Patterns and rules for sensitivity and elasticity in population projection matrices

Carslake, David; Townley, Stuart; Hodgson, David J.

doi:10.1890/08-1188.1

Cited by 24 publications

(34 citation statements)

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“…elasticity value) of juvenile survival to the population growth rate. This can directly be seen in these models: age of first reproduction determines how many juvenile classes there are [22],[44]. In age-based matrix models, as determined by loop analysis, the summed elasticity value of juvenile survival is equal to the summed elasticity value of fecundity times the number of juvenile classes.…”

Section: Resultsmentioning

confidence: 99%

Carnivora Population Dynamics Are as Slow and as Fast as Those of Other Mammals: Implications for Their Conservation

et al. 2013

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Of the 285 species of Carnivora 71 are threatened, while many of these species fulfill important ecological roles in their ecosystems as top or meso-predators. Population transition matrices make it possible to study how age-specific survival and fecundity affect population growth, extinction risks, and responses to management strategies. Here we review 38 matrix models from 35 studies on 27 Carnivora taxa, covering 11% of the threatened Carnivora species. We show that the elasticity patterns (i.e. distribution over fecundity, juvenile survival and adult survival) in Carnivora cover the same range in triangular elasticity plots as those of other mammal species, despite the specific place of Carnivora in the food chain. Furthermore, reproductive loop elasticity analysis shows that the studied species spread out evenly over a slow-fast continuum, but also quantifies the large variation in the duration of important life cycles and their contributions to population growth rate.These general elasticity patterns among species, and their correlation with simple life history characteristics like body mass, age of first reproduction and life span, enables the extrapolation of population dynamical properties to unstudied species. With several examples we discuss how this slow-fast continuum, and related patterns of variation in reproductive loop elasticity, can be used in the formulation of tentative management plans for threatened species that cannot wait for the results of thorough demographic studies. We argue, however, that such management programs should explicitly include a plan for learning about the key demographic rates and how these are affected by environmental drivers and threats.

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Section: Resultsmentioning

confidence: 99%

Carnivora Population Dynamics Are as Slow and as Fast as Those of Other Mammals: Implications for Their Conservation

et al. 2013

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“…2010). Simulation studies have also explored relationships between elasticities of matrix elements (Carslake, Townley & Hodgson 2009). In the vast majority of these cases, it has been reported that elasticity of asymptotic growth to survival is greater than elasticity to fecundity.…”

Section: Discussionmentioning

confidence: 99%

Boom or bust? A comparative analysis of transient population dynamics in plants

et al. 2010

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Summary1. Population dynamics often defy predictions based on empirical models, and explanations for noisy dynamics have ranged from deterministic chaos to environmental stochasticity. Transient (short-term) dynamics following disturbance or perturbation have recently gained empirical attention from researchers as further possible effectors of complicated dynamics. 2. Previously published methods of transient analysis have tended to require knowledge of initial population structure. However, this has been overcome by the recent development of the parametric Kreiss bound (which describes how large a population must become before reaching its maximum possible transient amplification following a disturbance) and the extension of this and other transient indices to simultaneously describe both amplified and attenuated transient dynamics. 3. We apply the Kreiss bound and other transient indices to a data base of matrix models from 108 plant species, in an attempt to detect ecological and mathematical patterns in the transient dynamical properties of plant populations. 4. We describe how life history influences the transient dynamics of plant populations: species at opposite ends of the scale of ecological succession have the highest potential for transient amplification and attenuation, whereas species with intermediate life history complexity have the lowest potential. 5. We find ecological relationships between transients and asymptotic dynamics: faster-growing populations tend to have greater potential magnitudes of transient amplification and attenuation, which could suggest that short-and long-term dynamics are similarly influenced by demographic parameters or vital rates. 6. We describe a strong dependence of transient amplification and attenuation on matrix dimension: perhaps signifying a potentially worrying artefact of basic model parameterization. 7. Synthesis. Transient indices describe how big or how small plant populations can get, en route to long-term stable rates of increase or decline. The patterns we found in the potential for transient dynamics, across many species of plants, suggest a combination of ecological and modelling strategy influences. This better understanding of transients should guide the formulation of management and conservation strategies for all plant populations that suffer disturbances away from stable equilibria.

