Population dynamics in river networks: analysis of steady states

Journal of Mathematical Biology - We study the population dynamics of an aquatic species in a river network. The habitat is viewed as a binary tree-like metric graph with the population density...     

Experimental evidence for the effect of habitat loss on the dynamics of migratory networks

Migratory animals present a unique challenge for understanding the consequences of habitat loss on population dynamics because individuals are typically distributed over a series of interconnected breeding and non‐breeding sites (termed migratory network). Using replicated breeding and non‐breeding populations of Drosophila melanogaster and a mathematical model, we investigated three hypotheses to explain how habitat loss influenced the dynamics of populations in networks with different degrees of connectivity between breeding and non‐breeding seasons. We found that habitat loss increased the degree of connectivity in the network and influenced population size at sites that were not directly connected to the site where habitat loss occurred. However, connected networks only buffered global population declines at high levels of habitat loss. Our results demonstrate why knowledge of the patterns of connectivity across a species range is critical for predicting the effects of environmental change and provide empirical evidence for why connected migratory networks are commonly found in nature.     

Population persistence in river networks

Organisms inhabiting river systems contend with downstream biased flow in a complex tree-like network. Differential equation models are often used to study population persistence, thus suggesting resolutions of the ‘drift paradox’, by considering the dependence of persistence on such variables as advection rate, dispersal characteristics, and domain size. Most previous models that explicitly considered network geometry artificially discretized river habitat into distinct patches. With the recent exception of Ramirez (J Math Biol 65:919–942, 2012), partial differential equation models have largely ignored the global geometry of river systems and the effects of tributary junctions by using intervals to describe the spatial domain. Taking advantage of recent developments in the analysis of eigenvalue problems on quantum graphs, we use a reaction–diffusion–advection equation on a metric tree graph to analyze persistence of a single population in terms of dispersal parameters and network geometry. The metric graph represents a continuous network where edges represent actual domain rather than connections among patches. Here, network geometry usually has a significant impact on persistence, and occasionally leads to dramatically altered predictions. This work ranges over such themes as model definition, reduction to a diffusion equation with the associated model features, numerical and analytical studies in radially symmetric geometries, and theoretical results for general domains. Notable in the model assumptions is that the zero-flux interior junction conditions are not restricted to conservation of hydrological discharge.     

Population synchrony in small-world networks

Network topography ranges from regular graphs (linkage between nearest neighbours only) via small-world graphs (some random connections between nodes) to completely random graphs. Small-world linkage is seen as a revolutionary architecture for a wide range of social, physical and biological networks, and has been shown to increase synchrony between oscillating subunits. We study small-world topographies in a novel context: dispersal linkage between spatially structured populations across a range of population models. Regular dispersal between population patches interacting with density-dependent renewal provides one ecological explanation for the large-scale synchrony seen in the temporal fluctuations of many species, for example, lynx populations in North America, voles in Fennoscandia and grouse in the UK. Introducing a small-world dispersal kernel leads to a clear reduction in synchrony with both increasing dispersal rate and small-world dispersal probability across a variety of biological scenarios. Synchrony is also reduced when populations are affected by globally correlated noise. We discuss ecological implications of small-world dispersal in the frame of spatial synchrony in population fluctuations.     

Population assignment reveals low migratory connectivity in a weakly structured songbird

