The genealogical decomposition of a matrix population model with applications to the aggregation of stages

Mapping Intimacies ◽

10.1101/067793 ◽

2016 ◽

Author(s):

François Bienvenu ◽

Erol Akçay ◽

Stéphane Legendre ◽

David M. McCandlish

Keyword(s):

Population Model ◽

Population Biology ◽

Projection Matrix ◽

Dominant Eigenvalue ◽

Matrix Population Model ◽

Ergodic Markov Chain ◽

Number Of Classes ◽

The Relationship ◽

Asymptotic Growth Rate ◽

Central Tool

AbstractMatrix projection models are a central tool in many areas of population biology. In most applications, one starts from the projection matrix to quantify the asymptotic growth rate of the population (the dominant eigenvalue), the stable stage distribution, and the reproductive values (the dominant right and left eigenvectors, respectively). Any primitive projection matrix also has an associated ergodic Markov chain that contains information about the genealogy of the population. In this paper, we show that these facts can be used to specify any matrix population model as a triple consisting of the ergodic Markov matrix, the dominant eigenvalue and one of the corresponding eigenvectors. This decomposition of the projection matrix separates properties associated with lineages from those associated with individuals. It also clarifies the relationships between many quantities commonly used to describe such models, including the relationship between eigenvalue sensitivities and elasticities. We illustrate the utility of such a decomposition by introducing a new method for aggregating classes in a matrix population model to produce a simpler model with a smaller number of classes. Unlike the standard method, our method has the advantage of preserving reproductive values and elasticities. It also has conceptually satisfying properties such as commuting with changes of units.

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A matrix population model to aid agency response to grass carp (Ctenopharyngodon idella) in the Great Lakes Basin - Lake Erie

Journal of Great Lakes Research ◽

10.1016/j.jglr.2020.06.022 ◽

2020 ◽

Author(s):

Mark R. DuFour ◽

Kelly F. Robinson ◽

Michael L. Jones ◽

Seth J. Herbst

Keyword(s):

Great Lakes ◽

Grass Carp ◽

Population Model ◽

Lake Erie ◽

Ctenopharyngodon Idella ◽

Matrix Population Model ◽

Great Lakes Basin ◽

Grass Carp Ctenopharyngodon Idella

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Transcranial direct current stimulation alters functional network structure in humans

10.1101/296657 ◽

2018 ◽

Author(s):

M. Ruttorf ◽

S. Kristensen ◽

L.R. Schad ◽

J. Almeida

Keyword(s):

Neuronal Activity ◽

Direct Current ◽

Transcranial Direct Current Stimulation ◽

Network Architecture ◽

Functional Magnetic Resonance ◽

Resonance Imaging ◽

Direct Current Stimulation ◽

Brain States ◽

The Relationship ◽

Central Tool

AbstractTranscranial direct current stimulation (tDCS) is routinely used in basic and clinical research, but its efficacy has been challenged on a methodological and statistical basis recently. The arguments against tDCS derive from insufficient understanding of how this technique interacts with brain processes physiologically. Because of its potential as a central tool in neuroscience, it is important to clarify whether and how tDCS affects neuronal activity. Here, we investigate influences of offline tDCS on network architecture measured by functional magnetic resonance imaging. Our results reveal a tDCS-induced reorganisation of a functionally-defined network that is dependent on whether we are exciting or inhibiting a node within this network, confirming in a functioning brain, and in a bias free and independent fashion that tDCS influences neuronal activity. Moreover, our results suggest that network-specific connectivity has an important role in defining the effects of tDCS and the relationship between brain states and behaviour.

