Using statistics to design and estimate vital rates in matrix population models for a perennial herb

Matrix population models are widely used to assess population status and to inform management decisions. Despite existing theories for building such models, model construction is often partially based on expert opinion. So far, model structure has received relatively little attention, although it may affect estimates of population dynamics. Here, we assessed the consequences of two published matrix structures (a 4 × 4 matrix based on expert opinion and a 10 × 10 matrix based on statistical modeling) for estimates of vital rates and stochastic population dynamics of the long-lived herb Astragalus scaphoides. We explored the ways in which choice of model structure alters the accuracy (i.e., mean) and precision (i.e., variance) of predicted population dynamics. We found that model structure had a negligible effect on the accuracy and precision of vital rates and stochastic stage distribution. However, the 10 × 10 matrix produced lower estimates of stochastic population growth rates than the 4 × 4 matrix, and more accurately predicted the observed trends in population abundance for three out of four study populations. Moreover, estimates of realized variation in population growth rate due to fluctuations in population stage structure over time were occasionally sensitive to matrix structure, suggesting differential roles of transient dynamics. Our study indicates that statistical modeling for choosing categories in matrix models might be preferable over expert opinion to accurately predict population trends and can provide a more objective way for model construction when the biological knowledge of the species is limited.     

Recruitment rates exhibit high elasticity and high temporal variation in populations of a short-lived perennial herb

Empirical studies for different life histories have shown an inverse relationship between elasticity (i.e. the proportional contribution to population growth rate) and temporal variation in vital rates. It is accepted that this relationship indicates the effect of selective pressures in reducing variation in those life‐history traits with a major impact on fitness. In this paper, we sought to determine whether changes in environmental conditions affect the relationship between elasticity of vital rates and their temporal variation, and whether vital rates with simultaneously large elasticity and temporal variation might represent a characteristic life‐history strategy. We used demographic data on 13 populations of the short‐lived Hypericum cumulicola over 5–6 years, in three time‐since‐fire classes. For each population of each time‐since‐fire, we computed the mean matrix over years and its respective elasticity matrix, and the coefficients of variation in matrix entries over study years as an estimate of temporal variability. We found that mean elasticity negatively significantly correlated with temporal variation in vital rates in populations (overall eight out of 13) included in each time‐since‐fire. However, seedling recruitment exhibited both high elasticity and high temporal variation in almost all study populations. These results indicated that (1) the general relationship between elasticity and temporal variation in vital rates was not modified by environmental changes due to time‐since‐fire, and (2) high elasticity and high temporal variation in seedling recruitment in H. cumulicola is a particular trait of the species' life history. After seed survival in the soil seed bank, seedling recruitment represents the most important life‐history trait influencing H. cumulicola population growth rate (and fitness). The high temporal variability in seedling recruitment suggests that this trait is determined by environmental cues, leading to an increase in population size and subsequent replenishment of the seed bank in favorable years.     

Seasonal variation in the population growth rate of a dominant zooplankter: what determines its population dynamics?

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Dynamics of age- and size-structured populations in fluctuating environments: Applications of stochastic matrix models to natural populations

Recent developments of the theory of stochastic matrix modeling have made it possible to estimate general properties of age- and size-structured populations in fluctuating environments. However, applications of the theory to natural populations are still few. The empirical studies which have used stochastic matrix models are reviewed here to examine whether predictions made by the theory can be generally found in wild populations. The organisms studied include terrestrial grasses and herbs, a seaweed, a fish, a reptile, a deer and some marine invertebrates. In all the studies, the stochastic population growth rate (ln λ _s ) was no greater than the deterministic population growth rate determined using average vital rates, suggesting that the model based only on average vital rates may overestimate growth rates of populations in fluctuating environments. Factors affecting ln λ _s include the magnitude of variation in vital rates, probability distribution of random environments, fluctuation in different types of vital rates, covariances between vital rates, and autocorrelation between successive environments. However, comprehensive rules were hardly found through the comparisons of the empirical studies. Based on shortcomings of previous studies, I address some important subjects which should be examined in future studies.     

