Predict Population Dynamics Research Articles

Modelling “Breaking Bad”: An economic model of drugs and population dynamics to predict how the series itself feeds back into the drug market

This stock&flow-model predicts population dynamics of crystal meth addicts related to the price development of drugs, inspired by the TV series “Breaking Bad”. The potential impact of the broadcasting of the TV series on the system is tested by using sudden (pulsed) changes of selected flows and rates to reveal the sensitivity of selected variables: Addicts, price relationship, dealers' saturation and Stock of Crystal Meth. While consumption, purchase and production show strong responses to those changes, other variables like getting addicted and weaning_off show weaker responses. These flows' reactions to pulsed changes of model parameters are analyzed and their significance is discussed.

¿Es relevante la ecología del comportamiento para entender y predecir la dinámica de las poblaciones?

Gonzalez-Suarez, M.A. 2014. Is behavioral ecology important for understanding and predicting population dynamics?. Ecosistemas 23(3): 93-97. Doi.: 10.7818/ECOS.2014.23-3.12 Population ecology is a discipline that studies changes in the number and composition (age, sex) of the individuals that form a population. Many of the mechanisms that generate these changes are associated with individual behavior, for example how individuals defend their territories, find mates or disperse. Therefore, it is important to model population dynamics considering the potential influence of behavior on the modeled dynamics. This study illustrates the diversity of behaviors that influence population dynamics describing several methods that allow integrating behavior into population models and range from simpler models that only consider the number of individuals to complex individual-based models that capture great levels of detail. A series of examples shows the importance of explicitly considering behavior in population modeling to avoid reaching erroneous conclusions. This integration is particularly relevant for conservation, as incorrect predictions regarding the dynamics of populations of conservation interest can lead to inadequate assessment and management. Improved predictions can favor effective protection of species and better use of the limited financial and human conservation resources.

Mixture of inhomogeneous matrix models for species‐rich ecosystems

Understanding how environmental factors could impact population dynamics is of primary importance for species conservation. Matrix population models are widely used to predict population dynamics. However, in species‐rich ecosystems with many rare species, the small population sizes hinder a good fit of species‐specific models. In addition, classical matrix models do not take into account environmental variability. We propose a mixture of regression models with variable selection allowing the simultaneous clustering of species into groups according to vital rate information (recruitment, growth and mortality) and the identification of group‐specific explicative environmental variables. We develop an inference method coupling the R packagesflexmixandglmnet. We first highlight the effectiveness of the method on simulated datasets. Next, we apply it to data from a tropical rain forest in the Central African Republic. We demonstrate the accuracy of the inhomogeneous mixture matrix model in successfully reproducing stand dynamics and classifying tree species into well‐differentiated groups with clear ecological interpretations. Copyright © 2014 John Wiley & Sons, Ltd.

Predicting population responses to environmental change: the importance of considering informed dispersal strategies in spatially structured population models

AbstractAimBecause of its complexity, dispersal has often been simplified when implemented in models aiming at understanding and predicting population dynamics and persistence in a context of environmental change. In particular, informed dispersal, that is the use of personal and social information to decide whether to leave a natal or current breeding site and where to settle, has seldom been considered. Informed dispersal could nevertheless be critical for predicting population dynamics, structure and persistence, as it could help populations track environmental change. Here, we develop a simulation model to examine the consequences of four dispersal strategies (informed, semi‐informed, fixed random dispersal and philopatry) on the dynamics, structure and persistence of a spatially structured population under different environmental scenarios.MethodsWe built and parameterized a metapopulation dynamic model using a long‐lived colonial seabird species as an example, the black‐legged kittiwake Rissa tridactyla, breeding on a set of distinct patches. Various scenarios of environmental variability and multiple factors potentially driving natal and breeding dispersal decisions (local habitat quality, individual and conspecific breeding success, personal and social information use) were considered to explore their respective effects.ResultsEnvironmental change and dispersal strategies strongly influenced metapopulation dynamics and structure. In spatially variable environments, informed and semi‐informed dispersal maintained populations in the long term, whereas philopatry and random dispersal led to extinction. Contrasted dynamics also arose: philopatry led to ecological traps, random and semi‐informed dispersal led to source‐sink dynamics and informed dispersal drove extinction–recolonization dynamics.Main conclusionsThis study demonstrates the importance of including informed dispersal in models aiming at predicting the dynamics of spatially structured populations. It also serves to highlight the urgent need to collect more empirical data on dispersal processes to properly parameterize such models.

