Population dynamics of a threatened cactus species: general assessment and effects of matrix dimensionality

Harrisia portoricensis is an endemic Caribbean cactus currently under threatened status. In this study we used population projection matrices to evaluate the conservation status of this species and we performed a systematic analysis of the effects of matrix dimensionality on the inferred demographic parameters. Results revealed that population growth rates (λ) were 0.946 and 0.961 for the 2007–2008 and 2008–2009 periods respectively, suggesting a declining population with limited persistence ability. Even when the highest elasticity values corresponded to the survival of adults, numerical simulations suggested that increases in either seedling establishment or fecundity could render λ > 1. Our empirical-based analysis using raw demographic data revealed a clear trend for λ values to decrease with increasing matrix dimension. Stasis and fecundity elasticities were also found to decrease whereas retrogression and growth elasticitites increased with increasing matrix dimension. These results are roughly insensitive to the method used to create matrices of different dimensions. For H. portoricensis, large matrices with narrow classifications were required to minimize variations in λ, highlighting the need for large data sets to assess the convergence of results with matrix dimensionality. Our combined results emphasize that under current scenarios the ability of H. portoricensis for population growth is severely limited. Any management strategy designed for the conservation of this species should consider long-term monitoring of populations as well as programs that enhance seedling establishment and adult survival.     

Differential effects of abandonment on the demography of the grassland perennial Succisa pratensis

Abandonment of traditional land-use practices can have strong effects on the abundance of species occurring in agricultural landscapes. However, the precise mechanisms by which individual performance and population dynamics are affected are still poorly understood. To assess how abandonment affects population dynamics of Succisa pratensis we used data from a 4-year field study in both abandoned and traditionally grazed areas in moist and mesic habitats to parameterize integral projection models. Abandoned populations had a lower long-term stochastic population growth rate (λ _S = 0.90) than traditionally managed populations (λ _S = 1.08), while λ _S did not differ between habitat types. The effect of abandonment differed significantly between years and had opposed effects on different vital rates. Individuals in abandoned populations experienced higher mortality rates and lower seedling establishment, but had higher growth rates and produced more flower heads per plant. Population viability analyses, based on a population survey of the whole study area in combination with our demographic models, showed that 32 % of the populations face a high risk of extinction (>80 %) within 20 years. These results suggest that immediate changes in management are needed to avoid extinctions and further declines in population sizes. Stochastic elasticity analyses and stochastic life table response experiments indicated that management strategies would be most effective if they increase survival of small plants as well as seedling establishment, while maintaining a high seed production. This may be achieved by varying the grazing intensity between years or excluding grazers when plants are flowering.     

Demography when history matters: construction and analysis of second-order matrix population models

History matters when individual prior conditions contain important information about the fate of individuals. We present a general framework for demographic models which incorporates the effects of history on population dynamics. The framework incorporates prior condition into the i-state variable and includes an algorithm for constructing the population projection matrix from information on current state dynamics as a function of prior condition. Three biologically motivated classes of prior condition are included: prior stages, linear functions of current and prior stages, and equivalence classes of prior stages. Taking advantage of the matrix formulation of the model, we show how to calculate sensitivity and elasticity of any demographic outcome. Prior condition effects are a source of inter-individual variation in vital rates, i.e., individual heterogeneity. As an example, we construct and analyze a second-order model of Lathyrus vernus, a long-lived herb. We present population growth rate, the stable population distribution, the reproductive value vector, and the elasticity of λ to changes in the second-order transition rates. We quantify the contribution of prior conditions to the total heterogeneity in the stable population of Lathyrus using the entropy of the stable distribution.     

