between time series. The features based on the Gompertz models capture trend, linear, and nonlinear dynamics. Our shape-match and feature-based time series clustering can cluster time series of different lengths and missing data. The Theil-Sen analysis generates an explicit estimate of linear trends and accounts for temporal autocorrelation. Since the true trends or patterns are often unknown, we recommend using two or all three methods of this study to assess the trends of wildlife populations.

Properties and interpretation of the Skellam model—A discrete‐time contest competition population model

AbstractThe Skellam model describes discrete‐time population dynamics of a single species assuming uniform (i.e., random or Poissonian) individual distribution and intraspecific contest competition. Apart from studies on individual‐based models derived from first principles it has been rarely applied in ecological research although in specific situations it may be more appropriate than, for instance, the frequently used Ricker model, which is derived assuming scramble competition among the individuals. In this article, we offer an insight into the first principles underlying the Skellam model and provide an alternative parameterization of the model in terms of two commonly used parameters: intrinsic rate of population increase and carrying capacity. We also provide guidelines and software for fitting the Skellam model to discrete population time series data. In light of these findings, the Skellam model may be a useful alternative for a range of purposes where it has been earlier overlooked.

A user-friendly guide to using distance measures to compare time series in ecology.

Time series are a critical component of ecological analysis, used to track changes in biotic and abiotic variables. Information can be extracted from the properties of time series for tasks such as classification (e.g., assigning species to individual bird calls); clustering (e.g., clustering similar responses in population dynamics to abrupt changes in the environment or management interventions); prediction (e.g., accuracy of model predictions to original time series data); and anomaly detection (e.g., detecting possible catastrophic events from population time series). These common tasks in ecological research all rely on the notion of (dis-) similarity, which can be determined using distance measures. A plethora of distance measures have been described, predominantly in the computer and information sciences, but many have not been introduced to ecologists. Furthermore, little is known about how to select appropriate distance measures for time-series-related tasks. Therefore, many potential applications remain unexplored. Here, we describe 16 properties of distance measures that are likely to be of importance to a variety of ecological questions involving time series. We then test 42 distance measures for each property and use the results to develop an objective method to select appropriate distance measures for any task and ecological dataset. We demonstrate our selection method by applying it to a set of real-world data on breeding bird populations in the UK and discuss other potential applications for distance measures, along with associated technical issues common in ecology. Our real-world population trends exhibit a common challenge for time series comparisons: a high level of stochasticity. We demonstrate two different ways of overcoming this challenge, first by selecting distance measures with properties that make them well suited to comparing noisy time series and second by applying a smoothing algorithm before selecting appropriate distance measures. In both cases, the distance measures chosen through our selection method are not only fit-for-purpose but are consistent in their rankings of the population trends. The results of our study should lead to an improved understanding of, and greater scope for, the use of distance measures for comparing ecological time series and help us answer new ecological questions.

Farmland practices are driving bird population decline across Europe

Declines in European bird populations are reported for decades but the direct effect of major anthropogenic pressures on such declines remains unquantified. Causal relationships between pressures and bird population responses are difficult to identify as pressures interact at different spatial scales and responses vary among species. Here, we uncover direct relationships between population time-series of 170 common bird species, monitored at more than 20,000 sites in 28 European countries, over 37 y, and four widespread anthropogenic pressures: agricultural intensification, change in forest cover, urbanisation and temperature change over the last decades. We quantify the influence of each pressure on population time-series and its importance relative to other pressures, and we identify traits of most affected species. We find that agricultural intensification, in particular pesticides and fertiliser use, is the main pressure for most bird population declines, especially for invertebrate feeders. Responses to changes in forest cover, urbanisation and temperature are more species-specific. Specifically, forest cover is associated with a positive effect and growing urbanisation with a negative effect on population dynamics, while temperature change has an effect on the dynamics of a large number of bird populations, the magnitude and direction of which depend on species' thermal preferences. Our results not only confirm the pervasive and strong effects of anthropogenic pressures on common breeding birds, but quantify the relative strength of these effects stressing the urgent need for transformative changes in the way of inhabiting the world in European countries, if bird populations shall have a chance of recovering.

