1
|
Giaimo S, Traulsen A. Age-specific sensitivity analysis of stable, stochastic and transient growth for stage-classified populations. Ecol Evol 2022; 12:e9561. [PMID: 36545365 PMCID: PMC9763023 DOI: 10.1002/ece3.9561] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/22/2022] [Accepted: 11/02/2022] [Indexed: 12/24/2022] Open
Abstract
Sensitivity analysis in ecology and evolution is a valuable guide to rank demographic parameters depending on their relevance to population growth. Here, we propose a method to make the sensitivity analysis of population growth for matrix models solely classified by stage more fine-grained by considering the effect of age-specific parameters. The method applies to stable population growth, the stochastic growth rate, and transient growth. The method yields expressions for the sensitivity of stable population growth to age-specific survival and fecundity from which general properties are derived about the pattern of age-specific selective forces molding senescence in stage-classified populations.
Collapse
Affiliation(s)
- Stefano Giaimo
- Department of Evolutionary TheoryMax Planck Institute for Evolutionary BiologyPlönGermany
| | - Arne Traulsen
- Department of Evolutionary TheoryMax Planck Institute for Evolutionary BiologyPlönGermany
| |
Collapse
|
2
|
Coste CFD, Bienvenu F, Ronget V, Ramirez-Loza JP, Cubaynes S, Pavard S. The kinship matrix: inferring the kinship structure of a population from its demography. Ecol Lett 2021; 24:2750-2762. [PMID: 34609786 DOI: 10.1111/ele.13854] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/14/2021] [Revised: 06/28/2021] [Accepted: 06/28/2021] [Indexed: 11/30/2022]
Abstract
The familial structure of a population and the relatedness of its individuals are determined by its demography. There is, however, no general method to infer kinship directly from the life cycle of a structured population. Yet, this question is central to fields such as ecology, evolution and conservation, especially in contexts where there is a strong interdependence between familial structure and population dynamics. Here, we give a general formula to compute, from any matrix population model, the expected number of arbitrary kin (sisters, nieces, cousins, etc) of a focal individual ego, structured by the class of ego and of its kin. Central to our approach are classic but little-used tools known as genealogical matrices. Our method can be used to obtain both individual-based and population-wide metrics of kinship, as we illustrate. It also makes it possible to analyse the sensitivity of the kinship structure to the traits implemented in the model.
Collapse
Affiliation(s)
- Christophe F D Coste
- Centre for Biodiversity Dynamics, Department of Biology, Norwegian University of Science and Technology, Trondheim, Norway
| | - François Bienvenu
- Department of Mathematics and Computer Science, Transilvania University of Braşov, Braşov, Romania.,Institut des Sciences de l'Evolution de Montpellier, Université de Montpellier, CNRS, IRD, EPHE, Montpellier, France.,UMR AGAP, Université de Montpellier, CIRAD, INRAE, L'institut Agro, Montpellier, France.,Department of Statistics, University of Oxford, Oxford, United Kingdom
| | - Victor Ronget
- Unité Eco-anthropologie (EA), Muséum National d'Histoire Naturelle, CNRS, Université Paris Diderot, Paris, France
| | - Juan-Pablo Ramirez-Loza
- CEFE, CNRS, Univ. Montpellier, Univ. Paul Valéry Montpellier 3, EPHE, IRD, Montpellier, France
| | - Sarah Cubaynes
- CEFE, CNRS, Univ. Montpellier, Univ. Paul Valéry Montpellier 3, EPHE, IRD, Montpellier, France
| | - Samuel Pavard
- Unité Eco-anthropologie (EA), Muséum National d'Histoire Naturelle, CNRS, Université Paris Diderot, Paris, France
| |
Collapse
|
3
|
Logofet DO, Salguero-Gómez R. Novel challenges and opportunities in the theory and practice of matrix population modelling: An editorial for the special feature. Ecol Modell 2021. [DOI: 10.1016/j.ecolmodel.2021.109457] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
|
4
|
Miller DH, Clark BW, Nacci DE. A multidimensional density dependent matrix population model for assessing risk of stressors to fish populations. ECOTOXICOLOGY AND ENVIRONMENTAL SAFETY 2020; 201:110786. [PMID: 32526589 PMCID: PMC11028404 DOI: 10.1016/j.ecoenv.2020.110786] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/13/2020] [Revised: 05/12/2020] [Accepted: 05/19/2020] [Indexed: 06/11/2023]
Abstract