Pair-wise analyses of the effects of demographic processes, vital rates, and life stages on the spatiotemporal variation in the population dynamics of the riparian tree Aesculus turbinata Blume

Population growth rates (λ) of the riparian tree Aesculus turbinata varied from 0.9988 to 1.0524 spatiotemporally. We conducted a series of pair-wise demographic and matrix analyses, including randomization tests, three types of life table response experiments (LTREs), analysis of variance and χ² tests, to test which life stages had the greatest effect on this variation in λ. Randomization tests detected significant variations in λ between plots affected or not by typhoons in three habitats and between periods with high and low recruitment in one habitat. Mixed-level LTREs identified that the demographic processes and life stages that had the strongest effect on the actual variation in λ were: (1) progressions of small and intermediate juveniles and (2) founding process from seeds to 1-year-old seedlings. These juvenile stages had medium sensitivities and variances that explained high upper-level LTRE contributions. Lower-level LTREs showed that the vital rates contributing the most were the growth rates of these juvenile stages. These findings demonstrate that progression from one stage to the next, growth rates of 1-year-old seedlings, and stunted aging juveniles are the most important stages in the population dynamics of this long-lived primary tree species. Transition matrix elements with high elasticities had little effect on the variation in λ, indicating that high-elasticity vital rates do not necessarily drive variation in population growth. As compared with the results of randomization tests, significant differences in vital rates examined using ANOVA or χ² tests showed that typhoon disturbance had the greatest effect on the demographic parameters of individual trees.     

The demography of native and non-native plant species in mountain systems: examples in the Greater Yellowstone Ecosystem

In mountainous areas, native and non-native plants will be exposed to climate change and increased disturbance in the future. Non-native plants may be more successful than natives in disturbed areas and thus be able to respond quicker to shifting climatic zones. In 2009, monitoring plots were established for populations of a non-native species (Linaria dalmatica) and a closely related native species (Castilleja miniata) on an elevation gradient in the Greater Yellowstone Ecosystem, USA. Population data were collected twice during the growing season for 3 years and used to calculate population vital rates for both species, and to construct population dynamics models for L. dalmatica. Linaria dalmatica vital rates were more associated with climatic/environmental factors than those of C. miniata. Population dynamics models for L. dalmatica showed no trend in population growth rate (λ) vs. elevation. The highest λ corresponded with the lowest vegetation and litter cover, and the highest bare ground cover. All populations with λ < 1 corresponded with the lowest measured winter minimum temperature. There was a negative association between λ and number of weeks of adequate soil moisture, and a weak positive association between λ and mean winter minimum temperature. Variance in vital rates and λ of L. dalmatica suggest broad adaptation within its current range, with the potential to spread further with or without future changes in climate. There is evidence that λ is negatively affected by persistent soil moisture which promotes the growth of other plant species, suggesting that it might expand further if other species were removed by disturbance.     

Mathematical analysis of the asymptotic behavior of the Leslie population matrix model

LetL be a Leslie population matrix. Leslie (1945) and others have shown that the matrixL has a leading positive eigenvalueλ ₀ and that in general: (1) $$\mathop {\lim }\limits_{t \to \infty } \frac{{L^t X}}{{\lambda _0^t }} = \gamma X_{\lambda _0 } $$ whereX _{λ 0} is an eigenvector corresponding toλ ₀,X is any initial population vector, and γ is a scalar quantity detormined byX. In this article we generalize (1) exhaustively by removing the mild restrictions on the fertility rates which most writers impose. The result is an oscillatory limit of a kind first noted by Bernardelli (1941) and Lewis (1942) and described by Bernardelli as “population waves”. We calculate in terms ofλ ₀ and the entries of the matrixL the values of this oscillatory limit as well as its time-independent average over one period. This calculation includes as its leading special case the result of (1), confirming incidentally that γ is nonzero. To stabilize a population, the matrixL must be adjusted so thatλ ₀=1. The limits calculated for the oscillatory and non-oscillatory cases then have maximum significance since they represent the limiting population vectors. We discuss a simple scheme for accomplishing stanbilization which yields as a byproduct an easily accessible scalar measure ofL's tendency to promote population growth. The reciprocal of this measure is the familiar net reproduction rate.     

