`Mean Crowding'

Lloyd, Monte

doi:10.2307/3012

Cited by 1,030 publications

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“…They calculated: (i) prevalence, that is proportion of ovitraps with eggs; (ii) mean intensity, that is mean number of eggs per positive ovitrap; (iii) mean density (md), which is the product of prevalence and mean intensity (or total eggs in traps divided by number of traps with eggs); (iv) Lloyd's (1967) mean crowding (me), which can be calculated as mean density (md) plus the variance (var.) divided by mean density (md) minus one, thus me = md + varlmd -1, and (v) patchiness, which is mean density (md) divided by mean crowding (me).…”

Section: ·0 Mosquito Ecology: Field Sampling Methodsmentioning

confidence: 99%

Sampling the Egg Population

Service

1993

Mosquito Ecology

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Section: ·0 Mosquito Ecology: Field Sampling Methodsmentioning

confidence: 99%

Sampling the Egg Population

Service

1993

Mosquito Ecology

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“…Additionally, in an attempt to clarify the factors generating the observed distributions of T. gasterostei the method of Iwao (1970) involving regression of mean crowding (x), (Lloyd, 1967) on mean density (x) was applied. This technique was usefully employed by Boxshall (1974b) to analyse the dispersion pattern of the parasitic copepod Lepeophtheirus pectoralis.…”

Section: Methodsmentioning

confidence: 99%

Thersitina gasterostei(Pagenstecher, 1861) (Copepoda : Ergasilidae) infecting the sticklebackPungitius pungitiusL. at Chalk Marshes, Gravesend, Kent

Donoghue

1986

Ann. Parasitol. Hum. Comp.

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Section: Analytic Approximationmentioning

confidence: 99%

“…Quantities such as σ and τ +/+ measure the local density of the population. Indeed, Harada and Iwasa (1994) show that τ +/+ is exactly the mean crowding index, if the latter is measured using only nearest-neighbor pairs (Lloyd, 1967).Suppose that the (finite) lattice contains L sites; by definition, Lρ(t) sites are occupied. At each occupied site, the death process is a Poisson process with parameter µ.…”

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confidence: 99%

Pair statistics clarify percolation properties of spatially explicit simulations

Achter

Webb

2006

Theoretical Population Biology

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Dispersal is a fundamental control on the spatial structure of a population. We investigate the precise mechanism by which a mixed strategy of short-and long-distance dispersal affects spatial patterning. Using techniques from pair approximation and percolation theory, we demonstrate that dispersal controls the extent to which a population is completely connected by modulating the proportion of neighboring sites which are simultaneously occupied. We show that near the percolation threshold this pair statistic, rather than other metrics proposed earlier, best explains clustering, and we suggest more general circumstances under which this may hold.Key words: dispersal, percolation, pair approximation, aggregation, spatial models, connectivity 2 Understanding the sources and consequences of spatial heterogeneity is a fundamental task in ecology (Levin, 1992). Both in terrestrial (Cain et al., 2000) and marine (Carlon and Olson, 1993) systems, dispersal is one of the basic forces which shapes the spatial structure of a population (Levin and Muller-Landau, 2000; Tilman and Kareiva, 1997). A poorly-dispersing species shows spatial autocorrelation, whereas long-distance dispersal contributes to the spatial mixing of a population (Reed et al., 2000). This spatial patterning has important consequences for phenomena such as species coexistence (Bolker and Pacala, 1999), vulnerability to and recovery from disturbance (Etter and Caswell, 1994;Hiebeler, 2004), and other aspects of ecosystem function (Pacala and Deutschman, 1995). Through such mechanisms, whether dispersal is highly localized, long-distance, or a mixture of the two can affect the spatiotemporal dynamics of a population.In this paper, we examine the effects of mixed dispersal strategies on the spatial structure of a population. To this end we consider a spatially explicit birth-death model, in which organisms have a mixed strategy of local and global dispersal. We will see that the exact strategy -that is, the relative frequency of local and global dispersal -has important consequences for the spatial structure of a population. Specifically, we show that whether a population is completely connected depends on the proportion of pairs of neighboring sites which are simultaneously occupied, and that dispersal influences patterns of aggregation by changing this pair statistic. (Earlier statements in the literature (Iwasa, 2000;Kubo et al., 1996) imply that clustering is determined by a conditional site occupation probability which is related to, but distinct from, the pair statistic.) Briefly, local density controls global connectedness.Much prior work on spatially-explicit, single-species systems has focused on the special case of either purely local (de Aguiar et al., 2004;Haraguchi and Sasaki, 2000) or purely global (Deredec and Courchamp, 2003;Tilman, 1994) dispersal. Other researchers have examined both cases simultaneously (Boots and Sasaki, 2000;Socolar et al., 2001), without considering intermediate or mixed strategies.A class of models which expli...

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`Mean Crowding'

Cited by 1,030 publications

References 0 publications

Sampling the Egg Population

Sampling the Egg Population

Thersitina gasterostei(Pagenstecher, 1861) (Copepoda : Ergasilidae) infecting the sticklebackPungitius pungitiusL. at Chalk Marshes, Gravesend, Kent

Pair statistics clarify percolation properties of spatially explicit simulations

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