Between‐species differences in demographic responses to temperature of coexisting cladocerans

Abstract In this work we report on the seasonal trends of abundances in terms of temperature exposure for four coexisting cladoceran species (Daphnia ambigua (Daphniidae), Ceriodaphnia dubia (Daphniidae), Diaphanosoma chilense (Sididae) and Moina micrura (Moinidae)) from a Chilean temperate lake. In order to compare the demographic response to temperature, we used life table experiments to parameterize matrix models for the four species at four fixed temperatures. From these life table response experiments we assessed the effects of temperature, species and their interaction on the variation in growth rate, as well as the contribution of juvenile survival, adult survival, fertility and age at first reproduction to the changes in growth rate. Our results showed interspecific differences in the effect of temperature on the growth rate. Species that present higher field abundance at lower temperature also exhibited, under controlled experiments, higher growth rates at low temperature and lower growth rates at high temperature, relative to the additive model. Conversely, species with higher abundances during the warmer seasons exhibited higher growth rates at higher experimental temperatures and lower growth rates at lower temperatures, relative to the additive model. The vital rates that most contributed to the variation in growth rate were age at first reproduction and fertility. Our growth rate estimates matched predictions of the metabolic ecology model.     

Contrasting effects of different landscape characteristics on population growth of a perennial forest herb

Anthropogenic changes in landscape structure, such as habitat loss, habitat subdivision and edge increase, can strongly affect the performance of plants, leading to population declines and extinctions. Many studies to date have focused on single characteristics of landscape structure or single life‐cycle phases, but they poorly discern the different pathways through which landscape change influences plant population dynamics via different vital rates. In this study, we evaluated the effect of two structural characteristics (habitat quantity and edge length) on vital rates and population growth rates of a perennial forest plant (Primula vulgaris) in a historically managed landscape. Areas with higher amounts of forest habitat had higher population growth rates due to higher recruitment, survival and growth of seedlings, while increased forest edge length was positively associated with population growth rates primarily due to a higher survival of reproductive individuals. Effects were stronger during the first of the two transition intervals studied. The results demonstrate that changes in different landscape structural characteristics may result in opposing effects acting via different vital rates, and highlight the need for integrative analyses to evaluate the effects of rapid landscape transformation on the current and long term plant population dynamics.     

Factors influencing rate of decline in a Merriam's wild turkey population

We investigated population growth rate (λ) for a Merriam's wild turkey (Meleagris gallopavo merriami) population in the northern Black Hills, South Dakota, USA. We constructed and evaluated a females-only matrix population model. Our estimate of asymptotic λ, derived from estimates of vital rates obtained from 2016–2018 was 0.74 (95% CI = 0.60, 0.88), which indicates that the vital rates were inadequate to sustain the population. Elasticity values were highest for changes in adult survival probability followed by, in order, changes in juvenile survival, yearling survival, and adult reproduction. We could only achieve stable or growing populations (i.e., λ ≥ 1) by increasing the probability of adult and yearling survival (holding all other vital rates constant). Estimated adult survival rate in the work reported here was lower than values reported for other populations in the Black Hills; therefore, managing for increased female survival (≥0.68) may be the most practical strategy for promoting wild turkey population growth in this system. We recommend no female harvest during any open turkey season.     

Asexual reproduction changes predator population dynamics in a life predator–prey system

Many organisms display oscillations in population size. Theory predicts that these fluctuations can be generated by predator–prey interactions, and empirical studies using life model systems, such as a rotifer-algae community consisting of Brachionus calyciflorus as predator and Chlorella vulgaris as prey, have been successfully used for studying such dynamics. B. calyciflorus is a cyclical parthenogen (CP) and clones often differ in their sexual propensity, that is, the degree to which they engage into sexual or asexual (clonal) reproduction. Since sexual propensities can affect growth rates and population sizes, we hypothesized that this might also affect population oscillations. Here, we studied the dynamical behaviour of B. calyciflorus clones representing either CPs (regularly inducing sex) or obligate parthenogens (OPs). We found that the amplitudes of population cycles to be increased in OPs at low nutrient levels. Several other population dynamic parameters seemed unaffected. This suggests that reproductive mode might be an important additional variable to be considered in future studies of population oscillations.     