Modeling exposure and recovery of fish and wildlife populations after stressor mitigation serves as a basis for evaluating remediation success. Herein, we develop a novel multidimensional density dependent matrix population model that analyzes both size-structure and age class-structure simultaneously. This modeling approach emphasizes application in conjunction with field monitoring efforts (e.g., through effects-based monitoring programs) and/or laboratory analysis to link effects due to stressors to outcomes in populations. We applied the model to investigate Atlantic killifish (Fundulus heteroclitus) exposed to 2,3,7,8-tetrachlorodibenzo-p-dioxin with effects on fertility and survival rates. The Atlantic killifish is an important and well-studied model organism for understanding the effects of pollutants and other stressors in estuarine and marine ecosystems. For each exposure concentration, the corresponding plots of total population size, population size structure, and age structure over time were generated. The present study serves as an example of how a multidimensional matrix population model can integrate effects across the life cycle, provide a linkage between endpoints observed in the individual and ecological risk to the population as a whole, and project outcomes for multiple generations.
Collapse
Affiliation(s)
- David H Miller
- United States Environmental Protection Agency, Great Lakes Toxicology and Ecology Division, Ann Arbor, MI, 48105, USA.
| | - Bryan W Clark
- United States Environmental Protection Agency, Atlantic Coastal Environmental Sciences Division, Narragansett, RI, 02882, USA
| | - Diane E Nacci
- United States Environmental Protection Agency, Atlantic Coastal Environmental Sciences Division, Narragansett, RI, 02882, USA
| |
Collapse
|
5
|
|
6
|
|
7
|
Coste CF, Pavard S. Analysis of a multitrait population projection matrix reveals the evolutionary and demographic effects of a life history trade-off. Ecol Modell 2020. [DOI: 10.1016/j.ecolmodel.2019.108915] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
|
8
|
Caswell H, de Vries C, Hartemink N, Roth G, van Daalen SF. Age × stage-classified demographic analysis: a comprehensive approach. ECOL MONOGR 2018; 88:560-584. [PMID: 30555177 PMCID: PMC6283253 DOI: 10.1002/ecm.1306] [Citation(s) in RCA: 39] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/12/2017] [Revised: 02/23/2018] [Accepted: 03/21/2018] [Indexed: 11/08/2022]
Abstract
This paper presents a comprehensive theory for the demographic analysis of populations in which individuals are classified by both age and stage. The earliest demographic models were age classified. Ecologists adopted methods developed by human demographers and used life tables to quantify survivorship and fertility of cohorts and the growth rates and structures of populations. Later, motivated by studies of plants and insects, matrix population models structured by size or stage were developed. The theory of these models has been extended to cover all the aspects of age-classified demography and more. It is a natural development to consider populations classified by both age and stage. A steady trickle of results has appeared since the 1960s, analyzing one or another aspect of age × stage-classified populations, in both ecology and human demography. Here, we use the vec-permutation formulation of multistate matrix population models to incorporate age- and stage-specific vital rates into demographic analysis. We present cohort results for the life table functions (survivorship, mortality, and fertility), the dynamics of intra-cohort selection, the statistics of longevity, the joint distribution of age and stage at death, and the statistics of life disparity. Combining transitions and fertility yields a complete set of population dynamic results, including population growth rates and structures, net reproductive rate, the statistics of lifetime reproduction, and measures of generation time. We present a complete analysis of a hypothetical model species, inspired by poecilogonous marine invertebrates that produce two kinds of larval offspring. Given the joint effects of age and stage, many familiar demographic results become multidimensional, so calculations of marginal and mixture distributions are an important tool. From an age-classified point of view, stage structure is a form of unobserved heterogeneity. From a stage-classified point of view, age structure is unobserved heterogeneity. In an age × stage-classified model, variance in demographic outcomes can be partitioned into contributions from both sources. Because these models are formulated as matrices, they are amenable to a complete sensitivity analysis. As more detailed and longer longitudinal studies are developed, age × stage-classified demography will become more common and more important.
