Theory Of Population Dynamics Research Articles

Population dynamics and cultural niche construction during the Late Holocene in a mediterranean ecosystem (central Chile, 32°S−36°S)

Understanding socio-ecological systems over the long term can shed light on past adaptive strategies in environmentally sensitive regions. Central Chile is an emblematic case study for mediterranean ecosystems, where a progressive and sustained population increase began approximately 2000 years ago alongside significant landscape changes. In this work we analyzed regional paleo-demographic trends by compiling a new database of archaeological dates over the last 3000 years, and integrating population dynamics theory with an analysis of the spatio-temporal variation of regional cultural stages. Results show three moments of marked acceleration in population growth: just before agricultural adoption, during the Archaic Period (c. 700-300 BCE); during the second half of the ECP (500–900 CE); and during the Late Intermediate Period (1200–1400 CE). We also identified periods of deceleration in per capita growth rates, although population size continued to increase (300 BCE−500 CE, 900–1200 CE and after 1400 CE). These large shifts in the per capita growth rates coincide with major cultural changes associated with social and economic aspects. The pulses of major occupation show in general terms a more intensive use of the valleys as the population size increased, although the remaining ecosystems never ceased to be occupied with different economic and symbolic emphases.

Towards understanding human–environment feedback loops: the Atacama Desert case

The overall trajectory for the human–environment interaction has been punctuated by demographic boom-and-bust cycles, phases of growth/overshooting as well as of expansion/contraction in productivity. Although this pattern has been explained in terms of an interplay between population growth, social upscaling, ecosystem engineering and climate variability, the evoked demographic–resource-complexity mechanisms have not been empirically tested. By integrating proxy data for population sizes, palaeoclimate and internal societal factors into empirical modelling approaches from the population dynamic theory, we evaluated how endogenous (population sizes, warfare and social upscaling) and exogenous (climate) variables module the dynamic in past agrarian societies. We focused on the inland Atacama Desert, where populations developed agriculture activities by engineering arid and semi-arid landscapes during the last 2000 years. Our modelling approach indicates that these populations experienced a boom-and-bust dynamic over the last millennia, which was coupled to structure feedback between population sizes, hydroclimate, social upscaling, warfare and ecosystem engineering. Thus, the human–environment loop appears closely linked with cooperation, competition, limiting resources and the ability of problem-solving. This article is part of the theme issue ‘Evolution and sustainability: gathering the strands for an Anthropocene synthesis’.

How does facilitation influence the outcome of species interactions?

Abstract Research on facilitation has not had the advantage of being explicitly underpinned by mathematical population dynamic theory. This has limited understanding of the role of facilitation on ecological dynamics and the integration of facilitation into general theory. I show that facilitative interactions can be classified into four categories likely to be dynamically similar to interaction types for which population‐dynamic theory does exist. This classification provides a useful population‐dynamic foundation for facilitation studies and reveals several fundamental questions unanswered by existing empirical work. While facilitation has typically been excluded from studies of ‘competitive’ coexistence, I also describe how coexistence theory does not always default to the assumption that species only compete; recent developments in coexistence theory fully accommodate the potentially important influence of facilitation. Simple models of multispecies population dynamics emphasize the importance of reciprocal interspecific interactions, intraspecific interactions, and density dependence for understanding the outcome of facilitative interactions. I point to approaches for aligning future empirical studies of facilitation with these features. Synthesis: Closely aligning at least some future empirical work on facilitation with existing mathematical population dynamic theory will further improve understanding of the effects of facilitation on ecological dynamics.

A step towards the integration of spatial dynamics in population dynamics models: Eastern Bering Sea snow crab as a case study

Considering spatial processes in population dynamics models can be difficult because of data limitations and computational costs. We adapted a high-resolution spatiotemporal assessment framework to better address fine-scale spatial heterogeneities based on theories of fish population dynamics and spatiotemporal statistics. Specifically, we developed a size-based state-space model for the snow crab (Chionoecetes opilio) population in the Eastern Bering Sea (EBS) to refine the representation of spatial processes in integrated population models, facilitate understanding of the drivers of spatiotemporal population dynamics, and provide new insights for management advice. The model fits to spatial survey and fishery-dependent catch data. It implicitly accounts for seasonal movement between the time of the survey and that of fishery to estimate fine-scale spatial population dynamic and fishing impacts, including potential environmental drivers. We quantify, for the first time, spatiotemporal variation in exploitable abundance, fishing mortality, recruitment, and mature and immature abundance. The model estimated declines in exploitable abundance and in fishing mortality with variable spatial distributions, and sporadic recruitment, spatially concentrated in the northeast EBS. Few spatial assessments have been used as the basis for management advice and we consider this study as a step towards the integration of spatial dynamics in stock assessment.