Dynamics of isolated <Emphasis Type="Italic">Saponaria bellidifolia</Emphasis> Sm. populations at northern range periphery

Four populations of Saponaria bellidifolia situated at the species’ northern range periphery (Apuseni Mountains, southeastern Carpathians) were monitored over a period of 5 years. They were chosen to represent different habitat types (rocky, fixed screes, open screes and grassy), disturbance regime (fire), and population sizes (categorized as large and small). The reproductive effort was quantified, and matrix models were used to describe the population dynamics and to assess population viability. Saponaria bellidifolia had very stable population dynamics in the harsh and stable abiotic conditions of the outcrops where populations occur. Habitat conditions exerted a notable influence on the species’ population reproductive performance, growth rate, and vital rates, whereas population size and climate did not have a clear-cut effect on the dynamics of the species. Saponaria bellidifolia maintains viable populations in the southeastern Carpathians, at its northern range periphery.     

Variation in the demographics of a rare central Oregon endemic, Astragalus peckii Piper (Fabaceae), with fluctuating levels of herbivory

Understanding variation in plant vital rates (survival, growth, and reproduction) and population demographic parameters for rare plant taxa facilitates effective management for long-term persistence. We evaluated demographics of the rare plant Astragalus peckii (Fabaceae), a state-listed Threatened plant in Oregon, USA, with particular emphasis on how a microlepidopteran herbivore, Sparganothis tunicana, impacted vital rates and population growth. Stage-based transition matrix models were used to compute population growth rate (λ) and elasticity from 2006 to 2009 at two populations: Bull Flat, which was located in the main population center; and Chiloquin, a naturally isolated population. Population growth at Bull Flat was stable to slightly declining (λ = 0.96, 95 % CI 0.91–1.00) whereas at Chiloquin, the isolated population, population growth was increasing (λ = 1.20, 95 % CI 1.15–1.24). Microlepidopteran herbivory was associated with different plant responses in each population. At Bull Flat, plant survival was lower with greater herbivore presence. At Chiloquin, reproduction was reduced in plants when herbivores were active earlier in the growing season. Despite these effects on plant vital rates, we found lower population growth only during one transition period at Bull Flat when we compared matrices with and without herbivory. In addition to herbivory, we also address the potential role precipitation plays as a contributor to site differences and temporal variation within sites. Overall, we illustrate how two populations can have different responses to the same disturbance factor and highlight implications for management of different populations across the landscape.     

Comparative demography of two giant caulescent rosettes (Espeletia timotensis and E. spicata) from the high tropical Andes

Using field data from previous studies we built matrix models for two populations of giant rosettes, Espeletia timotensis Cuatrec. and E. spicata Sch. Bip. Wedd., from the Andes Cordillera in Mérida, Venezuela. We analysed the models and calculated population growth rate (λ), sensitivities, elasticities and the sensitivity of the elasticities to changes in the vital rates. The analysis showed that the two species behave alike in general demographic terms. In both models, population growth rate is positive and sensitivities of λ to changes in vital rates decrease markedly in this order: plant establishment, progression of juvenile–adult, germination and survival. The relative contributions of vital rates to λ (elasticities) are very similar to those of other woody plant species: a higher contribution of survival and a very low contribution of fecundity. Transition from seedling to juvenile is most important and the younger established stages (juveniles and young adults) play a predominant demographic role in both populations. Seed banks and older adults are playing a relatively minor role in the dynamics of both populations. However, they may be important in relation to unpredictable, favourable or detrimental events. Perturbation analysis of elasticities showed that increasing the rate of plant establishment will decrease the relative importance of stasis. We conclude that both species are demographically very close, and similar to other long‐lived woody plant species. However, the two species differ in the role of the seed bank, which seems more important in the demography of E. spicata than in E. timotensis.     