Collapse
Affiliation(s)
- Hal Caswell
- Institute for Biodiversity and Ecosystem DynamicsUniversity of AmsterdamScience Park 9041098 XHAmsterdamThe Netherlands
| | - Charlotte de Vries
- Institute for Biodiversity and Ecosystem DynamicsUniversity of AmsterdamScience Park 9041098 XHAmsterdamThe Netherlands
| | - Nienke Hartemink
- Institute for Biodiversity and Ecosystem DynamicsUniversity of AmsterdamScience Park 9041098 XHAmsterdamThe Netherlands
| | - Gregory Roth
- Institute for Biodiversity and Ecosystem DynamicsUniversity of AmsterdamScience Park 9041098 XHAmsterdamThe Netherlands
| | - Silke F. van Daalen
- Institute for Biodiversity and Ecosystem DynamicsUniversity of AmsterdamScience Park 9041098 XHAmsterdamThe Netherlands
| |
Collapse
|
9
|
Okuyama T. Stage duration distributions in matrix population models. Ecol Evol 2018; 8:7936-7945. [PMID: 30250674 PMCID: PMC6144974 DOI: 10.1002/ece3.4279] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2018] [Revised: 05/18/2018] [Accepted: 05/21/2018] [Indexed: 11/14/2022] Open
Abstract
Matrix population models are a standard tool for studying stage-structured populations, but they are not flexible in describing stage duration distributions. This study describes a method for modeling various such distributions in matrix models. The method uses a mixture of two negative binomial distributions (parametrized using a maximum likelihood method) to approximate a target (true) distribution. To examine the performance of the method, populations consisting of two life stages (juvenile and adult) were considered. The juvenile duration distribution followed a gamma distribution, lognormal distribution, or zero-truncated (over-dispersed) Poisson distribution, each of which represents a target distribution to be approximated by a mixture distribution. The true population growth rate based on a target distribution was obtained using an individual-based model, and the extent to which matrix models can approximate the target dynamics was examined. The results show that the method generally works well for the examined target distributions, but is prone to biased predictions under some conditions. In addition, the method works uniformly better than an existing method whose performance was also examined for comparison. Other details regarding parameter estimation and model development are also discussed.
Collapse
|
10
|
Bernstein SF, Rehkopf D, Tuljapurkar S, Horvitz CC. Poverty dynamics, poverty thresholds and mortality: An age-stage Markovian model. PLoS One 2018; 13:e0195734. [PMID: 29768416 PMCID: PMC5955488 DOI: 10.1371/journal.pone.0195734] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/27/2017] [Accepted: 03/28/2018] [Indexed: 11/18/2022] Open
Abstract
Recent studies have examined the risk of poverty throughout the life course, but few have considered how transitioning in and out of poverty shape the dynamic heterogeneity and mortality disparities of a cohort at each age. Here we use state-by-age modeling to capture individual heterogeneity in crossing one of three different poverty thresholds (defined as 1×, 2× or 3× the “official” poverty threshold) at each age. We examine age-specific state structure, the remaining life expectancy, its variance, and cohort simulations for those above and below each threshold. Survival and transitioning probabilities are statistically estimated by regression analyses of data from the Health and Retirement Survey RAND data-set, and the National Longitudinal Survey of Youth. Using the results of these regression analyses, we parameterize discrete state, discrete age matrix models. We found that individuals above all three thresholds have higher annual survival than those in poverty, especially for mid-ages to about age 80. The advantage is greatest when we classify individuals based on 1× the “official” poverty threshold. The greatest discrepancy in average remaining life expectancy and its variance between those above and in poverty occurs at mid-ages for all three thresholds. And fewer individuals are in poverty between ages 40-60 for all three thresholds. Our findings are consistent with results based on other data sets, but also suggest that dynamic heterogeneity in poverty and the transience of the poverty state is associated with income-related mortality disparities (less transience, especially of those above poverty, more disparities). This paper applies the approach of age-by-stage matrix models to human demography and individual poverty dynamics. In so doing we extend the literature on individual poverty dynamics across the life course.