Explicit abstract neutral differential equations with state-dependent delay: Existence, uniqueness and local well-posedness

We study the local and global existence and uniqueness of strict solution and the local well-posedness for a class of abstract “explicit” neutral integro-differential equations with state-dependent delay. In the last section some examples motivated by explicit neutral ordinary integro-differential equations arising in the theory of population dynamics are presented.

Quantifying and Disentangling the Competition Effect of a Weed Community in a Long-Term Biennial Cereal-Legume Rotation

Weeds are a permanent constraint on crop productivity in agriculture. Due to the importance of the effect of weeds on the crop, there has been great interest in establishing the competitive ability of each species to optimize its control. This work presents a new methodology approach to determining the relative competitiveness of weed species based on population dynamics theory, which is applied to establish the competitiveness of Papaver rhoeas L. (PAP), Veronica hederifolia L. (VER), Descurainia sophia L. (DES) and Fumaria spp. (FUM) infesting a biennial cereal-legume rotation under conventional tillage. Data to fit the nonlinear population dynamic models were obtained from a long-term experiment (32 years) in Mediterranean drylands. The results showed asymmetric competitive interactions, and the competitive ability of weeds was crop specific. In cereals, the competitiveness ranking order was FUM > PAP > VER > DES, with strong interspecific competition; in legumes, it was VER > FUM > DES > PAP, with weak interspecific competition intensity. Overall, intraspecific competition was stronger than interspecific competition in the rotation system. The information gained in these studies can provide insights into the role of the intraspecific and interspecific competition in weed communities and help identify weed species that are relatively poor competitors in given crops.

Theoretical Advances in the Ecology and Evolution of Mutualistic Interactions – Review of a Symposium (SYMP 14) Organized at ESA + CSEE 2022 Joint Meeting

Theoretical Advances in the Ecology and Evolution of Mutualistic Interactions – Review of a Symposium (<scp>SYMP</scp> 14) Organized at <scp>ESA</scp> + <scp>CSEE</scp> 2022 Joint Meeting

Population dynamics models for various forms of adaptation.

Adaptability to changing environments is one of the universal characteristics of living organisms. Because individual modes of adaptation are diverse, a unified understanding of these diverse modes is essential to comprehend adaptation. Adaptations can be categorized from at least two perspectives with respect to information. One is the passivity and activity of adaptation and the other is the type of information transmission. In Darwinian natural selection, organisms are selected among randomly generated traits under which individual organisms are passive in the sense that they do not process any environmental information. On the other hand, organisms can also adapt by sensing their environment and changing their traits. This is an active adaptation in that it makes use of environmental information. In terms of information transfer, adaptation through phenotypic heterogeneity, such as bacterial bet-hedging, is intragenerational in which traits are not passed on to the next generation. In contrast, adaptation through genetic diversity is intergenerational. The theory of population dynamics enables us to unify these various modes of adaptations and their properties can be analyzed qualitatively and quantitatively using techniques from quantitative genetics and information thermodynamics. In addition, such methods can be applied to situations where organisms can learn from past experiences and pass them on from generation to generation. In this work, we introduce the unified theory of biological adaptation based on population dynamics and show its potential applications to evaluate the fitness value of information and to analyze experimental lineage tree data. Finally, we discuss future perspectives for its development. This review article is an extended version of the Japanese article in SEIBUTSU BUTSURI Vol. 57, p. 287-290 (2017).

RETRACTED: Dynamics of Stochastic Integrate-and-Fire Networks

A new theory of neural population dynamics incorporates biophysical nonlinearities not included in other models, bridging the gap between the complex biophysics of single neurons and simplified population-level models.