Linking vital rates to invasiveness of a perennial herb

Invaders generally show better individual performance than non-invaders and, therefore, vital rates (survival, growth, fecundity) could potentially be used to predict species invasiveness outside their native range. Comparative studies have usually correlated vital rates with the invasiveness status of species, while few studies have investigated them in relation to population growth rate. Here, I examined the influence of five vital rates (plant establishment, survival, growth, flowering probability, seed production) and their variability (across geographic regions, habitat types, population sizes and population densities) on population growth rate (λ) using data from 37 populations of an invasive, iteroparous herb (Lupinus polyphyllus) in a part of its invaded range in Finland. Variation in vital rates was often related to habitat type and population density. The performance of the populations varied from declining to rapidly increasing independently of habitat type, population size or population density, but differed between regions. The population growth rate increased linearly with plant establishment, and with the survival and growth of vegetative individuals, while the survival of flowering individuals and annual seed production were not related to λ. The vital rates responsible for rapid population growth varied among populations. These findings highlight the importance of both regional and local conditions to plant population dynamics, demonstrating that individual vital rates do not necessarily correlate with λ. Therefore, to understand the role of individual vital rates in a species ability to invade, it is necessary to quantify their effect on population growth rate.     

Climatic drivers of pinyon mouse Peromyscus truei population dynamics in a resource-restricted environment

Highly variable patterns in temperature and rainfall events can have pronounced consequences for small mammals in resource-restricted environments. Climatic factors can therefore play a crucial role in determining the fates of small mammal populations. We applied Pradel's temporal symmetry model to a 21-year capture–recapture dataset to study population dynamics of the pinyon mouse (Peromyscus truei) in a semi-arid mixed oak woodland in California, USA. We examined time-, season- and sex-specific variation in realized population growth rate (λ) and its constituent vital rates, apparent survival and recruitment. We also tested the influence of climatic factors on these rates. Overall monthly apparent survival was 0.81 ± 0.004 (estimate ± SE). Survival was generally higher during wetter months (October–May) but varied over time. Monthly recruitment rate was 0.18 ± 0.01, ranging from 0.07 ± 0.01 to 0.63 ± 0.07. Although population growth rate (λ) was highly variable, overall monthly growth rate was close to 1.0, indicating a stable population during the study period (λ ± SE = 0.99 ± 0.01). Average temperature and its variability negatively affected survival, whereas rainfall positively influenced survival and recruitment rates, and thus the population growth rate. Our results suggest that seasonal rainfall and variation in temperature at the local scale, rather than regional climatic patterns, more strongly affected vital rates in this population. Discerning such linkages between species' population dynamics and environmental variability are critical for understanding local and regional impacts of global climate change, and for gauging viability and resilience of populations in resource-restricted environments.     

Variation in pea aphid population development in three different habitats

Abstract.

• 1 Seasonal population growth rates for the pea aphid, Acyrthosiphon pisum Harris, were determined in three different host plant habitats; alfalfa, Medicago sativa (L.), clover, Trifolium pratense (L.), and peas, Pisum sativum (L.); over four years and eight places. It was possible to estimate a common intrinsic rate of increase for each host plant habitat.
• 2 An analysis of the relative influence of temporal, spatial and host plant habitat variation showed that the host plant habitat was most important in determining the growth rates of the populations, both in rate of build-up and decline.
• 3 Patterns of alate production in the three different habitats differed substantially between the annual peas and the two perennial legumes. During the summer, alate production was large and rapid in peas and remained low and constant in clover and alfalfa
• 4 Parasitism was highest in peas. The species composition of parasitoids differed between crops.
• 5 Aphids in annual peas had a higher intrinsic rate of increase and a faster rate of decline than in the two perennial legumes. This explains the presence of both migratory and sedentary forms among pea aphids.

