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Stochastic stable population growth in integral projection models: Theory and application
 J Math Biol 2007; 54: 227–256. PMID: 17123085
"... growth in integral projection ..."
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Global asymptotic stability of density dependent integral projection population models, submitted to Theoretical Population Biology
"... integral population projection models ..."
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Flowering lifehistory strategies differ between the native and introduced ranges of a monocarpic perennial. American Naturalist
"... abstract: Lifehistory theory makes several key predictions about reproductive strategies on the basis of demographic vital rates, particularly the relationship between juvenile and adult survival. Two such predictions concern the optimal time to begin reproducing and whether semelparity or iteropa ..."
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abstract: Lifehistory theory makes several key predictions about reproductive strategies on the basis of demographic vital rates, particularly the relationship between juvenile and adult survival. Two such predictions concern the optimal time to begin reproducing and whether semelparity or iteroparity is favored. I tested these lifehistory predictions and explored how they might differ between the native and introduced ranges of the monocarpic perennial Cynoglossum officinale. I first compared vital rates between ranges. I then used these vital rates to parameterize integral projection models to calculate the population growth rate (l) and net reproductive rate ( ) as surrogates for fitness to compare strategies within and beR 0 tween ranges. I found that both survival and growth were higher in the introduced range, where size at flowering was larger and iteroparity was much more common than in the native range. The observed and predicted strategies for size at flowering were similar in the native range. In the introduced range, however, even though plants flowered at a larger size, the observed size was not as large as the optimum predicted by l or the higher optimum predicted by . Iteroparity conferred higher fitness in both ranges, as measured R 0 by both fitness metrics, suggesting that severe constraints, potentially specialist herbivores, prevent this strategy from becoming more common in the native range.
Effects of Sample Size on Estimates of Population Growth Rates Calculated with Matrix Models
"... Background: Matrix models are widely used to study the dynamics and demography of populations. An important but overlooked issue is how the number of individuals sampled influences estimates of the population growth rate (l) calculated with matrix models. Even unbiased estimates of vital rates do no ..."
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Background: Matrix models are widely used to study the dynamics and demography of populations. An important but overlooked issue is how the number of individuals sampled influences estimates of the population growth rate (l) calculated with matrix models. Even unbiased estimates of vital rates do not ensure unbiased estimates of l–Jensen’s Inequality implies that even when the estimates of the vital rates are accurate, small sample sizes lead to biased estimates of l due to increased sampling variance. We investigated if sampling variability and the distribution of sampling effort among size classes lead to biases in estimates of l. Methodology/Principal Findings: Using data from a longterm field study of plant demography, we simulated the effects of sampling variance by drawing vital rates and calculating l for increasingly larger populations drawn from a total population of 3842 plants. We then compared these estimates of l with those based on the entire population and calculated the resulting bias. Finally, we conducted a review of the literature to determine the sample sizes typically used when parameterizing matrix models used to study plant demography. Conclusions/Significance: We found significant bias at small sample sizes when survival was low (survival = 0.5), and that sampling with a morerealistic inverse Jshaped population structure exacerbated this bias. However our simulations also demonstrate that these biases rapidly become negligible with increasing sample sizes or as survival increases. For many of
Faculty Publications in the Biological Sciences Papers in the Biological Sciences
, 2008
"... Monte Carlo analysis of parameter uncertainty in matrix models for the weed Cirsium vulgare ..."
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Monte Carlo analysis of parameter uncertainty in matrix models for the weed Cirsium vulgare
Matthiopoulos, Leslie New, and Len
, 2009
"... Biologically Significant Marine Mammal Behavior ’ proposed a framework, which they called PCAD Population Consequences of Acoustic Disturbance, that uses a series of transfer functions to link behavioural responses to sound with life functions, vital rates, and population change. The Committee sugg ..."