Bayesian estimates of transition probabilities in seven small lithophytic orchid populations: maximizing data availability from many small samples.

Predicting population dynamics for rare species is of paramount importance in order to evaluate the likelihood of extinction and planning conservation strategies. However, evaluating and predicting population viability can be hindered from a lack of data. Rare species frequently have small populations, so estimates of vital rates are often very uncertain due to lack of data. We evaluated the vital rates of seven small populations from two watersheds with varying light environment of a common epiphytic orchid using Bayesian methods of parameter estimation. From the Lefkovitch matrices we predicted the deterministic population growth rates, elasticities, stable stage distributions and the credible intervals of the statistics. Populations were surveyed on a monthly basis between 18–34 months. In some of the populations few or no transitions in some of the vital rates were observed throughout the sampling period, however, we were able to predict the most likely vital rates using a Bayesian model that incorporated the transitions rates from the other populations. Asymptotic population growth rate varied among the seven orchid populations. There was little difference in population growth rate among watersheds even though it was expected because of physical differences as a result of differing canopy cover and watershed width. Elasticity analyses of Lepanthes rupestris suggest that growth rate is more sensitive to survival followed by growth, shrinking and the reproductive rates. The Bayesian approach helped to estimate transition probabilities that were uncommon or variable in some populations. Moreover, it increased the precision of the parameter estimates as compared to traditional approaches.

Developing, testing and application of rodent population dynamics and capture models based on an adjusted Leslie matrix-based population approach

Small rodents in general and the multimammate rat Apodemus agrarius in particular, damage crops and cause major economic losses in China. Therefore, accurate predictions of the population size of A. agrarius and an efficient control strategy are urgently needed. We developed a population dynamics model by applying a Leslie matrix method, and a capture model based on optimal harvesting theory for A. agrarius. Our models were parametrized using demographic estimates from a capture–mark–recapture (CMR) study conducted on the Qinshui Forest Farm in Northwestern China. The population dynamics model incorporated 12 equally balanced age groups and included immigration and emigration parameters. The model was evaluated by assessing the predictions for four years based on the known starting population in 2004 from the 2004–2007 CMR data. The capture model incorporated two functional age categories (juvenile and adult) and used density-dependent and density-independent factors. The models were used to assess the effect of rodent control measures between 2004 and 2023 on population dynamics and the resulting numbers of rats. Three control measures affecting survival rates were considered. We found that the predicted population dynamics of A. agrarius between 2004 and 2007 compared favorably with the observed population dynamics. The models predicted that the population sizes of A. agrarius in the period between 2004 and 2023 under the control measure applied in August 2004 were very similar to the optimal population sizes, and no significant difference was found between the two population sizes. We recommend using the population dynamics and capture models based on CMR-estimated demographic schedules for rodent, provided these data are available. The models that we have developed have the potential to play an important role in predicting the effects of rodent management and in evaluating different control strategies.

Phenological responses and a comparative phylogenetic insight of Anarsia lineatella and Grapholita molesta between distinct geographical regions within the Mediterranean basin

AbstractA unique logistic model for predicting population dynamics of Anarsia lineatella and Grapholita molesta was evaluated on populations sampled from Italy and Greece. Intraspecific mtDNA divergence was additionally estimated in an effort to examine whether regional differences in moth phenologies are associated with genetic divergence. A. lineatella populations displayed closer similarities on phenological responses between the two observation regions. As a result, population fluctuations in both regions could be accurately predicted based on the constructed model. However, that was not the case for G. molesta as its populations exhibited a more regional behaviour, and thus, the model was less accurate. It is notable that degree‐day accumulations above the lower temperature thresholds were recorded in Italy on month earlier than in Greece (1st March in Calabria in contrast to 1st April in Veria). That kind of observed deviations in moth phenologies could be potentially attributed to regional environmental conditions or even genetic differentiation. Despite the low number of individuals analysed, this first attempt to study the levels of intraspecific divergence between Italian and Greek moth populations revealed that both species exhibit evidence of regional‐based separation. Our study provides the first comprehensive phenological comparison between populations of A. lineatella and G. molesta from Italy and Greece. At the same time, the population genetic structure data reveal differentiation between these two regions for both species, something that should be further investigated as it could provide a possible explanation for the observed phenological differences. Moreover, DNA barcoding confirmed that G. molesta pheromone blends attracted at least two morphologically close‐related tortricid moth species. This fact probably explains the phenological variations observed for this species as well as the difficulties in defining the number of non‐overlapping flights.