     

Relative effects of environment and direct species interactions on the population growth rate of an exotic ascidian

The success of exotic species can be influenced by both the abiotic environment and species interactions. Many studies have demonstrated significant effects of either type of factor on aspects of exotic success, but few have considered their relative effects on population growth rate, a more holistic measure of success. To quantify the relative effects of environment and direct competition on an exotic ascidian, Botrylloides violaceus, I manipulated direct contact interactions at four sites with different abiotic environments and tracked individual colonies over 3 years. I tested site and contact treatment effects on survival, growth and fecundity, and then conducted a life table response experiment on a periodic, size-structured population matrix model to test their effects on population growth rate. Both site and contact interaction were important to explaining variation in survival and growth. Contact interactions decreased the survival and growth of larger colonies but unexpectedly increased the survival of small colonies at some sites, which led to relatively weaker and spatially variable effects on overall population growth rates. Site effects on population growth rates were an order of magnitude larger than contact effects, and site variation in winter vital rates made the largest contributions to changes in population growth rate. The results of this study suggest that the abiotic environment plays a larger role in the success of B. violaceus. Thus, environmental variables, such as temperature and salinity, could be used to predict this exotic species’ success under different environmental scenarios, including global climate change.     

Population dynamics of Walia ibex (Capra walie) at Simien Mountains National Park,Ethiopia

Intensive total direct counts of Walia ibex (Capra walie) population were performed at Simien Mountains National Park (SMNP) in 2009. Historical data were collected from SMNP and literature reviews. Different models were suited to determine population growth rates and intrinsic rate of increase. The population size estimated was 745 animals. The correlation between the two repeated counts was significant (r = 0.99 and P < 0.01). Mean instantaneous growth rate (r), growth rate per capita (λ) and population annual growth rate (Λ) were 2.6 ± 2.6, 0.03 ± 0.18 and 19.5 ± 50.4, respectively. Instantaneous growth rate and growth rate per capita were positively correlated (r = 0.958, P < 0.01). Average growth rate (rΛ) and intrinsic rate of increase (rr) under ideal (r = 0.950, P < 0.01) and random environments (r = 0.810, P < 0.01) were positively correlated. The population grows by 2.5% under ideal environments with an intrinsic increase of 0.04 (0.006%) and by 0.13% under random environments with intrinsic rate of decrease of ?0.184 or ?0.025% per year, respectively. The mean rank of the flock structure of whole population was 3.13, 3.88, 2.00 and 1.00 for males, females, juveniles and unidentified, respectively.     

Impact of Spatial and Temporal Variation in Calf Survival on the Growth of Elk Populations

Abstract: The realized impact of a vital rate on population growth (λ) is determined by both the relative influence of the vital rate on λ (elasticity) and its magnitude of variability. We estimated mean survival and reproductive rates in elk (Cervus elaphus) and spatial and temporal variation in these rates from 37 sources located primarily across the Rocky Mountain region and northwestern United States. We removed sampling variance from estimates of process variance both within and across vital-rate data sets using the variance discounting method developed by White (2000). Deterministic elasticities calculated from a population matrix model parameterized with these mean vital rates ranked adult female survival (e_Scow = 0.869) much higher than calf survival (e_Scalf = 0.131). However, process variance in calf survival was >11 times greater than process variance in female survival across data sets and 10 times greater on average within studies. We conducted Life-Stage Simulation Analysis to incorporate both vital-rate elasticity patterns and empirical estimates of variability to identify those vital rates most influential in elk population dynamics. The overwhelming magnitude of variation in calf survival explained 75% of the variation in the population growth rates generated from 1,000 matrix replicates, compared to just 16% of the variation in λ explained by variation in female survival. Variation in calf survival greatly impacts elk population growth and calls into question the utility of classical elasticity analysis alone for guiding elk management. These results also suggest that the majority of interannual variability that wildlife managers document in late-winter and spring elk surveys is attributable to variation in calf survival over the previous year and less influenced by variation in the harvest of females during the preceding autumn. To meet elk population size objectives, managers should consider the inherent variation in calf survival, and its apparent sensitivity to management, in addition to female harvest.     