Fitting and evaluating univariate and multivariate models of within-lineage evolution.

The nature of phenotypic evolution within lineages is central to many unresolved questions in paleontology and evolutionary biology. Analyses of evolutionary time-series of ancestor-descendant populations in the fossil record are likely to make important contributions to many of these debates. However, the limited number of models that have been applied to these types of data may restrict our ability to interpret phenotypic evolution in the fossil record. Using uni- and multivariate models of trait evolution that make different assumptions regarding the dynamics of the adaptive landscape, I evaluate contrasting hypotheses to explain evolution of size in the radiolarian Eucyrtidium calvertense and armor in the stickleback Gaserosteus doryssus. Body size evolution in E. calvertense is best explained by a model where the lineage evolves as a consequence of a shift in the adaptive landscape that coincides with the initiation of neosympatry with its sister lineage. Multivariate evolution of armor traits in a stickleback lineage (Gasterosteus doryssus) show evidence of adaptation towards independent optima on the adaptive landscape at the same time as traits change in a correlated fashion. The fitted models are available in a the R package evoTS, which builds on the commonly used paleoTS framework.

Coefficient identification in a SIS fractional-order modelling of economic losses in the propagation of COVID-19

A fractional-order SIS (Susceptible–Infectious–Susceptible) model with time-dependent coefficients is used to analyse some effects of the novel coronavirus 2019 (COVID-19). This generalized model is suitable for describing the COVID dynamics since it does not presume permanent immunity after contagion. The fractional derivative activates the memory property of the dynamics of the susceptible and infectious population time series. A coefficient identification inverse problem is posed, which consists of reconstructing the time-varying transmission and recovery rates, which are of paramount importance in practice for both medics and politicians.The inverse problem is reduced to a minimization problem, which is solved in a least squares sense. The iterative predictor–corrector algorithm reconstructs the time-dependent parameters in a piecewise-linear fashion. The economic losses emerging from social distancing using the calibrated model are also discussed. A comparison between the results obtained by the classical model and the fractional-order model is included, which is validated by ample tests with synthetic and real data.

Seasonality, density dependence, and spatial population synchrony

Studies of spatial population synchrony constitute a central approach for understanding the drivers of ecological dynamics. Recently, identifying the ecological impacts of climate change has emerged as a new important focus in population synchrony studies. However, while it is well known that climatic seasonality and sequential density dependence influences local population dynamics, the role of season-specific density dependence in shaping large-scale population synchrony has not received attention. Here, we present a widely applicable analytical protocol that allows us to account for both season and geographic context-specific density dependence to better elucidate the relative roles of deterministic and stochastic sources of population synchrony, including the renowned Moran effect. We exemplify our protocol by analyzing time series of seasonal (spring and fall) abundance estimates of cyclic rodent populations, revealing that season-specific density dependence is a major component of population synchrony. By accounting for deterministic sources of synchrony (in particular season-specific density dependence), we are able to identify stochastic components. These stochastic components include mild winter weather events, which are expected to increase in frequency under climate warming in boreal and Arctic ecosystems. Interestingly, these weather effects act both directly and delayed on the vole populations, thus enhancing the Moran effect. Our study demonstrates how different drivers of population synchrony, presently altered by climate warming, can be disentangled based on seasonally sampled population time-series data and adequate population models.

A data set of distributed global population and water withdrawal from 1960 to 2020

Population and water withdrawal data sets are currently faced with difficulties in collecting, processing and verifying multi-source time series, and the spatial distribution characteristics of long series are also relatively lacking. Time series is the basic guarantee for the accuracy of data sets, and the production of long series spatial distribution is a realistic requirement to expand the application scope of data sets. Through the time-consuming and laborious basic processing work, this research focuses on the population and water intake time series, and interpolates and extends them to specific land uses to ensure the accuracy of the time series and the demand of spatially distributed data sets. This research provides a set of population density and water intensity products from 1960 to 2020 distributed to the administrative units or the corresponding regions. The data set fills the gaps in the multi-year data set for the accuracy of population density and the intensity of water withdrawal.