Double trouble at high density: cross-level test of resource-related adaptive plasticity and crowding-related fitness.

Population size is often regulated by negative feedback between population density and individual fitness. At high population densities, animals run into double trouble: they might concurrently suffer from overexploitation of resources and also from negative interference among individuals regardless of resource availability, referred to as crowding. Animals are able to adapt to resource shortages by exhibiting a repertoire of life history and physiological plasticities. In addition to resource-related plasticity, crowding might lead to reduced fitness, with consequences for individual life history. We explored how different mechanisms behind resource-related plasticity and crowding-related fitness act independently or together, using the water flea Daphnia magna as a case study. For testing hypotheses related to mechanisms of plasticity and crowding stress across different biological levels, we used an individual-based population model that is based on dynamic energy budget theory. Each of the hypotheses, represented by a sub-model, is based on specific assumptions on how the uptake and allocation of energy are altered under conditions of resource shortage or crowding. For cross-level testing of different hypotheses, we explored how well the sub-models fit individual level data and also how well they predict population dynamics under different conditions of resource availability. Only operating resource-related and crowding-related hypotheses together enabled accurate model predictions of D. magna population dynamics and size structure. Whereas this study showed that various mechanisms might play a role in the negative feedback between population density and individual life history, it also indicated that different density levels might instigate the onset of the different mechanisms. This study provides an example of how the integration of dynamic energy budget theory and individual-based modelling can facilitate the exploration of mechanisms behind the regulation of population size. Such understanding is important for assessment, management and the conservation of populations and thereby biodiversity in ecosystems.

Stability Analysis of Competing Insect Species for a Single Resource

The models explore the effects of resource and temperature on competition between insect species. A system of differential equations is proposed and analysed qualitatively using stability theory. A local study of the models is performed around axial, planar, and interior equilibrium points to successively estimate the effect of (i) one species interacting with a resource, (ii) two competing species for a single resource, and (iii) three competing species for a single resource. The local stability analysis of the equilibrium is discussed using Routh-Hurwitz criteria. Numerical simulation of the models is performed to investigate the sensitivity of certain key parameters. The models are used to predict population dynamics in the selected cases studied. The results show that when a single species interacts with a resource, the species will be able to establish and sustain a stable population. However, in competing situation, it is observed that the combinations of three parameters (half-saturation, growth rate, and mortality rate) determine which species wins for any given resource. Moreover, our results indicate that each species is the superior competitor for the resource for the range of temperature for which it has the lowest equilibrium resource.

On International Fisheries Agreements, Entry Deterrence and Ecological Uncertainty

From a game theoretical perspective, a prerequisite for an international fishery agreement (IFA) to be stable is that parties expect their benefits from joining the agreement to exceed the benefits from free riding on the agreement, and parties only comply with the agreement as long as this is true. The agreement, therefore, implicitly builds on an expectation of the ecological integrity of the natural resource. Typically, the game theoretical models assume that all parties have the same (often perfect) information of the resource and that the exploitation is an equilibrium use of the stock. As stated by experts in natural science, the fish ecology still has many open questions, e.g. how to predict population dynamics, migration patterns, food availability, etc. In some cases, parties disagree about the state, abundance, and migration of a stock, which can significantly disturb the possibilities of reaching an agreement for exploitation of the stock. This paper develops a model and applies it to the North-East Atlantic mackerel fishery, in order to analyze IFA under different ecological scenarios, and also combines the model with the economic theory of entry deterrence. The model is empirically used to determine whether the original parties to the agreement have an advantage in that the results from fishing the stock down to a smaller size prevents another party from entering into the fishery. The paper presents a novel method for illustrating the obstacles that have made an agreement for the North-East Atlantic mackerel so difficult to achieve.