Understanding migratory connectivity is essential for determining the drivers behind population dynamics and for implementing effective conservation strategies for migratory species. Genetic markers provide a means to describe migratory connectivity; however, they can be uninformative for species with weak population genetic structure, which has limited their application. Here, we demonstrated a genomic approach to describing migratory connectivity in the prothonotary warbler, Protonotaria citrea, a Neotropical songbird of conservation concern. Using 26,189 single nucleotide polymorphisms (SNPs), we revealed regional genetic structure between the Mississippi River Valley and the Atlantic Seaboard with overall weak genetic differentiation among populations (F_ST = 0.0055; 95% CI: 0.0051–0.0059). Genetic variation had a stronger association with geographic rather than environmental factors, with each explaining 14.5% and 8.2% of genetic variation, respectively. By varying the numbers of genomic markers used in population assignment models with individuals of known provenance, we identified a maximum assignment accuracy (89.7% to site, 94.3% to region) using a subset of 600 highly differentiated SNPs. We then assigned samples from nonbreeding sites to breeding region and found low migratory connectivity. Our results highlight the importance of filtering markers for informative loci in models of population assignment. Quantifying migratory connectivity for weakly structured species will be useful for expanding studies to a wider range of migratory species across taxonomic groups and may contribute to a deeper understanding of the evolution of migratory strategies.     

飞蝗的种群遗传学与亚种地位

飞蝗是一种重大农业害虫,其分布范围几乎覆盖了东半球的整个温带和热带地区。由于飞蝗的远距离迁移习性,不同地理种群间的基因交流非常复杂。基于形态学特征,飞蝗曾被建议划分为13个亚种。然而,这些亚种的分类地位一直存有争议,不同亚种或地理种群间的亲缘关系也不十分清楚。近年来飞蝗分子谱系地理学研究的开展,尤其是基于线粒体基因组序列的研究,为飞蝗的种群遗传关系提供了全新的观点。线粒体基因组研究结果表明,飞蝗起源于非洲,通过南北2个主要线路扩散到整个旧世界。分子证据证明世界范围内仅有2个飞蝗亚种,分布于欧亚大陆温带地区的飞蝗属于亚洲飞蝗Locusta migratoria migratoria,分布于非洲、大洋洲和欧亚大陆南部地区的飞蝗属于非洲飞蝗L.m.migratorioides,所有其它的亚种和地理宗都是这2个亚种的地理种群。文中就飞蝗的种群遗传学、亚种分类的研究历史和研究进展进行了综述,还就许多飞蝗地理种群的谱系地理关系进行了讨论。     

Climate patterns and the stochastic dynamics of migratory birds

We analyse time series data of 17 bird species trapped at Ottenby Bird Observatory, Sweden, during spring migration 1972–1999. The species have similar demography but respond differently to variation in the North Atlantic Oscillation (NAO) – a strong determinant of winter climate in the northern Hemisphere. Species wintering in northern Europe, compared to species having winter quarters in the Mediterranean area, tend to respond positively to variation in NAO. The variation within each group is high due to wide-ranging winter-distribution in many species, probably smoothing out the effect of spatial variation in NAO. Whereas mild winters (high NAO) is benign for many – but not all – birds wintering in northern Europe, the effect of drier-than-normal conditions in the Mediterranean area during high NAO index winters are uncertain. The work presented here goes beyond simple correlative studies and help identifying which species that are most affected by variation in winter climate. This is a first important step that calls for a more mechanistic approach when analysing possible changes to climate change.     

Population dynamics in ageing Helicobacter pylori

The aim of this work was to characterize population changes occurring in aged broth cultures of Helicobacter pylori. Experiments were performed using clinical strains cultured immediately after isolation and after multiple subcultures in solid medium. Morphological changes in the ageing bacteria during a 7-day broth culture were analysed by optical and electron microscopy. The expression of the virulence factor, CagA, together with the presence of the cell cycle regulator, cGMP, were also assessed. The transition from bacillary to coccoid forms was the main morphological change observed in freshly isolated bacteria, together with the increase in cGMP from 1 to 2.25 nmoles/mg of proteins within the first 7 days of broth culture. A similar trend of morphological and physiological changes was observed in cells after multiple subcultures in solid medium with a major presence of large cell clusters. The cagA gene product was always expressed in all experimental conditions evaluated. These data show a significant morphological and physiological diversity in fresh, ageing and aged cultures of H. pylori.     

