{"title":"Age-structured models: Short-term transient dynamics","authors":"L. Botsford, J. White, A. Hastings","doi":"10.1093/oso/9780198758365.003.0004","DOIUrl":"https://doi.org/10.1093/oso/9780198758365.003.0004","url":null,"abstract":"Linear age-structured models eventually grow geometrically, and reach a stable age distribution (as in Chapter 3). This chapter describes what happens before “eventually.” That is, it describes the short-term, “transient” dynamics that occur when a population is perturbed, then begins to return to its stable distribution. Transients involve eigenvalues other than the largest (real) one, so the chapter begins by showing how complex eigenvalues can produce population cycles. It then addresses factors that make transients shorter or longer. In some cases, frequent environmental disturbances may prevent populations from ever reaching equilibrium. That scenario can be described by switching from linear models to linearized models varying about an equilibrium. The chapter describes temporal characteristics of that variability (such as time scales and frequencies), which require new tools: Fourier transforms and wavelets. These reveal how age-structured populations are more sensitive to certain environmental frequencies than to others, a phenomenon termed cohort resonance.","PeriodicalId":422045,"journal":{"name":"Population Dynamics for Conservation","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128089323","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Applications to conservation biology","authors":"L. Botsford, J. White, A. Hastings","doi":"10.1093/oso/9780198758365.003.0010","DOIUrl":"https://doi.org/10.1093/oso/9780198758365.003.0010","url":null,"abstract":"This chapter describes how models can aid in managing populations to prevent extinction, given uncertainty about their state. From previous chapters, it is clear that avoiding extinction requires keeping both abundance and the replacement rate high. However, for both, the question remains, how high? The question of how high abundance should be to achieve a certain risk is addressed by existing population viability analyses (PVA). By contrast, the problem of maintaining high replacement has received little attention. This chapter describes how uncertainty in population parameters and the frequency spectrum of the environment both affect estimates of the probability of extinction, including examples of PVAs that pay greater attention to those complications. Additionally, an example is provided of tracking both abundance and replacement to avoid extinction for many different populations of a single taxon, Pacific salmon. Finally, the role of portfolio effects (diversity in variance among populations) is explored.","PeriodicalId":422045,"journal":{"name":"Population Dynamics for Conservation","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133176093","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}