When things go wrong: intra‐season dynamics of breeding failure in a seabird

During breeding, long‐lived species face important time and energy constraints that can lead to breeding failure when food becomes scarce. Despite the potential implications of intra‐season dynamics in breeding failure for individual behavior, carry‐over effects, dispersal decisions and population dynamics, little information is currently available on these dynamics at fine temporal scales. Here, we monitored the foraging behavior and the proportion of successful black‐legged kittiwake pairs from nest construction to chick fledging in a colony of the southern Barents Sea, to relate foraging effort to the dynamics of breeding failure over an entire breeding season, and to infer the environmental conditions leading to this failure. Specifically, we tracked kittiwakes with GPS and satellite tags during incubation and early chick‐rearing to document nest attendance, foraging range, time budgets and daily energy expenditures (DEE). We also monitored diet changes over time. We predicted that breeding failure would follow a non‐linear trend characterized by a break point after which breeding success would drop abruptly and would be related to a substantial increase in foraging effort. Kittiwakes showed contrasting foraging patterns between incubation and chick‐rearing: they extended their foraging range from 20 km during incubation to more than 450 km during chick‐rearing and switched diet. They also increased their DEE and readjusted their time budgets by increasing time spent at sea. These changes corresponded to a break point in breeding dynamics beyond which the proportion of successful pairs abruptly dropped. At the end of the season, less than 10% of kittiwake pairs raised chicks in the monitored plots. This integrative study confirms that breeding failure is a non‐linear process characterized by a threshold beyond which individuals face an energetic trade‐off and cannot simultaneously sustain high reproductive and self‐maintenance efforts. In this way, the occurrence of sudden environmental changes complicates our ability to predict population dynamics and poses conservation challenges.

Characteristics and Drivers of High-Altitude Ladybird Flight: Insights from Vertical-Looking Entomological Radar

Understanding the characteristics and drivers of dispersal is crucial for predicting population dynamics, particularly in range-shifting species. Studying long-distance dispersal in insects is challenging, but recent advances in entomological radar offer unique insights. We analysed 10 years of radar data collected at Rothamsted Research, U.K., to investigate characteristics (altitude, speed, seasonal and annual trends) and drivers (aphid abundance, air temperature, wind speed and rainfall) of high-altitude flight of the two most abundant U.K. ladybird species (native Coccinella septempunctata and invasive Harmonia axyridis). These species cannot be distinguished in the radar data since their reflectivity signals overlap, and they were therefore analysed together. However, their signals do not overlap with other, abundant insects so we are confident they constitute the overwhelming majority of the analysed data. The target species were detected up to ∼1100 m above ground level, where displacement speeds of up to ∼60 km/h were recorded, however most ladybirds were found between ∼150 and 500 m, and had a mean displacement of 30 km/h. Average flight time was estimated, using tethered flight experiments, to be 36.5 minutes, but flights of up to two hours were observed. Ladybirds are therefore potentially able to travel 18 km in a “typical” high-altitude flight, but up to 120 km if flying at higher altitudes, indicating a high capacity for long-distance dispersal. There were strong seasonal trends in ladybird abundance, with peaks corresponding to the highest temperatures of mid-summer, and warm air temperature was the key driver of ladybird flight. Climatic warming may therefore increase the potential for long-distance dispersal in these species. Low aphid abundance was a second significant factor, highlighting the important role of aphid population dynamics in ladybird dispersal. This research illustrates the utility of radar for studying high-altitude insect flight and has important implications for predicting long-distance dispersal.

Exposing eggs to high temperatures affects the development, survival and reproduction of Harmonia axyridis

The multicolored Asian lady beetle, Harmonia axyridis (Pallas) (Coleoptera: Coccinellidae), is a well-known biological control agent for aphids and soft-bodied insects. We investigated the developmental, survival and reproductive traits of H. axyridis when its eggs were exposed to 25 (control), 37, 39 and 41°C for 1h, and then transferred to ambient condition (25°C). The effects of heat stress on the hatching success greatly differed among temperature treatments. No H. axyridis larvae hatched out at 41°C. The development, survival, weight, reproduction and longevity of H. axyridis exhibited significant differences with temperature treatment and gender. The survival rate of immatures declined, while the adult fresh weight of both sexes markedly increased with the increase of temperature. Heat exposure of the eggs caused a subsequent reduction in longevity, oviposition period and reproduction, while the pre-oviposition period became longer as the temperature increased. These may imply that the reproductive investment increased in higher level stressful environments, and the response of adult individuals could be linked to the experiences from early stages of the life history. Our findings provide useful information for predicting population dynamics and understanding the potential for H. axyridis as a biological control agent under variable environments.