A 17-year time-series of diatom populations‘ flux and composition in the Mauritanian coastal upwelling

Understanding seasonal and multiyear variability of primary producers’ populations in the Mauritanian coastal upwelling system along the northwestern African margin may help to predict future impact of climate change (e.g., nutrient availability, productivity, and phyto- and zooplankton dynamics). For this, continuous, long time-series are required. A major challenge in obtaining these time-series is the logistics associated with the uninterrupted, in-situ sampling over several years. Sediment traps represent a reliable alternative. In this study, we assess the variations of the diatom community in samples almost continuously collected between June 2003 and March 2020 with 17 sediment traps deployed at site CBeu (=Cape Blanc eutrophic), located at c. 20°N-18°45’W, offshore Mauritania in the Canary Current Eastern Boundary Upwelling Ecosystems (CC-EBUE). In addition to describing the multiyear dynamics of the total diatom flux and major shifts in the species-specific composition of the populations, our study addresses questions such as (i) how constant is the intrannual pattern of populations’ occurrence, (ii) what the amplitude of annual changes is, and (iii) how populations’ shifts relate to physical setting dynamics. Matching the occurrence of most intense seasonal upwelling, highest diatom flux maxima mainly occur in spring and summer between 2003 and 2020. The diverse diatom community (e.g., benthic, coastal upwelling, coastal planktonic, and open-ocean diatoms) closely follows the annual cycle of atmospheric and hydrologic conditions. Benthic diatoms dominate during spring and summer (e.g., upwelling season), while open-ocean diatoms contribute the most in fall and winter when the upper water column stratifies. As no persistent –either decreasing or increasing trend of diatom productivity over the 17 sampled years, our results are at odds with Bakun’s hypothesis of upwelling intensification. Anchoring temporal changes of diatoms in a wider environmental frame allows for insights into the complex dynamics of the Mauritanian upwelling ecosystem and the populations’ response to climate forcing. This helps in establishing the scientific basis for modeling future states of the CC-EBUE and/or comparable environments.

Understanding China’s urban functional patterns at the county scale by using time-series social media data

ABSTRACT Understanding urban functions help with government planning and resource allocation to promote economic development. Few studies have reflected the influence of population movement and migration on urban functions overtime on a large scale. This study adopted the time-series social media data and points of interest to analyse urban functions’ distribution at the county scale. By employing dynamic time warping distance and K-Medoids to cluster cities, the result of China’s hourly population distribution over different periods achieves a high accuracy (Pearson’s R = 0.821, R2 = 0.668). From the clustering results, time-series population data effectively reflect cities’ socioeconomic characteristics and identify the spatial distribution of China’s urban functional patterns. We select four representative urban agglomerations to deeply analyse their urban function patterns. Furthermore, urban functions can also influence changes in time-series populations. This study explores the correlations between time-series population mobility and urban functions, which could help analyse urban functions and urban socioeconomic conditions.

Sharkipedia: a curated open access database of shark and ray life history traits and abundance time-series

A curated database of shark and ray biological data is increasingly necessary both to support fisheries management and conservation efforts, and to test the generality of hypotheses of vertebrate macroecology and macroevolution. Sharks and rays are one of the most charismatic, evolutionary distinct, and threatened lineages of vertebrates, comprising around 1,250 species. To accelerate shark and ray conservation and science, we developed Sharkipedia as a curated open-source database and research initiative to make all published biological traits and population trends accessible to everyone. Sharkipedia hosts information on 58 life history traits from 274 sources, for 170 species, from 39 families, and 12 orders related to length (n = 9 traits), age (8), growth (12), reproduction (19), demography (5), and allometric relationships (5), as well as 871 population time-series from 202 species. Sharkipedia relies on the backbone taxonomy of the IUCN Red List and the bibliography of Shark-References. Sharkipedia has profound potential to support the rapidly growing data demands of fisheries management, international trade regulation as well as anchoring vertebrate macroecology and macroevolution.