Equivalence relationships between stage-structured population models

Yearsley, Jonathan M.; Fletcher, David

doi:10.1016/s0025-5564(02)00119-0

Cited by 18 publications

(12 citation statements)

References 33 publications

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“…Our findings generally support their result, although our data set also included several herbaceous and woody species whose elasticity values showed an opposite pattern. Similar to Yearsley and Fletcher (2002), we observed that the elasticity of l to fecundity increased due to reduced matrix dimensionality. When matrices of different sizes are compared, it is important to be aware that some differences in elasticity values among matrices may be artifacts caused by different matrix dimensionalities.…”

Section: Discussionsupporting

confidence: 71%

“…Although a narrow classification produces a larger matrix describing population dynamics more accurately, more data are required to produce reliable estimates compared to a wider classification (Caswell 1997). Hence, matrix dimensionality affects the reliability of estimated transition probabilities, λ, and the elasticity of λ (Vandermeer 1978, Moloney 1986, Enright et al 1995, Yearsley and Fletcher 2002).…”

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confidence: 99%

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Matrix dimensionality in demographic analyses of plants: when to use smaller matrices?

Ramula¹,

Lehtilä²

2005

Oikos

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Ramula, S. and Lehtilä, K. 2005. Matrix dimensionality in demographic analyses of plants: when to use smaller matrices? Á/ Oikos 111: 563 Á/573.Large data requirements may restrict the use of matrix population models for analysis of population dynamics. Less data are required for a small population matrix than for a large matrix because the smaller matrix contains fewer vital rates that need to be estimated. Smaller matrices, however, tend to have a lower precision. Based on 37 plant species, we studied the effects of matrix dimensionality on the long-term population growth rate (l) and the elasticity of l in herbaceous and woody species. We found that when matrix dimensionality was reduced, changes in l were significantly larger for herbaceous than for woody species. In many cases, l of woody species remained virtually the same after a substantial decrease in matrix dimensionality, suggesting that woody species are less susceptible to matrix dimensionality. We demonstrated that when adjacent stages of a transition matrix are combined, the magnitude of a change in l depends on the distance of the population structure from a stable stage distribution, and the difference in the combined vital rates weighted by their reproductive values. Elasticity of l to survival and fecundity usually increased, whereas elasticity to growth decreased both in herbaceous and in woody species with reduced matrix dimensionality. Changes in elasticity values tended to be larger for herbaceous than for woody species. Our results show that by reducing matrix dimensionality, the amount of demographic data can be decreased to save time, money, and field effort. We recommend the use of a small matrix dimensionality especially when a limited amount of data is available, and for slow-growing species having a simple matrix structure that mainly consists of stasis and growth to the next stage.

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Section: Discussionsupporting

confidence: 71%

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confidence: 99%

Matrix dimensionality in demographic analyses of plants: when to use smaller matrices?

Ramula¹,

Lehtilä²

2005

Oikos

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“…Moreover, other algebraic relationships than (1) could be used to collapse into . In particular, it is mathematically feasible to collapse a transition matrix into a smaller matrix while maintaining the same dominant eigenvalue and eigenvectors [10], [25], [28]–[30]. If such algebraic relationships were to be used rather than (1) to collapse matrices (and there is no theoretical reason for not doing it) then, by construction, would not depend on the class width.…”

Section: Methodsmentioning

confidence: 99%

Matrix Models for Size-Structured Populations: Unrealistic Fast Growth or Simply Diffusion?

Picard

Liang

2014

PLoS ONE

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Matrix population models are widely used to study population dynamics but have been criticized because their outputs are sensitive to the dimension of the matrix (or, equivalently, to the class width). This sensitivity is concerning for the population growth rate () because this is an intrinsic characteristic of the population that should not depend on the model specification. It has been suggested that the sensitivity of to matrix dimension was linked to the existence of fast pathways (i.e. the fraction of individuals that systematically move up a class), whose proportion increases when class width increases. We showed that for matrix population models with growth transition only from class to class , was independent of the class width when the mortality and the recruitment rates were constant, irrespective of the growth rate. We also showed that if there were indeed fast pathways, there were also in about the same proportion slow pathways (i.e. the fraction of individuals that systematically remained in the same class), and that they jointly act as a diffusion process (where diffusion here is the movement in size of an individual whose size increments are random according to a normal distribution with mean zero). For 53 tree species from a tropical rain forest in the Central African Republic, the diffusion resulting from common matrix dimensions was much stronger than would be realistic. Yet, the sensitivity of to matrix dimension for a class width in the range 1–10 cm was small, much smaller than the sampling uncertainty on the value of . Moreover, could either increase or decrease when class width increased depending on the species. Overall, even if the class width should be kept small enough to limit diffusion, it had little impact on the estimate of for tree species.

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“…The life cycles also contain “fertility arrows,” specifying reproduction from adult stages back to the first developmental stage. Life cycle graph construction deserves careful thought, and Caswell (2001), Yearsley and Fletcher (2002) and Cooch et al (in press) provide more treatment of this topic.…”

Section: Overview Of Demographic Conceptsmentioning

confidence: 99%

Demographic concepts and research pertaining to the study of wild primate populations

Lawler

2011

American J Phys Anthropol

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Demography is the study of individuals as members of a population. The dynamics of a population are determined by collectively analyzing individual schedules of survival, growth, and reproduction. Together, these schedules are known as the vital rates of the population. The vital rates, along with dispersal, contribute to population structure, which refers to how the population is organized by age, sex, density, and social groups. I briefly review the history of anthropological demography as it pertains to wild primates and then I discuss basic demographic concepts and approaches for studying wild primate populations. I then turn to demographic studies of wild primate demography. Primates are generally characterized by high adult survival probabilities relative to survival at other age/stage classes and most primate populations have population growth rates near equilibrium. Changes in adult survival have the greatest impact on population growth rate (i.e., fitness) relative to other demographic traits such as juvenile/yearling survival or age at first reproduction. I discuss how these demographic patterns, and others, connect to topics and issues in behavioral ecology, life history theory, population genetics, and conservation biology. These connections help reaffirm the fact that the vital rates are both targets and agents of evolutionary change. In this regard, demographic studies of wild primates provide a critical link between the proximate socioecological processes that operate in a species and the long-term phylogenetic patterns that characterize a species. Yrbk Phys Anthropol 54: 63-85, 2011. V

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Equivalence relationships between stage-structured population models

Cited by 18 publications

References 33 publications

Matrix dimensionality in demographic analyses of plants: when to use smaller matrices?

Matrix dimensionality in demographic analyses of plants: when to use smaller matrices?

Matrix Models for Size-Structured Populations: Unrealistic Fast Growth or Simply Diffusion?

Demographic concepts and research pertaining to the study of wild primate populations

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