Reevaluating the self-thinning boundary line for ponderosa pine (Pinus ponderosa) forests

The self-thinning rule has been used extensively to predict population dynamics under intraspecific and interspecific competition. In forestry, it is an important silvicultural concept for maintaining stand health in the face of climate change and biotic stress, but uncertainty exists because traditional self-thinning limits were set subjectively without regard to site quality. We addressed this by analyzing ponderosa pine (Pinus ponderosa Lawson & C. Lawson) data from 109 research plots measured repeatedly and 59 inventory plots measured once across California. Self-thinning boundaries were fitted to the data with quantile regression and stochastic frontier function (SFF) techniques with and without site index (SI) as a covariate. The models from both methods fitted the data well with either research plots or all plots. Slopes for size-density trajectories were –0.45 with the 0.99 quantile and –0.47 for SFF. Maximum stand density indices (SDI) were 1250 trees per hectare (TPH) with the 0.99 quantile and 1050–1060 TPH with SFF. Mortality occurred when site occupancy from SFF reached 0.75, suggesting a zone of imminent mortality. Curvilinear trends in maximum SDI across SI for both methods indicate that self-thinning varies with site quality. Any management regimes that increase site quality and productivity will increase the self-thinning boundary.

Body masses, functional responses and predator–prey stability

The stability of ecological communities depends strongly on quantitative characteristics of population interactions (type-II vs. type-III functional responses) and the distribution of body masses across species. Until now, these two aspects have almost exclusively been treated separately leaving a substantial gap in our general understanding of food webs. We analysed a large data set of arthropod feeding rates and found that all functional-response parameters depend on the body masses of predator and prey. Thus, we propose generalised functional responses which predict gradual shifts from type-II predation of small predators on equally sized prey to type-III functional-responses of large predators on small prey. Models including these generalised functional responses predict population dynamics and persistence only depending on predator and prey body masses, and we show that these predictions are strongly supported by empirical data on forest soil food webs. These results help unravelling systematic relationships between quantitative population interactions and large-scale community patterns.

Predicting Population Dynamics from the Properties of Individuals: A Cross-Level Test of Dynamic Energy Budget Theory

Individual-based models (IBMs) are increasingly used to link the dynamics of individuals to higher levels of biological organization. Still, many IBMs are data hungry, species specific, and time-consuming to develop and analyze. Many of these issues would be resolved by using general theories of individual dynamics as the basis for IBMs. While such theories have frequently been examined at the individual level, few cross-level tests exist that also try to predict population dynamics. Here we performed a cross-level test of dynamic energy budget (DEB) theory by parameterizing an individual-based model using individual-level data of the water flea, Daphnia magna, and comparing the emerging population dynamics to independent data from population experiments. We found that DEB theory successfully predicted population growth rates and peak densities but failed to capture the decline phase. Further assumptions on food-dependent mortality of juveniles were needed to capture the population dynamics after the initial population peak. The resulting model then predicted, without further calibration, characteristic switches between small- and large-amplitude cycles, which have been observed for Daphnia. We conclude that cross-level tests help detect gaps in current individual-level theories and ultimately will lead to theory development and the establishment of a generic basis for individual-based models and ecology.

Seasonal variation in the population growth rate of a dominant zooplankter: what determines its population dynamics?