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A multi-class extension of the mean field Bolker–Pacala population model

Random Operators and Stochastic Equations ◽

10.1515/rose-2018-0013 ◽

2018 ◽

Vol 26 (3) ◽

pp. 163-174 ◽

Cited By ~ 1

Author(s):

Mariya Bessonov ◽

Stanislav Molchanov ◽

Joseph Whitmeyer

Keyword(s):

Population Model ◽

Limit Theorems ◽

Mean Field ◽

Field Approximation ◽

Mean Field Approximation ◽

Geometric Ergodicity ◽

Equilibrium Solutions ◽

The Mean ◽

Number Of Classes ◽

Population Suppression

Abstract We extend our earlier mean field approximation of the Bolker–Pacala model of population dynamics by dividing the population into N classes, using a mean field approximation for each class but also allowing migration between classes as well as possibly suppressive influence of the population of one class over another class. For {N\geq 2} , we obtain one symmetric nontrivial equilibrium for the system and give global limit theorems. For {N=2} , we calculate all equilibrium solutions, which, under additional conditions, include multiple nontrivial equilibria. Lastly, we prove geometric ergodicity regardless of the number of classes when there is no population suppression across the classes.

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Savanna canopy trees under fire: long‐term persistence and transient dynamics from a stage‐based matrix population model

Ecosphere ◽

10.1002/ecs2.2706 ◽

2019 ◽

Vol 10 (5) ◽

Cited By ~ 5

Author(s):

Patricia A. Werner ◽

Stephanie J. Peacock

Keyword(s):

Population Model ◽

Transient Dynamics ◽

Matrix Population Model ◽

Canopy Trees

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Modelling patterns of parasite aggregation in natural populations: trichostrongylid nematode–ruminant interactions as a case study

Parasitology ◽

10.1017/s0031182000075867 ◽

1995 ◽

Vol 111 (S1) ◽

pp. S135-S151 ◽

Cited By ~ 97

Author(s):

B. T. Grenfell ◽

K. Wilson ◽

V. S. Isham ◽

H. E. G. Boyd ◽

K. Dietz

Keyword(s):

Population Biology ◽

Negative Binomial ◽

Natural Populations ◽

Parasite Load ◽

Host Immunity ◽

Moment Closure ◽

The Mean ◽

Parasite Aggregation ◽

The Impact ◽

The Relationship

SUMMARYThe characteristically aggregated frequency distribution of macroparasites in their hosts is a key feature of host–parasite population biology. We begin with a brief review of the theoretical literature concerning parasite aggregation. Though this work has illustrated much about both the sources and impact of parasite aggregation, there is still no definitive analysis of both these aspects. We then go on to illustrate the use of one approach to this problem – the construction of Moment Closure Equations (MCEs), which can be used to represent both the mean and second moments (variances and covariances) of the distribution of different parasite stages and phenomenological measures of host immunity. We apply these models to one of the best documented interactions involving free-living animal hosts – the interaction between trichostrongylid nematodes and ruminants. The analysis compares patterns of variability in experimental infections of Teladorsagia circumcincta in sheep with the equivalent wildlife situation – the epidemiology of T. circumcincta in a feral population of Soay sheep on St Kilda, Outer Hebrides. We focus on the relationship between mean parasite load and aggregation (inversely measured by the negative binomial parameter, k) for cohorts of hosts. The analysis and empirical data indicate that k tracks the increase and subsequent decline in the mean burden with host age. We discuss this result in terms of the degree of heterogeneity in the impact of host immunity or parasite-induced mortality required to shorten the tail of the parasite distribution (and therefore increase k) in older animals. The model is also used to analyse the relationship between estimated worm and egg counts (since only the latter are often available for wildlife hosts). Finally, we use these results to review directions for future work on the nature and impact of parasite aggregation.

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Holocene palynology: I principles, population and community ecology, palaeoclimatology

Progress in Physical Geography Earth and Environment ◽

10.1177/030913339101500303 ◽

1991 ◽

Vol 15 (3) ◽

pp. 261-289 ◽

Cited By ~ 16

Author(s):

Glen M. MacDonald ◽

Kevin J. Edwards

Keyword(s):