Collapse
Affiliation(s)
- Shayna Fae Bernstein
- Department of Biology, Institute for Theoretical and Mathematical Ecology (ITME), University of Miami, Coral Gables, FL, United States of America
- * E-mail:
| | - David Rehkopf
- School of Medicine, Division of Primary Care and Population Health, Stanford University, Stanford, CA, United States of America
| | - Shripad Tuljapurkar
- Department of Biology, Stanford University, Stanford, CA, United States of America
| | - Carol C. Horvitz
- Department of Biology, Institute for Theoretical and Mathematical Ecology (ITME), University of Miami, Coral Gables, FL, United States of America
| |
Collapse
|
11
|
Caswell H, Vindenes Y. Demographic variance in heterogeneous populations: matrix models and sensitivity analysis. OIKOS 2018. [DOI: 10.1111/oik.04708] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Hal Caswell
- Inst. for Biodiversity and Ecosystem Dynamics; Univ. of Amsterdam; PO Box 94248, NL-1090n GE Amsterdam the Netherlands
| | - Yngvild Vindenes
- Centre for Ecological and Evolutionary Synthesis; Univ. of Oslo; Oslo Norway
| |
Collapse
|
12
|
Flockhart DTT, Coe JB. Multistate matrix population model to assess the contributions and impacts on population abundance of domestic cats in urban areas including owned cats, unowned cats, and cats in shelters. PLoS One 2018; 13:e0192139. [PMID: 29489854 PMCID: PMC5830044 DOI: 10.1371/journal.pone.0192139] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/19/2017] [Accepted: 01/17/2018] [Indexed: 11/20/2022] Open
Abstract
Concerns over cat homelessness, over-taxed animal shelters, public health risks, and environmental impacts has raised attention on urban-cat populations. To truly understand cat population dynamics, the collective population of owned cats, unowned cats, and cats in the shelter system must be considered simultaneously because each subpopulation contributes differently to the overall population of cats in a community (e.g., differences in neuter rates, differences in impacts on wildlife) and cats move among categories through human interventions (e.g., adoption, abandonment). To assess this complex socio-ecological system, we developed a multistate matrix model of cats in urban areas that include owned cats, unowned cats (free-roaming and feral), and cats that move through the shelter system. Our model requires three inputs-location, number of human dwellings, and urban area-to provide testable predictions of cat abundance for any city in North America. Model-predicted population size of unowned cats in seven Canadian cities were not significantly different than published estimates (p = 0.23). Model-predicted proportions of sterile feral cats did not match observed sterile cat proportions for six USA cities (p = 0.001). Using a case study from Guelph, Ontario, Canada, we compared model-predicted to empirical estimates of cat abundance in each subpopulation and used perturbation analysis to calculate relative sensitivity of vital rates to cat abundance to demonstrate how management or mismanagement in one portion of the population could have repercussions across all portions of the network. Our study provides a general framework to consider cat population abundance in urban areas and, with refinement that includes city-specific parameter estimates and modeling, could provide a better understanding of population dynamics of cats in our communities.