Ecological theory of mutualism: Robust patterns of stability and thresholds in two-species population models.

Mutualisms are ubiquitous in nature, provide important ecosystem services, and involve many species of interest for conservation. Theoretical progress on the population dynamics of mutualistic interactions, however, comparatively lagged behind that of trophic and competitive interactions, leading to the impression that ecologists still lack a generalized framework to investigate the population dynamics of mutualisms. Yet, over the last 90 years, abundant theoretical work has accumulated, ranging from abstract to detailed. Here, we review and synthesize historical models of two‐species mutualisms. We find that population dynamics of mutualisms are qualitatively robust across derivations, including levels of detail, types of benefit, and inspiring systems. Specifically, mutualisms tend to exhibit stable coexistence at high density and destabilizing thresholds at low density. These dynamics emerge when benefits of mutualism saturate, whether due to intrinsic or extrinsic density dependence in intraspecific processes, interspecific processes, or both. We distinguish between thresholds resulting from Allee effects, low partner density, and high partner density, and their mathematical and conceptual causes. Our synthesis suggests that there exists a robust population dynamic theory of mutualism that can make general predictions.

Mapping input noise to escape noise in integrate-and-fire neurons: a level-crossing approach

Noise in spiking neurons is commonly modeled by a noisy input current or by generating output spikes stochastically with a voltage-dependent hazard rate (“escape noise”). While input noise lends itself to modeling biophysical noise processes, the phenomenological escape noise is mathematically more tractable. Using the level-crossing theory for differentiable Gaussian processes, we derive an approximate mapping between colored input noise and escape noise in leaky integrate-and-fire neurons. This mapping requires the first-passage-time (FPT) density of an overdamped Brownian particle driven by colored noise with respect to an arbitrarily moving boundary. Starting from the Wiener–Rice series for the FPT density, we apply the second-order decoupling approximation of Stratonovich to the case of moving boundaries and derive a simplified hazard-rate representation that is local in time and numerically efficient. This simplification requires the calculation of the non-stationary auto-correlation function of the level-crossing process: For exponentially correlated input noise (Ornstein–Uhlenbeck process), we obtain an exact formula for the zero-lag auto-correlation as a function of noise parameters, mean membrane potential and its speed, as well as an exponential approximation of the full auto-correlation function. The theory well predicts the FPT and interspike interval densities as well as the population activities obtained from simulations with colored input noise and time-dependent stimulus or boundary. The agreement with simulations is strongly enhanced across the sub- and suprathreshold firing regime compared to a first-order decoupling approximation that neglects correlations between level crossings. The second-order approximation also improves upon a previously proposed theory in the subthreshold regime. Depending on a simplicity-accuracy trade-off, all considered approximations represent useful mappings from colored input noise to escape noise, enabling progress in the theory of neuronal population dynamics.

Structural identifiability of the generalized Lotka-Volterra model for microbiome studies.

Population dynamic models can be used in conjunction with time series of species abundances to infer interactions. Understanding microbial interactions is a prerequisite for numerous goals in microbiome research, including predicting how populations change over time, determining how manipulations of microbiomes affect dynamics and designing synthetic microbiomes to perform tasks. As such, there is great interest in adapting population dynamic theory for microbial systems. Despite the appeal, numerous hurdles exist. One hurdle is that the data commonly obtained from DNA sequencing yield estimates of relative abundances, while population dynamic models such as the generalized Lotka–Volterra model track absolute abundances or densities. It is not clear whether relative abundance data alone can be used to infer parameters of population dynamic models such as the Lotka–Volterra model. We used structural identifiability analyses to determine the extent to which a time series of relative abundances can be used to parametrize the generalized Lotka–Volterra model. We found that only with absolute abundance data to accompany relative abundance estimates from sequencing can all parameters be uniquely identified. However, relative abundance data alone do contain information on relative interaction strengths, which is sufficient for many studies where the goal is to estimate key interactions and their effects on dynamics. Using synthetic data of a simple community for which we know the underlying structure, local practical identifiability analysis showed that modest amounts of both process and measurement error do not fundamentally affect these identifiability properties.