Population dynamics in tumor growth modeling

A new approach based on local interaction between cancer and tissue cells was applied to the problem of the onset and growth of solid tumors in homogeneous tissues and effects associated with dramatic changes in tumor growth after crossing the boundary between different tissues. The characteristic sizes and growth rates of spherical tumors, the points of the beginning and the end of spherical growth, and the further development of complex structures from the spherical ones (rough interface between the tumor and the host tissue, elongate outgrowths, dendritic structures, and metastases) were inferred assuming that the reproduction rate of a population of cancer cells is a nonmonotone function of their local concentration and thus of the local curvature of the tumor surface.     

Population dynamics in modeling tumor growth

A new approach based on local interaction between cancer and tissue cells is applied to the problem of the onset and growth of solid tumors in homogeneous tissues and effects associated with dramatic changes in tumor growth after crossing the boundary between different tissues. The characteristic sizes and growth rates of spherical tumors, the points of the beginning and the end of spherical growth, and further development of complex structures from the spherical ones (rough interface between the tumor and the host tissue, elongate outgrowths, dendritic structures, and metastases) are inferred assuming that the reproduction rate of a population of cancer cells is a nonmonotonous function of their local concentration and thus of the local curvature of the tumor surface. The growth behavior changes dramatically when the tumor crosses a boundary between two tissues.     

Spatiotemporal dynamics in large-scale cortical networks

Investigating links between nervous system function and behavior requires monitoring neuronal activity at a range of spatial and temporal scales. Here, we summarize recent progress in applying two distinct but complementary approaches to the study of network dynamics in the neocortex. Mesoscopic calcium imaging allows simultaneous monitoring of activity across most of the cortex at moderate spatiotemporal resolution. Electrophysiological recordings provide extremely high temporal resolution of neural signals at multiple targeted locations. A number of recent studies have used these tools to reveal novel patterns of activity across distributed cortical subnetworks. This growing body of work strongly supports the hypothesis that the dynamic coordination of spatially distinct regions is a fundamental aspect of cortical function that supports cognition and behavior.     

Correlated dynamics in egocentric communication networks

We investigate the communication sequences of millions of people through two different channels and analyse the fine grained temporal structure of correlated event trains induced by single individuals. By focusing on correlations between the heterogeneous dynamics and the topology of egocentric networks we find that the bursty trains usually evolve for pairs of individuals rather than for the ego and his/her several neighbours, thus burstiness is a property of the links rather than of the nodes. We compare the directional balance of calls and short messages within bursty trains to the average on the actual link and show that for the trains of voice calls the imbalance is significantly enhanced, while for short messages the balance within the trains increases. These effects can be partly traced back to the technological constraints (for short messages) and partly to the human behavioural features (voice calls). We define a model that is able to reproduce the empirical results and may help us to understand better the mechanisms driving technology mediated human communication dynamics.     

Threshold learning dynamics in social networks

Social learning is defined as the ability of a population to aggregate information, a process which must crucially depend on the mechanisms of social interaction. Consumers choosing which product to buy, or voters deciding which option to take with respect to an important issue, typically confront external signals to the information gathered from their contacts. Economic models typically predict that correct social learning occurs in large populations unless some individuals display unbounded influence. We challenge this conclusion by showing that an intuitive threshold process of individual adjustment does not always lead to such social learning. We find, specifically, that three generic regimes exist separated by sharp discontinuous transitions. And only in one of them, where the threshold is within a suitable intermediate range, the population learns the correct information. In the other two, where the threshold is either too high or too low, the system either freezes or enters into persistent flux, respectively. These regimes are generally observed in different social networks (both complex or regular), but limited interaction is found to promote correct learning by enlarging the parameter region where it occurs.     