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Biologically Significant Marine Mammal Behavior ’ proposed a framework, which they called PCAD Population Consequences of Acoustic Disturbance, that uses a series of transfer functions to link behavioural responses to sound with life functions, vital rates, and population change. The Committee suggested that the best understood transfer functions are those linking vital rates to population change. One of the main aims of this report is to document that understanding. However, we also show how the existing frameworks for modelling the dynamics of marine mammal populations can be extended to include the effects of behavioural responses on vital rates. In Chapter 1 we introduce the central concept of the rate of increase ( ) of a population, which we believe is the most useful measure of the effects of behavioural responses on the dynamics of a population. If the value of exceeds one, then the population will increase over time; if it is less than one it will decrease. We show how changes in provide a measure of the impact of human activities (such as exploitation, conservation, or disturbance) on a population. We also introduce structured population models, which take account of the fact that all individuals in a population are not
RESEARCH ARTICLE Effects of Harvest on the Sustainability and Leaf Productivity of Populations of Two Palm Species in Maya Homegardens
, 1371
"... Traditional management practices are usually thought to be sustainable. The Maya manage Sabal (Arecaceae) palms in homegardens, using their leaves for thatching. The sustainability of such production systems depends on the longterm persistence of palm populations, whereas resource availability al ..."
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Traditional management practices are usually thought to be sustainable. The Maya manage Sabal (Arecaceae) palms in homegardens, using their leaves for thatching. The sustainability of such production systems depends on the longterm persistence of palm populations, whereas resource availability also depends on the number of leaves on individual palms. We examined how leaf harvest affects Sabal yapa and S.mexicana population growth rates (λ) and leaf production, comparing traditional and alternative harvest regimes in terms of sustainability and productivity. Demographic, harvest and leaf production data were recorded for three years in two homegardens. We used general integral projection models linked to leafproduction models to describe population dynamics and productivity. Harvest had no effect on S. yapa’s vital rates or on λ, but it changed the growth rate of individuals of S.mexicana, with a negligible impact on λ. Homegardens affected λ values, reflecting the species ’ ecological affinities. S.mexicana, introduced from mesic forests, required watering and shade; therefore, its population declined rapidly in the homegarden that lacked both water and shade. The λ of the xerophilic S. yapa was slightly larger without watering than with watering. Palms usually compensated for leaf extraction, causing the number of leaves harvested per individual to increase with harvest intensity. Nevertheless, traditional management is relatively mild, allowing standing leaves to accumulate but reducing the homegarden’s yield. Apparently, the Maya do not seek to maximize annual production but to ensure the availability of large numbers of leaves in homegardens. These leaves may then be used when the entire roof of a hut needs to be replaced every few years.
SPECIAL FEATURE
"... Prolonged dormancy interacts with senescence for two perennial herbs ..."
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Temporally variable dispersal and demography can accelerate the spread of invading species
, 2012
"... a b s t r a c t We analyze how temporal variability in local demography and dispersal combine to affect the rate of spread of an invading species. Our model combines statestructured local demography (specified by an integral or matrix projection model) with general dispersal distributions that may ..."
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a b s t r a c t We analyze how temporal variability in local demography and dispersal combine to affect the rate of spread of an invading species. Our model combines statestructured local demography (specified by an integral or matrix projection model) with general dispersal distributions that may depend on the state of the individual or its parent. It allows very general patterns of stationary temporal variation in both local demography and in the frequency and distribution of dispersal distances. We show that expressions for the asymptotic spread rate and its sensitivity to parameters, which have been derived previously for less general models, continue to hold. Using these results we show that random temporal variability in dispersal can accelerate population spread. Demographic variability can further accelerate spread if it is positively correlated with dispersal variability, for example if highfecundity years are also years in which juveniles tend to settle further away from their parents. A simple model for the growth and spread of patches of an invasive plant (perennial pepperweed, Lepidium latifolium) illustrates these effects and shows that they can have substantial impacts on the predicted speed of an invasion wave. Temporal variability in dispersal has received very little attention in both the theoretical and empirical literature on invasive species spread. Our results suggest that this needs to change.
HIERARCHICAL HETEROGENITY OF POPULATIONS: MODELING BY THE OPEN
"... System of ordinary quadratic differential equations, asymptotic stability, biological population. The case of a biological population, which consists of several subpopulations (different kinds of the population ”social ” groups: families, bevies, etc.), has been considered. For description of no ..."
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System of ordinary quadratic differential equations, asymptotic stability, biological population. The case of a biological population, which consists of several subpopulations (different kinds of the population ”social ” groups: families, bevies, etc.), has been considered. For description of nontrivial interactions between these groups, a model of ”open the Eigen hypercycle ” has been proposed. Its bifurcation analysis for 3dimension case has been carried out. Ecological interpretation of the results has been discussed.