scholarly journals Building integral projection models with non-independent vital rates

2021 ◽  
Author(s):  
Yik Leung Fung ◽  
Ken Newman ◽  
Ruth King ◽  
Perry de Valpine
Keyword(s):  
Population Dynamics ◽  
Temporal Variation ◽  
Life History Evolution ◽  
Ovis Aries ◽  
Individual Heterogeneity ◽  
Parameter Estimates ◽  
Vital Rates ◽  
Integral Projection Models ◽  
Integral Projection ◽  
Demographic Processes

Population dynamics are functions of several demographic processes including survival, reproduction, somatic growth, and maturation. The rates or probabilities for these processes can vary by time, by location, and by individual. These processes can co-vary and interact to varying degrees, e.g., an animal can only reproduce when it is in a particular maturation state. Population dynamics models that treat the processes as independent may yield somewhat biased or imprecise parameter estimates, as well as predictions of population abundances or densities. However, commonly used integral projection models (IPMs) typically assume independence across these demographic processes. We examine several approaches for modelling between process dependence in IPMs, and include cases where the processes co-vary as a function of time (temporal variation), co-vary within each individual (individual heterogeneity), and combinations of these (temporal variation and individual heterogeneity). We compare our methods to conventional IPMs, which treat vital rates independent, using simulations and a case study of Soay sheep (Ovis aries). In particular, our results indicate that correlation between vital rates can moderately affect variability of some population-level statistics. Therefore, including such dependent structures is generally advisable when fitting IPMs to ascertain whether or not such between vital rate dependencies exist, which in turn can have subsequent impact on population management or life-history evolution.

Integral projection models

2021 ◽  
pp. 181-196
Author(s):  
Edgar J. González ◽  
Dylan Z. Childs ◽  
Pedro F. Quintana-Ascencio ◽  
Roberto Salguero-Gómez
Keyword(s):  
Population Dynamics ◽  
Environmental Variables ◽  
Linear Models ◽  
Vital Rates ◽  
Matrix Population Models ◽  
Generalised Linear Models ◽  
Integral Projection Models ◽  
Integral Projection ◽  
Over Time

Integral projection models (IPMs) allow projecting the behaviour of a population over time using information on the vital processes of individuals, their state, and that of the environment they inhabit. As with matrix population models (MPMs), time is treated as a discrete variable, but in IPMs, state and environmental variables are continuous and are related to the vital rates via generalised linear models. Vital rates in turn integrate into the population dynamics in a mechanistic way. This chapter provides a brief description of the logic behind IPMs and their construction, and, because they share many of the analyses developed for MPMs, it only emphasises how perturbation analyses can be performed with respect to different model elements. The chapter exemplifies the construction of a simple and a more complex IPM structure with an animal and a plant case study, respectively. Finally, inverse modelling in IPMs is presented, a method that allows population projection when some vital rates are not observed.

Statistical modelling of annual variation for inference on stochastic population dynamics using Integral Projection Models

2015 ◽  
Vol 6 (9) ◽  
pp. 1007-1017 ◽  
Author(s):  
C. Jessica E. Metcalf ◽  
Stephen P. Ellner ◽  
Dylan Z. Childs ◽  
Roberto Salguero‐Gómez ◽  
Cory Merow ◽  
...  
Keyword(s):  
Population Dynamics ◽  
Annual Variation ◽  
Statistical Modelling ◽  
Integral Projection Models ◽  
Integral Projection ◽  
Stochastic Population Dynamics

Predicting the effects of climate change on bird population dynamics

2019 ◽  
pp. 74-90
Author(s):  
Bernt-Erik Sæther ◽  
Steinar Engen ◽  
Marlène Gamelon ◽  
Vidar Grøtan
Keyword(s):  
Climate Change ◽  
Population Dynamics ◽  
Population Size ◽  
Environmental Stochasticity ◽  
Population Estimates ◽  
Parameter Estimates ◽  
Vital Rates ◽  
Statistical Sense ◽  
High Level ◽  
Avian Populations