Stochastic LTRE analysis of the effects of herbivory on the population dynamics of a perennial grassland herb

Herbivores can have strong deleterious effects on vital rates (growth, reproduction, and survival) and thus negatively impact the population dynamics of plant species. In practice, however, these effects might be strongly correlated, for example as a result of tradeoffs between vital rates. To get better insights into the effects of herbivory on the population dynamics of the long‐lived grassland plant Primula veris population projection matrices were constructed from demographic data collected between 1999 and 2008 (nine annual transitions). Data were collected in two large grassland populations, each of which was subjected to two treatments (grazing by cattle versus a mowing treatment), yielding a total of 36 matrices. We applied a lower‐level vital rate life table response experiment (LTRE) using the small noise approximation (SNA) of the stochastic population growth rate to disentangle the contributions of changes in mean vital rates, variability in vital rates, correlations between vital rates and vital rate elasticities to the difference in the stochastic growth rate. Stochastic growth rates (a= log λ_S) were significantly lower in grazed than in mown plots (a= 0.0185 and 0.1019, respectively). SNA LTRE analysis showed that contributions of mean vital rates by far made the largest contribution to the observed difference in a between grazed and control plots. In particular, changes in sexual reproduction rates made the largest contributions to lower the stochastic growth rate in grazed plots: both adult flowering probabilities and flower and seed production were importantly lower in grazed populations, but these negative effects were largely buffered by increased establishment and seedling survival rates. Among the stochastic terms of the SNA decomposition, contributions of covariance and correlations between vital rates had the largest impact, whereas contributions of elasticities were smaller. The strongest correlation driver was the association between adult survival and seedling establishment, suggesting that environmental conditions favouring adult survival also are beneficial for seedling establishment. Overall, our results show that herbivory had a strong negative effect on the long‐term population growth rate of P. veris that was primarily mediated by differences in fecundity (flower and seed production) and germination.     

Demographic responses of Pinguicula ionantha to prescribed fire: a regression-design LTRE approach

This study describes the use of periodic matrix analysis and regression-design life table response experiments (LTRE) to investigate the effects of prescribed fire on demographic responses of Pinguicula ionantha, a federally listed plant endemic to the herb bog/savanna community in north Florida. Multi-state mark–recapture models with dead recoveries were used to estimate survival and transition probabilities for over 2,300 individuals in 12 populations of P. ionantha. These estimates were applied to parameterize matrix models used in further analyses. P. ionantha demographics were found to be strongly dependent on prescribed fire events. Periodic matrix models were used to evaluate season of burn (either growing or dormant season) for fire return intervals ranging from 1 to 20 years. Annual growing and biannual dormant season fires maximized population growth rates for this species. A regression design LTRE was used to evaluate the effect of number of days since last fire on population growth. Maximum population growth rates calculated using standard asymptotic analysis were realized shortly following a burn event (<2 years), and a regression design LTRE showed that short-term fire-mediated changes in vital rates translated into observed increases in population growth. The LTRE identified fecundity and individual growth as contributing most to increases in post-fire population growth. Our analyses found that the current four-year prescribed fire return intervals used at the study sites can be significantly shortened to increase the population growth rates of this rare species. Understanding the role of fire frequency and season in creating and maintaining appropriate habitat for this species may aid in the conservation of this and other rare herb bog/savanna inhabitants. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Spatial covariation of fish population vital rates in a stream network

Animal populations are spatially structured in heterogeneous landscapes, in which local patches with differing vital rates are connected by dispersal of individuals to varying degrees. Although there is evidence that vital rates differ among local populations, much less is understood about how vital rates covary among local patches in spatially heterogeneous landscapes. In this study, we conducted a nine-year annual mark–recapture survey to characterize spatial covariation of survival and growth for two Japanese native salmonids, white-spotted charr Salvelinus leucomaenis japonicus and red-spotted masu salmon Oncorhynchus masou ishikawae, in a headwater stream network composed of distinctly different tributary and mainstem habitats. Spatial structure of survival and growth differed by species and age class, but results provided support for negative covariation between vital rates, where survival was higher in the tributary habitat but growth was higher in the mainstem habitat. Thus, neither habitat was apparently more important than the other, and local habitats with complementary vital rates may make this spatially structured population less vulnerable to environmental change (i.e. portfolio effect). Despite the spatial structure of vital rates and possibilities that fish can exploit spatially distributed resources, movement of fish was limited due partly to a series of low-head dams that prevented upstream movement of fish in the study area. This study shows that spatial structure of vital rates can be complex and depend on species and age class, and this knowledge is likely paramount to elucidating dynamics of spatially structured populations.