Using integral projection models to compare population dynamics of four closely related species

Demographic processes, such as survival, growth, and reproduction, can inform us about invasion risk, extinction risk, and trade-offs in life history strategies. The population dynamics of four Amaranthaceae species in southern Illinois, USA were examined using integral projection models (IPMs) to determine whether vital rates reflect life history among these closely related species. Two of the species, Amaranthus palmeri and Amaranthus tuberculatus, are summer annuals and considered to be some of the most problematic agricultural weeds in the US Midwest. Achyranthes japonica is a relatively new invasive exotic species that primarily inhabits forests. Iresine rhizomatosa, is an endangered species in the study area, which also inhabits forests. Two populations of each species were studied from 2012 to 2014 in which height of individuals were measured and used as the state variable in the IPMs. The Amaranthus species and Achyranthes japonica had an estimated population growth rate >1, projecting increases in population size. By contrast, λ was <1 for I. rhizomatosa, projecting a decline in population size demonstrating its endangered status. Germination rates and seed viability were dependent on species and varied over time. Elasticity analyses showed that survival and growth contributed most to λ for the perennial species; whereas, for the annual species population dynamics were driven primarily by fecundity. Overall, Achyranthes japonica and the Amaranthus species show similar trends in demographic processes that align with their invasive nature and not with their life histories. Furthermore, this study demonstrates that more research on the competitive nature of Achyranthes japonica is needed.     

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.     

Demographic effects of warming,elevated soil nitrogen and thinning on the colonization of a perennial plant

Global change is causing significant modifications to native plant communities. These effects can be direct through changes in productivity, or indirect through the spread of invading species. Identifying vital traits important for individual species’ response to environmental variation could be useful for making predictions about how entire communities may respond to global change. I studied the effects of factors associated with global change on the demography of an experimentally introduced species, Pityopsis aspera. In a Florida old-field, I investigated how warming, increased soil nitrogen and thinning of the extant plant community affected survival, growth and reproduction of P. aspera using a life table response experiment. The estimated population growth rate (λ) of P. aspera was reduced by nitrogen addition, as a result of decreased fecundity. However, λ increased in response to the warming treatment, as a result of increased fecundity. In the presence of thinning, both warming and nitrogen served to increase λ as a result of an increase in the growth of young individuals. This experiment illustrates how different vital rates contribute to the population level responses of an experimentally introduced plant to warming, and nitrogen deposition. Results also show how these demographic responses may occur via indirect effects through established species. This work highlights the importance of studying interactions among temperature, soil nitrogen and demography across the entire life cycle in order to capture the complex and, often, non-additive relationships mediating global change effects.     

Sensitivity of the population growth rate to demographic variability within and between phases of the disturbance cycle

For species in disturbance-prone ecosystems, vital rates (survival, growth and reproduction) often vary both between and within phases of the cycle of disturbance and recovery; some of this variation is imposed by the environment, but some may represent adaptation of the life history to disturbance. Anthropogenic changes may amplify or impede these patterns of variation, and may have positive or negative effects on population growth. Using stochastic population projection matrix models, we develop stochastic elasticities (proportional derivatives of the long-run population growth rate) to gauge the population effects of three types of change in demographic variability (changes in within- and between-disturbance-phase variability and phase-specific changes). Computing these elasticities for five species of disturbance-influenced perennial plants, we pinpoint demographic rates that may reveal adaptation to disturbance, and we demonstrate that species may differ in their responses to different types of changes in demographic variability driven by climate change.     

Facilitated by nature and agriculture: performance of a specialist herbivore improves with host-plant life history evolution, domestication, and breeding