Climate variation strongly influences fluctuations in size of avian populations. In this chapter, we show that it is difficult to predict how the abundance of birds will respond to climate change. A major reason for this is that most available time series of fluctuations in population size are in a statistical sense short, thus often resulting in large uncertainties in parameter estimates. We therefore argue that reliable population predictions must be based on models that capture how climate change will affect vital rates as well as including other processes (e.g. density-dependences) known to affect the population dynamics of the species in question. Our survey of examples of such forecast studies show that reliable predictions necessarily contain a high level of uncertainty. A major reason for this is that avian population dynamics are strongly influenced by environmental stochasticity, which is for most species, irrespective of their life history, the most important driver of fluctuations in population size. Credible population predictions must therefore assess the effects of such uncertainties as well as biases in population estimates.

scholarly journals Reconstructing population dynamics of a threatened marine mammal using multiple data sets

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Jeffrey A. Hostetler ◽  
Julien Martin ◽  
Michael Kosempa ◽  
Holly H. Edwards ◽  
Kari A. Rood ◽  
...  
Keyword(s):  
Population Dynamics ◽  
Marine Mammal ◽  
Conservation Status ◽  
Age Distribution ◽  
Credible Interval ◽  
Parameter Estimates ◽  
Observation Data ◽  
Vital Rates ◽  
Multiple Sources ◽  
Multiple Data Sets

AbstractModels of marine mammal population dynamics have been used extensively to predict abundance. A less common application of these models is to reconstruct historical population dynamics, filling in gaps in observation data by integrating information from multiple sources. We developed an integrated population model for the Florida manatee (Trichechus manatus latirostris) to reconstruct its population dynamics in the southwest region of the state over the past 20 years. Our model improved precision of key parameter estimates and permitted inference on poorly known parameters. Population growth was slow (averaging 1.02; 95% credible interval 1.01–1.03) but not steady, and an unusual mortality event in 2013 led to an estimated net loss of 332 (217–466) manatees. Our analyses showed that precise estimates of abundance could be derived from estimates of vital rates and a few input estimates of abundance, which may mean costly surveys to estimate abundance don’t need to be conducted as frequently. Our study also shows that retrospective analyses can be useful to: (1) model the transient dynamics of age distribution; (2) assess and communicate the conservation status of wild populations; and (3) improve our understanding of environmental effects on population dynamics and thus enhance our ability to forecast.

scholarly journals Exploring population responses to environmental change when there's never enough data; a factor analytic approach

2017 ◽  
Author(s):  
Bethan J. Hindle ◽  
Mark Rees ◽  
Andy W. Sheppard ◽  
Pedro F. Quintana-Ascencio ◽  
Eric S. Menges ◽  
...  
Keyword(s):  
Population Dynamics ◽  
Life History ◽  
Latent Variable ◽  
Life History Evolution ◽  
Environmental Drivers ◽  
Time Varying ◽  
Simulation Studies ◽  
Vital Rates ◽  
Time Varying Parameters ◽  
History Evolution

Temporal variability in the environment drives variation in individuals' vital rates, with consequences for population dynamics and life history evolution. Integral projection models (IPMs) are data-driven models widely used to study population dynamics and life history evolution of structured populations in temporally variable environments. However, many data sets have insufficient temporal replication for the environmental drivers of vital rates to be identified with confidence, limiting their use for evaluating population level responses to environmental change. Parameter selection, where the kernel is constructed at each time step by randomly selecting the time-varying parameters from their joint probability distribution, is one approach to including stochasticity in IPMs. We consider a factor analytic (FA) approach for modelling the covariance matrix of time-varying parameters, whereby latent variable(s) describe the covariance among vital rate parameters. This decreases the number of parameters estimated and, where the covariance is positive, the latent variable can be interpreted as a measure of environmental quality. We demonstrate this using simulation studies and two case studies. The simulation studies suggest the FA approach provides similarly accurate estimates of stochastic population growth rate to estimating an unstructured covariance matrix. We demonstrate how the latent parameter can be perturbed to show how selection on reproductive delays in the monocarp Carduus nutans changes under different environmental conditions. We develop a demographic model of the fire dependent herb Eryngium cuneifolium to show how a causal indicator (i.e. a driver of the changes in the environmental quality) can be incorporated with the addition of a single parameter. Using perturbation analyses we determine optimal management strategies for this species. This approach estimates fewer parameters than previous approaches and allows novel eco-evolutionary insights. Predictions on population dynamics and life history evolution under different environmental conditions can be made without necessarily identifying causal factors. Environmental drivers can be incorporated with relatively few parameters, allowing for predictions on how populations will be affected by changes to these drivers.

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