Summary Most demographic studies predict population dynamics from known vital rates. In natural plankton populations, in contrast, the ecologist faces the ‘inverse problem’ to estimate the vital rates from observations of a population's dynamics. Since this problem is complex, many studies only present time series of abundance data from the field and vital rates estimated from laboratory experiments. Here, however, we estimate vital rates of the copepod Arctodiaptomus salinus from a stage‐dependent matrix model developed from time series of abundances. We show how each vital rate contributes to the observed variation in the population growth rate (retrospective analyses) and how potential changes in vital rates could affect this growth rate (prospective analyses). Such perturbation analyses can be expected to become very useful management tools, because they show how sensitive the population is to changes in its different life traits and to detect potential disturbances in its habitat. The models showed that the finite population growth rate (λ) varied seasonally. The population decreased during the summer and was very close to steady state in autumn and winter. The drop in λ in summer was caused mainly by reductions in fertility and in the probability of growth of pre‐adult stages. Fertility and survival of pre‐adult and adult stages were the vital rates contributing most to the variation on λ in autumn. The increment of pre‐adult stage survival determined the increment of λ in winter. During autumn and winter λ was more sensitive to changes to the probabilities of survival than to the probabilities of growth to the following stage, but in summer the opposite was observed. During the whole of the study period, λ was not very sensitive to changes to fertility. Since at high temperatures λ decays and the study pond is warm most of the year, global warming might have dramatic consequences for this A. salinus population even in the short term. Results suggest that pre‐adult stages of A. salinus may over‐summer as quiescence stages, which could be a useful strategy for coping with the warming of the pond and, consequently, global warming.

Experimental Test of an Eco-Evolutionary Dynamic Feedback Loop between Evolution and Population Density in the Green Peach Aphid

An eco-evolutionary feedback loop is defined as the reciprocal impacts of ecology on evolutionary dynamics and evolution on ecological dynamics on contemporary timescales. We experimentally tested for an eco-evolutionary feedback loop in the green peach aphid, Myzus persicae, by manipulating initial densities and evolution. We found strong evidence that initial aphid density alters the rate and direction of evolution, as measured by changes in genotype frequencies through time. We also found that evolution of aphids within only 16 days, or approximately three generations, alters the rate of population growth and predicts density compared to nonevolving controls. The impact of evolution on population dynamics also depended on density. In one evolution treatment, evolution accelerated population growth by up to 10.3% at high initial density or reduced it by up to 6.4% at low initial density. The impact of evolution on population growth was as strong as or stronger than that caused by a threefold change in intraspecific density. We found that, taken together, ecological condition, here intraspecific density, alters evolutionary dynamics, which in turn alter concurrent population growth rate (ecological dynamics) in an eco-evolutionary feedback loop. Our results suggest that ignoring evolution in studies predicting population dynamics might lead us to over- or underestimate population density and that we cannot predict the evolutionary outcome within aphid populations without considering population size.

Predicting responses to climate change requires all life‐history stages

In Focus: Radchuk, V., Turlure, C. & Schtickzelle, N. (2013) Each life stage matters: the importance of assessing response to climate change over the complete life cycle in butterflies. Journal of Animal Ecology, 82, 275-285. Population-level responses to climate change depend on many factors, including unexpected interactions among life history attributes; however, few studies examine climate change impacts over complete life cycles of focal species. Radchuk, Turlure & Schtickzelle () used experimental and modelling approaches to predict population dynamics for the bog fritillary butterfly under warming scenarios. Although they found that warming improved fertility and survival of all stages with one exception, populations were predicted to decline because overwintering larvae, whose survival declined with warming, were disproportionately important contributors to population growth. This underscores the importance of considering all life history stages in analyses of climate change's effects on population dynamics.

Population dynamics of species‐rich ecosystems: the mixture of matrix population models approach

SummaryMatrix population models are widely used to predict population dynamics, but when applied to species‐rich ecosystems with many rare species, the small population sample sizes hinder a good fit of species‐specific models. This issue can be overcome by assigning species to groups to increase the size of the calibration data sets. However, the species classification is often disconnected from the matrix modelling and from the estimation of matrix parameters, thus bringing species groups that may not be optimal with respect to the predicted community dynamics.We proposed here a method that jointly classified species into groups and fit the matrix models in an integrated way. The model was a special case of mixture with unknown number of components and was cast in a Bayesian framework. An MCMC algorithm was developed to infer the unknown parameters: the number of groups, the group of each species and the dynamics parameters.We applied the method to simulated data and showed that the algorithm efficiently recovered the model parameters.We applied the method to a data set from a tropical rain forest in French Guiana. The mixture matrix model classified tree species into well‐differentiated groups with clear ecological interpretations. It also accurately predicted the forest dynamics over the 16‐year observation period.Our model and algorithm can straightforwardly be adapted to any type of matrix model, using the life cycle diagram. It can be used as an unsupervised classification technique to group species with similar population dynamics.