Plant defenses against herbivores are predicted to change as plant lineages diversify, and with domestication and subsequent selection and breeding in the case of crop plants. We addressed whether defense against a specialist herbivore declined coincidently with life history evolution, domestication, and breeding within the grass genus Zea (Poaceae). For this, we assessed performance of corn leafhopper (Dalbulus maidis) following colonization of one of four Zea species containing three successive transitions: the evolutionary transition from perennial to annual life cycle, the agricultural transition from wild annual grass to primitive crop cultivar, and the agronomic transition from primitive to modern crop cultivar. Performance of corn leafhopper was measured through seven variables relevant to development speed, survivorship, fecundity, and body size. The plants included in our study were perennial teosinte (Zea diploperennis), Balsas teosinte (Zea mays parviglumis), a landrace maize (Zea mays mays), and a hybrid maize. Perennial teosinte is a perennial, iteroparous species, and is basal in Zea; Balsas teosinte is an annual species, and the progenitor of maize; the landrace maize is a primitive, genetically diverse cultivar, and is ancestral to the hybrid maize; and, the hybrid maize is a highly inbred, modern cultivar. Performance of corn leafhopper was poorest on perennial teosinte, intermediate on Balsas teosinte and landrace maize, and best on hybrid maize, consistent with our expectation of declining defense from perennial teosinte to hybrid maize. Overall, our results indicated that corn leafhopper performance increased most with the agronomic transition, followed by the life history transition, and least with the domestication transition.     

Demographic response of plant populations to habitat fragmentation and temporal environmental variability

Many plant species currently exist in fragmented populations of different sizes, while they also experience unpredictable climatic fluctuation over time. However, we still understand little about how plant demography responds to such spatial and temporal environmental variability. We studied population dynamics of an understory perennial herb Trillium camschatcense in the Tokachi plain of Hokkaido, Japan, where a significant effect of forest fragmentation on seedling recruitment was previously reported. Four populations across a range of fragment sizes were studied for 6 years, and the data were analyzed using matrix population models. Per capita fecundity (the number of recruits per plant) varied greatly among populations, but the variation in population growth rates (λ) was mainly driven by the variation in stasis and growth rates, suggesting that the general trend of reduced fecundity in fragmented populations may not be readily translated into subsequent dynamics. Temporal variation in λ among years was more than 2 times larger than spatial variation among populations, and this result was likely attributable to the contrasting response of correlation structures among demographic rates. The among-population variation in λ was dampened by negative covariation between matrix elements possibly due to density-dependent regulation as well as an inherent constraint that some elements are not independent, whereas positive covariation between matrix elements resulted in large temporal variation in λ. Our results show that population dynamics responded differently to habitat fragmentation and temporal variability of the environment, emphasizing the need to discriminate these spatial and temporal variations in demographic models. Although no populations were projected to be declining in stochastic simulations, correlation between current habitat size and plant density implies historical λ is positively related to habitat size.     

The impact of seed extraction on the population dynamics of Pinus maximartinezii

Pinus maximartinezii is a rare, endemic, threatened species known from a single small population in the state of Zacatecas, Mexico. Among the pine species that produce edible nuts, it produces one of the largest and most nutritious seeds. The seeds of P. maximartinezii have historically been used for human consumption. The cones are harvested directly from the trees, and the seeds are sold illegally in local, national and international markets. However, the effects of seed extraction must be thoroughly evaluated to determine the potential impacts on population stability. To assess the impact of different rates of seed harvesting on the demography of this species, a 2-yr study of population dynamics was conducted in three 0.1-ha plots. A 9 × 9 size-structured matrix model was used to simulate changes in population growth over time in conjunction with increasing stepwise reductions in fecundity. The population growth rate (λ) of P. maximartinezii was 1.1175, with a 95% confidence interval (CI) from 1.1008 to 1.1321, and it was relatively insensitive to changes in fecundity and growth. Under a seed extraction intensity of 99%, λ decreased to 1.0241, with a CI from 1.0177 to 1.0361. Elasticity analysis was then performed to identify the combined effects of proportional changes in fecundities and the largest stasis elements on λ. The results suggest that a sound conservation strategy should focus on improving the survival of juveniles and adults during their first reproductive events and on the largest adults, as well as on protecting the habitat of this threatened endemic species.     