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“…The results of such analyses identify which demographic rates of which life stages have the greatest effect on population growth. By targeting conservation research and management on those rates and life stages, vulnerable populations can be protected from further decline (Benton & Grant, 1999; Carslake, Townley & Hodgson, 2009). Our elasticity analysis revealed that the population growth rate is most sensitive to change in either the adult survival rate or the rate at which juveniles survive but stay in the juvenile stage (i.e., do not mature into adults).…”

Section: Discussionmentioning

confidence: 99%

“…Subsequently, we conducted elasticity analyses for all combinations of yearling, juvenile and adult survival rates to ascertain which demographic rate (rate at which individuals survive and stay in the same life stage; survive and grow into the next life stage; reproduce offspring) of which life stage (yearling, juvenile or adult) has the greatest influence on the population growth rate. Elasticity analysis is widely used by conservation biologists, because the results obtained can be used to prioritise conservation research and management for those life stages that have the greatest effect on population growth (Benton & Grant, 1999; Carslake, Townley & Hodgson, 2009). Because much less is known about yearling and juvenile survival rates than adult survival rates (Marshall et al, 2011a; Dulvy et al, 2014), investigating a range of yearling and juvenile survival rates will elucidate if and how reef manta ray population responses vary with variation in survival rates.…”

Section: Introductionmentioning

confidence: 99%

Effects of yearling, juvenile and adult survival on reef manta ray (Manta alfredi) demography

Smallegange

Ouderaa

Tibiriçá³

2016

PeerJ

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BackgroundThe trade in manta ray gill plates has considerably increased over the last two decades. The resulting increases in ray mortality, in addition to mortality caused by by-catch, has caused many ray populations to decrease in size. The aim of this study was to ascertain how yearling and juvenile growth and survival, and adult survival and reproduction affect reef manta ray (Manta alfredi) population change, to increase our understanding of manta ray demography and thereby improve conservation research and measures for these fish.MethodsWe developed a population projection model for reef manta rays, and used published life history data on yearling and juvenile growth and adult reproduction to parameterise the model. Because little is known about reef manta ray yearling and juvenile survival, we conducted our analyses using a range of plausible survival rate values for yearlings, juveniles and adults.ResultsThe model accurately captured observed variation in population growth rate, lifetime reproductive success and cohort generation time in different reef manta ray populations. Our demographic analyses revealed a range of population consequences in response to variation in demographic rates. For example, an increase in yearling or adult survival rates always elicited greater responses in population growth rate, lifetime reproductive success and cohort generation time than the same increase in juvenile survival rate. The population growth rate increased linearly, but lifetime reproductive success and cohort generation time increased at an accelerating rate with increasing yearling or adult survival rates. Hence, even a small increase in survival rate could increase lifetime reproductive success by one pup, and cohort generation time by several years. Elasticity analyses revealed that, depending on survival rate values of all life stages, the population growth rate is either most sensitive to changes in the rate with which juveniles survive but stay juveniles (i.e., do not mature into adults) or to changes in adult survival rate. However, when assessing these results against estimates on population growth and adult survival rates for populations off the coasts of Mozambique and Japan, we found that the population growth rate is predicted to be always most sensitive to changes in the adult survival rate.DiscussionIt is important to gain an in-depth understanding of reef manta ray life histories, particularly of yearling and adult survival rates, as these can influence reef manta ray population dynamics in a variety of ways. For declining populations in particular, it is crucial to know which life stage should be targeted for their conservation. For one such declining population off the coast of Mozambique, adult annual survival rate has the greatest effect on population growth, and by increasing adult survival by protecting adult aggregation sites, this population’s decline could be halted or even reversed.

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Patterns and rules for sensitivity and elasticity in population projection matrices

Cited by 24 publications

References 34 publications

Carnivora Population Dynamics Are as Slow and as Fast as Those of Other Mammals: Implications for Their Conservation

Carnivora Population Dynamics Are as Slow and as Fast as Those of Other Mammals: Implications for Their Conservation

Boom or bust? A comparative analysis of transient population dynamics in plants

Effects of yearling, juvenile and adult survival on reef manta ray (Manta alfredi) demography

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