Population Biology ◽

Plant Population ◽

Fossil Pollen ◽

Pollen Data ◽

Plant Populations ◽

Climate Reconstructions ◽

Large Databases ◽

Temporal And Spatial ◽

The Relationship ◽

Important Progress

The latter half of the past decade witnessed important progress in elucidating the principles of fossil pollen analysis and in the application of palynology to the study of palaeoecology and palaeoclimatology. Areas with particularly notable efforts include: 1) the theoretical consideration of the spatial representation of fossil pollen records and the relationships of pollen proportions to the abundance of contributing plant populations; 2) the quest for palynological data with increasingly fine temporal and spatial resolution; 3) the development of large databases of modern and fossil pollen data for macroscale palaeoecological and palaeoclimatic studies; 4) the application of palynology to questions of plant population biology, most notably the study of plant invasion and implications for invading and pre-existing plant populations; 5) the demonstration of the relatively ephemeral nature of major vegetation types; 6) the refinement and development of techniques for providing quantitative estimates of past climate and testing climate reconstructions. Despite this progress important uncertainties remain regarding the relationship between plant abundance and pollen representation and the nature of climate-vegetation relationships, particularly at the meso- and microscales. Resolution of these questions is particularly important for plant population and climatic studies based on fossil pollen data.

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Pleomerism, the Widespread Tendency Among Related Fish Species for Vertebral Number to be Correlated with Maximum Body Length

Journal of the Fisheries Research Board of Canada ◽

10.1139/f75-283 ◽

1975 ◽

Vol 32 (12) ◽

pp. 2453-2469 ◽

Cited By ~ 80

Author(s):

C. C. Lindsey

Keyword(s):

Body Length ◽

Fish Species ◽

Population Biology ◽

Maximum Size ◽

Maximum Length ◽

Latitudinal Gradients ◽

Vertebral Number ◽

Sea Snakes ◽

The Relationship ◽

Maximum Body

Data for 3137 fish species were analyzed for possible correlations, among related species, between mean vertebral number (V) and maximum recorded body length (L). Of 118 families having counts for over 4 species, 90 show a positive correlation; statistically significant correlations are positive in 45 and negative in only 2 families. The relationship can be expressed by the power function V = CLm, in which C and m are constants characteristic of each family or taxon. Among families with a significant correlation between V and L, the median value of m is 0.12 (representing about 10% vertebral increase for each doubling of length) but m ranges widely, from −0.033 to +0.416. Families with high mean vertebral counts tend to have high m values. The phenomenon, termed pleomerism, occurs within genera as well as within families, and sometimes between races, between populations, or even between the sexes. It exists in widely different shapes of fishes (e.g. sharks, mackerels, sea horses, sand lances, and lumpfish), and in caecilians and in sea snakes. Latitudinal gradients in vertebral number (Jordan’s rule) are often reinforced by pleomerism coupled with latitudinal gradients in maximum length, but gradients in vertebral numbers persist even when effect of maximum length is removed. Although its cause is unknown, pleomerism is taxonomically useful in predicting adult sizes of species known only from young specimens, and in unmasking synonymies of "species" based on young of other named species. Vertebral number considered in conjunction with maximum size is more reliable for making taxonomic judgments at all levels than is vertebral number alone. Moreover, if the cause of pleomerism is functional, it may provide information on locomotory mechanisms and on population biology, since mean vertebral number in each population may be matched to that body size at which selection operates most significantly.

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PREDATOR REPRODUCTION AND THE OVERALL PREDATOR-PREY RELATIONSHIP

The Canadian Entomologist ◽

10.4039/ent1131015-11 ◽

1981 ◽

Vol 113 (11) ◽

pp. 1015-1024 ◽

Cited By ~ 16

Author(s):

B. D. Frazer ◽

N. Gilbert ◽

P. M. Ives ◽

D. A. Raworth

Keyword(s):

Biological Control ◽

Optimal Foraging ◽

Population Model ◽

Field Data ◽

Optimal Foraging Theory ◽

Large Field ◽

Predator Prey ◽

Aphid Density ◽

Pea Aphids ◽

The Relationship

AbstractPrevious work described the effects of predation of pea aphids by adult coccinellids. That work has been extended to cover the entire reproductive cycle of the coccinellids. The relationship between amount of aphids eaten, and numbers of coccinellid eggs produced, was determined in the laboratory and used to predict numbers of eggs produced in the field. The survival rate of the eggs to adults, as a function of aphid density, was estimated in large field cages and in small enclosures. These relationships were incorporated into a population model for both predators and prey. The model has been validated against field data. It suggests that predator reproduction is optimized when conditions are very good. The significance for optimal foraging theory and biological control is discussed.

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