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...f type-x individuals at time t to type-y individuals at time t + 1. Much of the basic theory for the deterministic matrix model (1) has recently been extended to a general class of deterministic IPMs =-=[15]-=-. A stochastic IPM has randomly time-varying kernels; in empirical applications these are specified typically as K(y, x, θ(t)) where θ(t) is a vectorvalued stochastic process representing variation ov...

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...screte-time, linear population projection models of the form xt+1 = P xt . Here xt is the stage-structured population at time t ∈ N and xt is in a Banach space X. In an integral projection model (see =-=[1, 3, 6, 7, 8, 15, 16]-=-), X = L1 (Ω) for some set of stages Ω. In a matrix projection model (see [2]), X = Rn . The population projection operator P is in L(X), the space of bounded operators from X into itself, and capture...

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...ies were arcsine square root transformed to meet assumptions of equal variance. Model Structure I used integral projection models (IPMs) to calculate l and as surrogates for the individual fitness of life-R 0 history strategies at each site, both for considering a range of flowering sizes and for comparing semelparity with it664 The American Naturalist eroparity. Integral projection models are similar to sizebased demographic matrix models, but they use continuous relationships between size and vital rates rather than dividing the population into discrete size classes (Easterling et al. 2000; Ellner and Rees 2006). They are better suited for examining life-history differences that vary continuously with plant size than are traditional stage-based matrix models, and they have recently been used for this reason to explore the optimal threshold flowering size in semelparous plants (Rees and Rose 2002; Metcalf et al. 2003; Rose et al. 2005; Hesse et al. 2008; Kuss et al. 2008). Here I incorporate four discrete stages into the IPM framework: three discrete early-life stages for current-year seed production, seeds in the soil, and seedlings, as well as one class for iteroparous plants (fig. 1; Rees et al. 20...

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...id in the development of appropriate sampling protocols for matrix models. In addition, biases due to sampling variance could potentially be eliminated entirely by using ‘‘Integral ProjectionModels’’ =-=[35,36]-=- to analyze demography, although we know of no studies have evaluated this possibility. Finally, we were surprised to find that 24% of the studies we reviewed failed to report the sample sizes on whic...

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...1). To be realistic, however, such models requiresmultiple parameters, and one constraint on wider use issthe availability of sufficient data to estimate model parameters. Integral projection models (=-=Ellner & Rees 2006-=-) oftensrequire fewer parameters, and maximum likelihood andsBayesian methods can estimate missing or incompletelysknown parameters, using time series data (Hilborn & Mangel 1997; Gross, Craig, & Hutc...

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...well (2001) and was outlined in Chapters 1-3. Far less research has been conducted into models with discrete time but continuous states. However, Integral Projection Models (Easterling et al., 2000b; =-=Ellner and Rees, 2006-=-, section 9.2), which can be fully continuous in state and time or continuous in state but discrete in time, appear to have the analytic tractability of matrix population models. One problem with this...

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...ibe stemmed palms. Thus, we used a general integral projection model (GIPM) that allowed us to model populations that are structured by both discrete developmental categories and continuous variables =-=[22]-=-. To do so we recognized two domains:D, corresponding to individuals without the aboveground stem, which were categorized into five groups (Table 1); and O, in which plant behavior is described as a f...

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...studies on senescence, age is obviously essential (Charlesworth 1980; Roach 2004). As current demographic tools and techniques enable the modelling of vital rates as a function of multiple variables (=-=Ellner & Rees 2006-=-; Caswell 2012), the size and age of individuals together with environmental variables can be simultaneously included in a demographic model to address eco-evolutionary questions (see e.g. Childs et a...

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... small fluctuations, but we also provide a simple geometric explanation for the effect of dispersal variability. We then use an empiricallybased model for the spread of an invasive plant (perennial pepperweed) to show that our results continue to hold at very high levels of variability and that dispersal variability and dispersal–demography covariance can have appreciable effects on population spread rate. 2. Model and assumptions We consider a continuously structured population in which the state z of an individual (e.g. size or age) lies in a compact set of all possible individual states Z (Ellner and Rees, 2006). These individuals disperse along a one dimensional transect of their environment (however, rates of spread in a two dimensional region can be computed by ‘‘marginalizing’’ a two-dimensional dispersal kernel along the direction of interest Lewis et al., 2006). Consequently, the location x of an individual can be identified with a point on the line X = (−∞, ∞). Let nt(x, z) denote the population density at location x, state z, and time t . In the absenceof density dependence (which we will consider in Section 4), the most general form of the model is nt+1(x, z) = Kt(x, z, x0, z0)nt(x0, z0)d...