Collapse
Affiliation(s)
- D. T. Tyler Flockhart
- Department of Population Medicine, Ontario Veterinary College, University of Guelph, Guelph, Ontario, Canada
- Department of Integrative Biology, University of Guelph, Guelph, Ontario, Canada
| | - Jason B. Coe
- Department of Population Medicine, Ontario Veterinary College, University of Guelph, Guelph, Ontario, Canada
| |
Collapse
|
13
|
Roth G, Caswell H. Occupancy time in sets of states for demographic models. Theor Popul Biol 2018; 120:62-77. [PMID: 29407846 PMCID: PMC5861321 DOI: 10.1016/j.tpb.2017.12.007] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/06/2017] [Revised: 12/14/2017] [Accepted: 12/20/2017] [Indexed: 10/26/2022]
Abstract
As an individual moves through its life cycle, it passes through a series of states (age classes, size classes, reproductive states, spatial locations, health statuses, etc.) before its eventual death. The occupancy time in a state is the time spent in that state over the individual's life. Depending on the life cycle description, the occupancy times describe different demographic variables, for example, lifetime breeding success, lifetime habitat utilisation, or healthy longevity. Models based on absorbing Markov chains provide a powerful framework for the analysis of occupancy times. Current theory, however, can completely analyse only the occupancy of single states, although the occupancy time in a set of states is often desired. For example, a range of sizes in a size-classified model, an age class in an age×stage model, and a group of locations in a spatial stage model are all sets of states. We present a new mathematical approach to absorbing Markov chains that extends the analysis of life histories by providing a comprehensive theory for the occupancy of arbitrary sets of states, and for other demographic variables related to these sets (e.g., reaching time, return time). We apply this approach to a matrix population model of the Southern Fulmar (Fulmarus glacialoides). The analysis of this model provides interesting insight into the lifetime number of breeding attempts of this species. Our new approach to absorbing Markov chains, and its implementation in matrix oriented software, makes the analysis of occupancy times more accessible to population ecologists, and directly applicable to any matrix population models.
Collapse
Affiliation(s)
- Gregory Roth
- Institute for Biodiversity and Ecosystem Dynamics, University of Amsterdam, Netherlands.
| | - Hal Caswell
- Institute for Biodiversity and Ecosystem Dynamics, University of Amsterdam, Netherlands
| |
Collapse
|
14
|
Coste CFD, Austerlitz F, Pavard S. Trait level analysis of multitrait population projection matrices. Theor Popul Biol 2017; 116:47-58. [PMID: 28757374 DOI: 10.1016/j.tpb.2017.07.002] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/21/2016] [Revised: 07/05/2017] [Accepted: 07/10/2017] [Indexed: 11/30/2022]
Abstract
In most matrix population projection models, individuals are characterized according to, usually, one or two traits such as age, stage, size or location. A broad theory of multitrait population projection matrices (MPPMs) incorporating larger number of traits was long held back by time and space computational complexity issues. As a consequence, no study has yet focused on the influence of the structure of traits describing a life-cycle on population dynamics and life-history evolution. We present here a novel vector-based MPPM building methodology that allows to computationally-efficiently model populations characterized by numerous traits with large distributions, and extend sensitivity analyses for these models. We then present a new method, the trait level analysis consisting in folding an MPPM on any of its traits to create a matrix with alternative trait structure (the number of traits and their characteristics) but similar asymptotic properties. Adding or removing one or several traits to/from the MPPM and analyzing the resulting changes in spectral properties, allows investigating the influence of the trait structure on the evolution of traits. We illustrate this by modeling a 3-trait (age, parity and fecundity) population designed to investigate the implications of parity-fertilitytrade-offs in a context of fecundity heterogeneity in humans. The trait level analysis, comparing models of the same population differing in trait structures, demonstrates that fertility selection gradients differ between cases with or without parity-fertility trade-offs. Moreover it shows that age-specific fertility has seemingly very different evolutionary significance depending on whether heterogeneity is accounted for. This is because trade-offs can vary strongly in strength and even direction depending on the trait structure used to model the population.
Collapse
Affiliation(s)
- Christophe F D Coste
- UMR 7206 EcoAnthropologie et Ethnobiologie, MNHN, Université Paris Diderot, F-75016, Paris, France.
| | - Frédéric Austerlitz
- UMR 7206 EcoAnthropologie et Ethnobiologie, MNHN, Université Paris Diderot, F-75016, Paris, France
| | - Samuel Pavard
- UMR 7206 EcoAnthropologie et Ethnobiologie, MNHN, Université Paris Diderot, F-75016, Paris, France
| |
Collapse
|
15
|
Introducing a Non-Stationary Matrix Model for Stand-Level Optimization, an Even-Aged Pine (Pinus Sylvestris L.) Stand in Finland. FORESTS 2017. [DOI: 10.3390/f8050163] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
|