Population dynamics of gene transfer

Horizontal transfer of nucleic acid sequences is a widespread process of genetic change in bacterial populations, one taking on a variety of specific forms. A model capturing some of the general features of this process is formulated. Two major subsidiary variants of this model are analyzed. The first lacks competition between cells. In this case, the transferred genetic element can approach fixation asymptotically if cells bearing it are viable, but not otherwise. The second variant of the proposed model has competition. This gives rise to complex dynamical possibilities, but never fixation of the transferred genetic element. It is argued that the evolutionary transition from gene transfer polymorphism to obligatory genetic exchange, and thus the origin of sex, requires either population dynamics which are not subject to growth rate density-dependence or cell-dependence on transferred genetic elements, although such dependence does not require that the element be beneficial.     

Population dynamics of obligate cooperators

Obligate cooperative breeding species demonstrate a high rate of group extinction, which may be due to the existence of a critical number of helpers below which the group cannot subsist. Through a simple model, we study the population dynamics of obligate cooperative breeding species, taking into account the existence of a lower threshold below which the instantaneous growth rate becomes negative. The model successively incorporates (i) a distinction between species that need helpers for reproduction, survival or both, (ii) the existence of a migration rate accounting for dispersal, and (iii) stochastic mortality to simulate the effects of random catastrophic events. Our results suggest that the need for a minimum number of helpers increases the risk of extinction for obligate cooperative breeding species. The constraint imposed by this threshold is higher when helpers are needed for reproduction only or for both reproduction and survival. By driving them below this lower threshold, stochastic mortality of lower amplitude and/or lower frequency than for non-cooperative breeders may be sufficient to cause the extinction of obligate cooperative breeding groups. Migration may have a buffering effect only for groups where immigration is higher than emigration; otherwise (when immigrants from nearby groups are not available) it lowers the difference between actual group size and critical threshold, thereby constituting a higher constraint.     

Population response to environmental productivity throughout the annual cycle in a migratory songbird

Environmental factors affect migratory animal populations in every phase of their annual cycle and have significant impacts on breeding success and survival. The Breeding Bird Survey provides a long-term database for examining population trends in North American birds, allowing us to examine large-scale environmental factors that influence population abundance. We examined plant productivity as measured by normalized difference vegetation index (NDVI) over a 24-year period from 1983–2006 in bird conservation regions (BCRs) that overlapped Bullock's oriole (Icterus bullockii) breeding, moult, and wintering ranges to ask whether plant productivity in 1 year influences population abundance in the subsequent breeding season. Bullock's orioles have a moult-migration strategy, with a stopover moult in the Mexican monsoon region, which necessitates examining each stationary phase of the bird's annual cycle to understand the impacts of environmental factors on population abundance. Our results show increased breeding abundance in three (Great Basin, Coastal California and Shortgrass Prairies) of the six BCRs in which the species breeds following years with high NDVI values. We did not detect a response of breeding abundance to high NDVI values in the previous year in either the moulting region or in their primary over-wintering area in central Mexico. Our results demonstrate that large-scale annual variation in primary productivity on the breeding grounds can have an impact on breeding abundance in the following season, but further studies on migratory connectivity and on ecological mechanisms during the non-breeding seasons are needed to understand why we did not detect an influence of productivity during these periods.     

Population dynamics of flocculating yeasts

Abstract: The problem of understanding the recognition and specific interactions in a population of yeast flocculating cells is discussed. The biochemistry, physiology and genetics of flocculation is briefly reviewed. Yeast flocculation requires the expression of a specific protein (lectin) on flocculent cells, and carbohydrate (receptors) on neighbouring cells. Adhesion experiments performed with cells whose flocculation is repressed by growth conditions, indicating that the inhibition of flocculation is due to inhibition or inactivation of 'lectin-like' component. Additionally, using adhesion experiments, it is demonstrated that cells of non-flocculent strain interact by establishing a true bond with flocculent cells rather than by entrapment inside the floc matrix. As phenotypic expression of flocculation, for several strains, is shown to be repressed, modulated or induced by modifying growth conditions, the constitutiveness and inducibility of flocculation are also discussed.