Variation in vital-rate sensitivity between populations of Texas horned lizards

Demographic studies of imperiled populations can aid managers in planning conservation actions. However, applicability of findings for a single population across a species’ range is sometimes questionable. We conducted long-term studies (8 and 9 years, respectively) of 2 populations of the lizard Phrynosoma cornutum separated by 1000 km within the historical distribution of the species. The sites were a 15-ha urban wildlife reserve on Tinker Air Force Base (TAFB) in central Oklahoma and a 6000-ha wildland site in southern Texas, the Chaparral Wildlife Management Area (CWMA). We predicted a trade-off between the effect of adult survival and fecundity on population growth rate (λ), leading to population-specific contributions of individual vital rates to λ and individualized strategies for conservation and management of this taxon. The CWMA population had lower adult survival and higher fecundity than TAFB. As predicted, there was a trade-off in the effects of adult survival and fecundity on λ between the two sites; fecundity affected λ more at CWMA than at TAFB. However, adult survival had the smallest effect on λ in both populations. We found that recruitment in P. cornutum most affected λ at both sites, with hatchling survival having the strongest influence on λ. Management strategies focusing on hatchling survival would strongly benefit both populations. As a consequence, within the constraint of the need to more accurately estimate hatchling survival, managers across the range of species such as P. cornutum could adopt similar management priorities with respect to stage classes, despite intra-population differences in population vital rates.     

Assessing seed and microsite limitation on population dynamics of a gypsophyte through experimental soil crust disturbance and seed addition

Understanding the factors limiting population growth is crucial for species management and conservation. We assessed the effects of seed and microsite limitation, along with climate variables, on Helianthemum squamatum, a gypsum soil specialist, in two sites in central Spain. We evaluated the effects of experimental seed addition and soil crust disturbance on H. squamatum vital rates (survival, growth and reproduction) across four years. We used this information to build integral projection models (IPMs) for each combination of management (seed addition or soil disturbance), site and year. We examined differences in population growth rate (λ) due to management using life table response experiments. Soil crust disturbance increased survival of mid to large size individuals and germination. Contributions to λ of positive individual growth (progression) and negative individual growth (retrogression) due to managements varied among years and sites. Soil crust disturbance increased λ in the site with the highest plant density, and seed addition had a moderate positive effect on λ in the site with lowest plant density. Population growth rate (λ) decreased by half in the driest year. Differences in management effects between sites may represent a shift from seed to microsite limitation at increasing densities. This shift underscores the importance of considering what factors limit population growth when selecting a management strategy.     

Population dynamics of the perennial Plantago media in semi‐natural grasslands

Abstract. In this study we investigated population dynamics of a perennial forb, Plantago media, in semi‐natural grasslands in southeastern Sweden. Plantago media is a rather common inhabitant of grasslands in this region, but it has been shown to experience dispersal limitations both among managed grassland sites and at potential dispersal routes along road verges. The demography of P. media was studied in 22 permanent plots at two sites over five years. A seed sowing experiment was also performed at each site. The life‐cycle of P. media includes seedlings, juveniles, small vegetative rosettes, large vegetative rosettes and flowering rosettes. The population growth rates (λ‐values) were negative for both populations, with one exception: the first year transition matrix at one site. The projected life span for individuals surviving from seedlings to flowering rosettes varied between 19.6 yr and 227.8 yr. Elasticity analysis showed that remaining in the large rosette stages, both vegetative and flowering, was the most important factor influencing population growth rate. LTRE analysis gave similar results, indicating that spatial and temporal variation have similar effects on the population growth rate. The expected time to extinction in populations with an initial size of between 100 and 1000 individuals varied between 60 and 200 yr. The seed sowing experiment showed that seedling emergence was enhanced by both seed addition and disturbance, suggesting that recruitment is limited by seed and microsite availability. Recruitment was not found to have much impact on population growth rate. However, long‐term population maintenance may depend on occasional small‐scale disturbances that enhance pulses of recruitment. Fragmented landscape is likely to effect plant populations including rare and endangered species as well as more common species which have limited dispersal mechanisms.     