Uncertain Linear Stationary Model of Population Density in a Bounded Habitat

The purpose of this article is to identify an uncertain linear time-invariant (LTI) model of the spatial distribution of a specimen over 1-D habitual space. Population density is described by a nonlinear reaction-diffusion partial differential equation (PDE) following the population dynamics theory. The nonlinear PDE is approximated with a linear parameter varying state-space model from the 120th order with two inputs and 100 outputs, which describe the spatial distribution where the manipulated variable in the model is the length of the habitat. A random excitation signal is applied corresponding to expansion or contraction of the habitual space to assess the dynamical response of the population density. The collected data are used to estimate 100 Box and Jenkins (BJ) models, which describe the reaction of population density across the habitat. Then, a single uncertain LTI model is identified from the magnitude frequency response of the BJ models to cover all of them.

Voevodsky's unfinished project: Filling the gap between pure and applied mathematics

In a series of lectures given in 2003, soon after receiving the Fields Medal for his results in the Algebraic Geometry, Vladimir Voevodsky (1966–2017) identifies two strategic goals for mathematics, which he plans to pursue in his further research. The first goal is to develop a ‘‘computerised library of mathematical knowledge,’’ which supports an automated proof-verification. The second goal is to ‘‘bridge pure and applied mathematics.’’ Voevodsky's research towards the first goal brought about the new Univalent foundations of mathematics. In view of the second goal Voevodsky in 2004 started to develop a mathematical theory of Population Dynamics, which involved the Categorical Probability theory. This latter project did not bring published results and was abandoned by Voevodsky in 2009 when he decided to focus his efforts on the Univalent foundations and closely related topics. In the present paper, which is based on Voevodsky's archival sources, I present Voevodsky's views of mathematics and its relationships with natural sciences, critically discuss these views, and suggest how Voevodsky's ideas and approaches in the applied mathematics can be further developed and pursued. A special attention is given to Voevodsky's original strategy to bridge the persisting gap between pure and applied mathematics where computers and the computer-assisted mathematics play a major role.

Comments on Vladimir Voevodsky's biologically motivated works

Vladimir Voevodsky's contribution to Algebraic K-Theory is well known and was recognised by awarding him the Fields Medal. He became widely known in mathematical circles for his daring project of reforming the Foundations of Mathematics, a project he pursued until his untimely death. His ideas on the so-called “univalent” foundations of mathematics were taken up by a broad community of mathematicians and continue to be developed today. Less well known is that he devoted several years of his life to a biologically motivated project aimed at developing a mathematical theory of population dynamics. He never published anything about it. The aim of the article is to summarise his ideas on this project and to draw them to the attention of the scientific community.

Spatial and temporal shift in the factors affecting the population dynamics of Calanus copepods in the North Sea.

The swap in abundance between two Calanus species in the North Sea during the 1980s constitutes a quintessential example of regime shift, with important ecosystemic and economic repercussions because these copepods constitute a major component of the diet of larval and juvenile cods. It is hypothesized that this transition was driven by gradual changes in primary productivity, the North Atlantic Oscillation (NAO) and sea surface temperatures (SST), and yet how these factors contribute to the population dynamics of these two species and the overall regime shift remains unclear. Here, we combine a highly resolved and spatially structured longitudinal dataset with population dynamics theory-based models to obtain a thorough and more detailed description of populations' responses to the regime shift observed in the North Sea. Our analyses highlight that this transition exhibits a clear spatial structure and involved a decoupling between the dynamics of Calanus finmarchicus and the NAO in western regions and between Calanus helgolandicus and SST in the eastern regions of the North Sea. Consequently, the observed switch in abundance between these species reflects the interaction between species-specific attributes, a well-defined spatial structure with a marked east-west axis and a decoupling between the ecological drivers and Calanus population dynamics following the shift. Succinctly, we suspect that higher water temperatures have favored C. helgolandicus and resulted in restrictive conditions for C. finmarchicus, eventually overshadowing the effects of NAO detected in historical records. Overall, our study illustrates how population dynamics theory can be successfully employed to disentangle the complex and multifactorial nature of a regime shift in response to gradually changing environmental conditions.

