On the True Rate of Natural Increase

Dublin, Louis I.; Lotka, Alfred J.

doi:10.2307/2965517

Cited by 130 publications

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“…The following parameters were estimated based on values of age (X), age-specific survival rate (lx) and age-specific fecundity rate (mx): net reproductive rate: Ro = ∑lx.mx; mean generation time: T = ∑ (lx.mx.X) / ∑ (lx.mx); intrinsic rate of natural increase (r), calculated from Lotka equation (Dublin and Lotka, 1925): ∑lx.mx.e -r(x+0.5) =1. The initial value for r was obtained through an iteration process starting from an analytical approximation for r given as r = Ln(Ro) / T (Rabinovich, 1980;Carey, 1993); finite rate of increase: λ = e r ; doubling time: DT = Ln 2 / r.…”

Section: Methodsmentioning

confidence: 99%

Life table of Hypothenemus hampei (Ferrari) in relation to coffee berry phenology under Colombian field conditions

Ruiz-Cárdenas

Baker

2010

Sci. agric. (Piracicaba, Braz.)

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The overlap of generations of coffee berry borer (CBB), Hypothenemus hampei (Ferrari) under field conditions in countries like Colombia hinders the construction of life tables by the sampling of natural populations. In this paper, a field methodology to carry out regular measurements of CBB cohorts inside coffee berries of different ages until harvest, both in coffee trees and in infested berries placed on the ground, is developed and used to compare the life history parameters of CBB. Populations with berries at six ages in three experimental stations (without CBB control) and in a commercial farm in Colombia (with chemical CBB control regularly carried out) were used. The duration of the pre-oviposition period as well as the mortality and survival rates of founder females and the proportion of founders leaving infested berries were strongly influenced by the consistency of berries, with optimum conditions for CBB reproduction as from 120-150 days after flowering. No differences were found between stations for the number of CBB developmental stages; but they had larger values than the commercial farm. The latter also had more than twice the average rate of founders leaving infested berries recorded in the stations. Survival functions (cumulative probabilities of survival) for the pest differed among treatments and between the plant and ground micro-environments. Age of berries at infestation was positively related to the intrinsic rate of increase of borer population; whilst generation time and doubling time were inversely related. No differences were found between sites for the main demographic parameters of the pest. Key words: coffee berry borer, population parameters, integrated pest management Tabela de vida de Hypothenemus hampei (Ferrari) em relação à fenologia do fruto de café, sob condições de campo, na Colômbia RESUMO: A superposição de gerações da broca do café, Hypothenemus hampei (Ferrari) em condições de campo em países como a Colômbia dificulta a confecção de tabelas de vida pela amostragem de populações naturais. Desenvolveu-se uma metodologia de campo para realizar medições regulares de coortes da broca em frutos de café de diferentes idades até a colheita, tanto nas plantas quanto em frutos infestados colocados no solo. O método é usado para comparar parâmetros populacionais da praga em frutos de seis idades, em três estações experimentais (sem controle da praga) e em uma fazenda comercial (com controle químico da praga), na Colômbia. A duração do período de pre-oviposição, assim como as taxas de mortalidade e sobrevivência das fêmeas fundadoras e a proporção de fêmeas fundadoras que abandonaram frutos infestados foram fortemente influenciadas pela consistência dos frutos, com condições ótimas para a reprodução da praga a partir de 120-150 dias depois da floração. Não houve diferenças entre estações para o número de estágios de desenvolvimento da praga, mas os valores nestas foram maiores que na fazenda comercial. Esta última teve uma taxa de frutos abandonados duas vezes maior que a...

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Section: Methodsmentioning

confidence: 99%

Life table of Hypothenemus hampei (Ferrari) in relation to coffee berry phenology under Colombian field conditions

Ruiz-Cárdenas

Baker

2010

Sci. agric. (Piracicaba, Braz.)

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“…On the other hand, as we see in the Appendix, we can formulate the renewal equation for the target population to calculate other demographic indices, including the generation time, the intrinsic growth rate and the momentum of population growth, which are also useful to study the impact of heterogeneous individual behaviour on population dynamics as a whole. Historically speaking, as Heesterbeek (2002) pointed out, the concept of the net reproduction rate R 0 was already established at least in 1925 by Dublin and Lotka (Dublin and Lotka 1925;Lotka 1998) in demography, 19 while it has taken more than 50 years for the concept to mature in epidemiology. Moreover it was not until recently that stable population theory became a popular tool in mathematical epidemiology (Wallinga and Lipsitch 2007) and I believe that there are still many ideas and concepts in demography that should be learned by epidemiologists.…”

Section: Discussionmentioning

confidence: 99%

“…According to the classical stable population theory (Dublin and Lotka 1925;Lotka 1998;Keyfitz and Caswell 2005), λ 0 is a unique real root of the Lotka's characteristic equation:…”

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confidence: 99%

The net reproduction rate and the type-reproduction number in multiregional demography

Inaba¹

2010

Populationyearbook

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In order to study effects of migration on demographic changes of multiregional populations, multiregional population modelling is a useful traditional tool. Although multiregional mathematical demography has been extensively explored since the beginning of the 1970s, its key concept, the multiregional net reproduction rate, has been long neglected. In this review, we focus on a multiregional stable population system and elaborate the definition of the multiregional net reproduction rate. Next we introduce the type-reproduction number from mathematical epidemiology and show that it becomes a useful index to formulate a simple control relation for a multiregional population. Mathematical ideas presented here will help us to reconsider multiregional mathematical demography, which is a useful theoretical framework to study effects of interregional migration on population dynamics and composition.

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“…It implies that if one applies a constant set of fertility, mortality, and migration rates to two arbitrarily chosen age distribution, no matter how different, the two age distributions will ultimately converge to the same age distribution. Alfred J. Lotka is generally credited with formulating the idea of a stable population and exploring many of its important features, including the finding that in the absence of migration, a population subject to constant fertility and mortality rates would eventually have a constant rate of natural increase [4,5]. Continuing the analytical tradition established by Lotka, many researchers have examined the idea of a stable population and refined its underlying theory and extended its applications [2,3,[6][7][8][9][10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Exploring Stable Population Concepts from the Perspective of Cohort Change Ratios

Swanson

Tedrow²

2013

TODEMOJ

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Abstract. Cohort Change Ratios (CCRs) have a long history of use in demography. In spite of their history of use, they appear, however, to have been overlooked in regard to the major canon of formal demography, stable population theory. In this paper, CCRs are explored as a tool for examining the idea of a stable population. In comparing the approach using CCRs to the traditional analytical approach, benefits and drawbacks are noted. The paper also introduces an Index of Stability, which is used in a regression model to estimate the number of years before the population in question becomes (approximately) stable. The regression model works reasonably well and, as such, provides something not available in the traditional analytical approach, which is an estimate of the time to (approximate) stability for a given population.

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On the True Rate of Natural Increase

Cited by 130 publications

References 0 publications

Life table of Hypothenemus hampei (Ferrari) in relation to coffee berry phenology under Colombian field conditions

Life table of Hypothenemus hampei (Ferrari) in relation to coffee berry phenology under Colombian field conditions

The net reproduction rate and the type-reproduction number in multiregional demography

Exploring Stable Population Concepts from the Perspective of Cohort Change Ratios

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