Modeling vital rates improves estimation of population projection matrices

Population projection matrices are commonly used by ecologists and managers to analyze the dynamics of stage-structured populations. Building projection matrices from data requires estimating transition rates among stages, a task that often entails estimating many parameters with few data. Consequently, large sampling variability in the estimated transition rates increases the uncertainty in the estimated matrix and quantities derived from it, such as the population multiplication rate and sensitivities of matrix elements. Here, we propose a strategy to avoid overparameterized matrix models. This strategy involves fitting models to the vital rates that determine matrix elements, evaluating both these models and ones that estimate matrix elements individually with model selection via information criteria, and averaging competing models with multimodel averaging. We illustrate this idea with data from a population of Silene acaulis (Caryophyllaceae), and conduct a simulation to investigate the statistical properties of the matrices estimated in this way. The simulation shows that compared with estimating matrix elements individually, building population projection matrices by fitting and averaging models of vital-rate estimates can reduce the statistical error in the population projection matrix and quantities derived from it.     

Yearly variation in recruitment and its effect on population dynamics inYoldia notabilis (Mollusca: Bivalvia), analyzed using projection matrix model

Long-term variation in recruitment was estimated by constructing projection matrices for a marine bivalve, Yoldia notabilis, at two stations in Otsuchi Bay, northeastern Japan, and the effects of its variation on population dynamics were examined using a simple matrix model. The matrix model was developed from the Leslie matrix, in which the population growth rate λ was expressed as a function of recruitment rate r₀. The equilibrium recruitment rate r_s, or the recruitment rate required to maintain population at constant size (λ=1), was expressed by the reciprocal of the reproductive value of a newly recruited individual. The estimates of r_s for the field population were lower at the shallower station than at the deeper station, reflecting higher survivorship and fecundity. Past recruitment rate estimated both by the field samplings for 3 years and by the back-calculation from the current age structure for over 10 years showed large yearly variation, ranging between 0 and 58.6×10⁻⁴. The estimates were larger than r_s, and hence, large enough to increase population size (λ>1) only in approximately one-third of the estimated years. This suggests that the population has been maintained by occasional successful recruitment occurring once every few years.     

Spatial data replacing temporal data in population viability analyses: An empirical investigation for plants

In conservation management, there is an urgent need for estimates of population viability and for knowledge of the contributions of different life-history stages to population growth rates. Collection of long-term demographic data from a study population is time-consuming and may considerably delay the start of proper management actions. We examined the possibility of replacing a long-term temporal data set (demographic data from several years within a population) with a short-term spatial data set (demographic data from different populations for the same subset of two continuous years) for stochastic estimates of population viability. Using matrix population models for ten perennial plant species, we found that the matrix elements of spatial data sets often deviated from those of temporal data sets and that matrix elements generally varied more spatially than temporally. The appropriateness of replacing temporal data with spatial data depended on the subset of years and populations used to estimate stochastic population growth rates (log λ_s). Still, the precision of log λ_s estimates measured as variation in the yearly change of logarithmic population size rarely differed significantly between the spatial and temporal data sets. Since a spatiotemporal comparison of matrix elements and their variation cannot be used to assess whether spatial and temporal data sets are interchangeable, we recommend further research on the topic.     

Response of population size to changing vital rates in random environments

Population size and population growth rate respond to changes in vital rates like survival and fertility. In deterministic environments change in population growth rate alone determines change in population size. In random environments, population size at any time t is a random variable so that change in population size obeys a probability distribution. We analytically show that, in a density-independent population, the proportional change in population size with respect to a small proportional change in a vital rate has an asymptotic normal distribution. Its mean grows linearly at a rate equal to the elasticity of the long-term stochastic growth rate λ _S while the standard deviation scales as $\sqrt t$ . Consequently, a vital rate with a larger elasticity of λ _S may produce a larger mean change in population size compared to one with a smaller elasticity of λ _S. But a given percentage change in population size may be more likely when the vital rate with smaller elasticity is perturbed. Hence, the response of population size to perturbation of a vital rate depends not only on the elasticity of the population growth rate but also on the variance in change in population size. Our results provide a formula to calculate the probability that population size changes by a given percentage that works well even for short time periods.