Long-range Coulomb interactions and nonhydrodynamic behavior in thermal quenches in spin ice

When spin ice systems undergo a sudden thermal quench, they have been shown to enter long-lived metastable states where the monopole excitations form so-called noncontractible pairs [Phys. Rev. Lett. 104, 107201 (2010)]. While the nature of these states is well understood, the dynamical mechanisms underpinning their formation remain largely unexplored and are the subject of this study. We find that the long-range tail of the Coulomb interactions between monopoles plays a central role by suppressing the monopole-assisted decay of noncontractible pairs with respect to monopole-antimonopole annihilation. In conjunction with low final quench temperatures, where the system enters a nonhydrodynamic regime in which the monopoles effectively move at terminal velocity in the direction of the local force acting on them, the interactions lead to a metastable plateau that persists in the thermodynamic limit. This is a remarkable phenomenon, reminiscent of jamming and some instances of glassiness: A transient modification of the short-time dynamics of the system allows it to enter a metastable state whose lifetime can easily be astronomically large at (experimentally relevant) low temperatures. We demonstrate this using Monte Carlo simulations and mean field population dynamics theory, and we provide an analytical understanding of the mechanisms at play. When the interactions between monopoles are truncated to finite range, the metastable plateau reduces to a finite size effect. We derive the finite size scaling behaviour of the density of noncontractible pairs in the metastable plateau for both short- and long-range interactions, and discuss the experimental implications of our results.

Defining spatial structure for fishery stock assessment

In principle, the spatial extent of fishery stock assessment should reflect the biological population, and major fishing patterns or population heterogeneity within the area should be represented. However, these theoretical requirements are commonly dismissed in practice, often when there is compelling evidence that spatial scope and structure is mis-specified and without testing if the mis-specified model performs well for informing fishery management. Population dynamics theory, case studies in fishery management as well as simulation tests demonstrate that accurately accounting for spatial structure in stock assessments can improve model performance, and ignoring spatial structure can lead to misperceptions of stock status and failures in fisheries management. Therefore, the development of stock assessment applications should include an evaluation of the most appropriate spatial scope and structure. Some common challenges in defining and modeling spatial structure can be addressed by adopting general best practices, but each species and its fisheries are unique. Accordingly, determining the most appropriate spatial structure involves 1) an interdisciplinary synthesis of all available information to determine the most plausible paradigms of population structure and fishing patterns, 2) the development of spatial operating models that are conditioned on these paradigms, and 3) testing the performance of estimation models and management strategies that are based on the current spatial management unit as well as alternative spatial scopes and structures that reflect population structure and fishing patterns.

Many-body perturbation theory and fluctuation relations for interacting population dynamics.

Population dynamics deals with the collective phenomena of living organisms, and it has attracted much attention since it is expected to explain how not only living organisms but also human beings have been adapted to varying environments. However, it is quite difficult to insist on a general statement on living organisms since mathematical models heavily depend on phenomena that we focus on. Recently, it was reported that the fluctuation relations on the fitness of living organisms held for a quite general problem setting. But, interactions between organisms were not incorporated in the problem setting, though interaction plays critical roles in collective phenomena in physics and population dynamics. In this paper, we propose interacting models for population dynamics and provide the perturbative theory of population dynamics. Then, we derive the variational principle and fluctuation relations for interacting population dynamics.

La red teórica de la dinámica de poblaciones

The general aim of this article is to carry out a reconstruction of the theory of Population Dynamics (DP) in Ecology, according to Castle’s (2001) general stance with regard to the semantic view of theories, but doing it within the framework of metatheoretical structuralism. Thus, we will first identify Population Dynamics’ basic theory-element: its core K(DP) – with the class of potential models, the class of models (through the identification of its fundamental law) and the class of partial potential models (though leaving aside the identification of its constraints and its intertheoretical links) –, and its domain of intended applications I(DP). Then, we will establish the general guiding lines of its theory-net, developing in some detail one of its main lines of specialization – namely, that related to the so-called “continuous growing” of the considered populations –, with DP’s principal “models”, and leave developing of the other of its main lines of specialization – namely, that related to the so-called “discrete growing” of the considered populations – for a further publication.