Ability of matrix models to explain the past and predict the future of plant populations

The shifting importance of abiotic and biotic factors across the life cycles of wild pollinators

Organisms living in seasonal environments are exposed to different environmental conditions as they transition from one life stage to the next across their life cycle. How different life stages respond to these varying conditions, and the extent to which different life stages are linked, are fundamental components of the ecology of an organism. Nevertheless, the influence of abiotic and biotic factors on different parts of an organism's life cycle is often not accounted for, which limits our understanding of the ecological consequences of environmental change. We investigated the relative importance of climate conditions, food availability, and previous life-stage abundance in an assemblage of seven wild bumble bee species, asking: how do these three factors directly influence bee abundance at each life stage? To do so, we used a 7-year dataset where we monitored climate conditions, floral resources, and abundances of bees in each life stage across the active colony life cycle in a highly seasonal subalpine ecosystem in the Colorado Rocky Mountains, USA. Bee abundance at different life stages responded to abiotic and biotic conditions in a broadly consistent manner across the seven species: the survival and recruitment stage of the life cycle (overwintered queens) responded negatively to longer winters; the growth stage (workers) responded positively to floral resource availability; and the reproductive stage (males) was positively related to the abundance of the previous life stage (workers). Most species also exhibited some idiosyncratic responses. Our long-term examination of annual bumble bees reveals a general set of responses in the abundance of each life stage to climate conditions, floral resource availability, and previous life stage. Across species, these three factors each directly influenced a distinct life stage, illustrating how their relative importance can shift throughout the life cycle. The life-cycle approach that we have taken highlights that important details about demography can be overlooked without considering life-stage-specific responses. Ultimately, it is these life-stage-specific responses that shape population outcomes, not only for animal pollinators but also for many organisms living in seasonal environments.

Six-Year Demographic Study of the Terrestrial Orchid, Crepidium acuminatum: Implications for Conservation

Studies on population dynamics are helpful for understanding the factors determining population development and predicting the effects of disturbances, such as harvesting of plant species. In an investigation of the demography of a terrestrial medicinal orchid known as Crepidium acuminatum, the effects of harvesting on its population dynamics were recorded. Data on recruitment, growth and survival were collected in three populations of C. acuminatum over a 6-year period (2012–2017) in central Nepal. A matrix modeling method was used to determine the effect of different harvesting regimes on the population growth and survival of this species. Population growth rates (λ) of unharvested populations were relatively similar and stable in different years of the study. Harvesting significantly reduced λ. The results of this study indicate that the sustainable survival of a population that is subject to harvesting can only occur when it is either selective (only flowering individuals or only small amounts of vegetative individuals) or rotational (once every 3–5 or more years). This study demonstrates the necessity of using a sustainable method when harvesting natural populations. Our results are useful for developing efficient management strategies for this species. As each species has a different biology, similar studies are needed for other rare and/or economically important species in the Himalayan region and in other understudied parts of the world.

Comparing demography inferred from age vs. stage in a perennial plant

Life history theories analyze and predict variation in vital rates, such as survival and reproduction, based on age. The age-from-stage method to derive age-specific vital rates from stage data was developed because age-specific data are rarely obtained for plants. Age-specific vital rates derived by this method might underestimate effects of age on vital rates, because the models assume that vital rates do not vary within stage classes. Consequently, population models and life history summaries relying on these vital rates could be biased against detecting senescence. Here, we perform a comparative study of methods to estimate age-specific vital rates using monitoring data with known age and stage. We derived age-, stage-, and age-and-stage-specific vital rates with demographic data from a long-lived perennial, Silene spaldingii. Then, we derived three age-specific population matrix models (age, age-from-stage, and age-and-stage). For each model, we derived life history summaries commonly used in ecology: population growth rate, net reproductive value, relative reproductive values, stable age distribution, generation time, and sensitivity and elasticity of population growth rate. Many vital rates depended on both age and stage in S. spaldingii. However, this species does not senesce; in fact, the number of flowers increased with age. As expected, the age-from-stage method was not able to accurately recreate the age dependence in some life history summaries, such as relative reproductive value. The age-from-stage model suggested faster reproductive dynamics in S. spaldingii than the models based on known age, i.e., plants started to reproduce earlier, and fertility remained constant thereafter, which may lead to biased predictions about evolutionary consequences of age-dependent life history traits. However, population growth rate, generation time, and net reproductive rate did not differ significantly among the models. Our study demonstrated that some metrics are robust to imprecision in model structure, while others are more sensitive. In spite of these biases, this case study provides another example of the diversity of aging patterns in plants. Age can be essential information when studying senescence in plants, but demographic metrics that were not about age per se were similar across model structures.

What processes must we understand to forecast regional-scale population dynamics?

An urgent challenge facing biologists is predicting the regional-scale population dynamics of species facing environmental change. Biologists suggest that we must move beyond predictions based on phenomenological models and instead base predictions on underlying processes. For example, population biologists, evolutionary biologists, community ecologists and ecophysiologists all argue that the respective processes they study are essential. Must our models include processes from all of these fields? We argue that answering this critical question is ultimately an empirical exercise requiring a substantial amount of data that have not been integrated for any system to date. To motivate and facilitate the necessary data collection and integration, we first review the potential importance of each mechanism for skilful prediction. We then develop a conceptual framework based on reaction norms, and propose a hierarchical Bayesian statistical framework to integrate processes affecting reaction norms at different scales. The ambitious research programme we advocate is rapidly becoming feasible due to novel collaborations, datasets and analytical tools.

Experimental migration upward in elevation is associated with strong selection on life history traits

One of the strongest biological impacts of climate change has been the movement of species poleward and upward in elevation. Yet, what is not clear is the extent to which the spatial distribution of locally adapted lineages and ecologically important traits may also shift with continued climate change. Here, we take advantage of a transplant experiment mimicking up-slope seed dispersal for a suite of ecologically diverse populations of yellow monkeyflower (Mimulus guttatus sensu lato) into a high-elevation common garden during an extreme drought period in the Sierra Nevada mountains, California, USA. We use a demographic approach to quantify fitness and test for selection on life history traits in local versus lower-elevation populations and in normal versus drought years to test the potential for up-slope migration and phenotypic selection to alter the distribution of key life history traits in montane environments. We find that lower-elevation populations tend to outperform local populations, confirming the potential for up-slope migration. Although selection generally favored some local montane traits, including larger flowers and larger stem size at flowering, drought conditions tended to select for earlier flowering typical of lower-elevation genotypes. Taken together, this suggests that monkeyflower lineages moving upward in elevation could experience selection for novel trait combinations, particularly under warmer and drier conditions that are predicted to occur with continued climate change.

How can we augment the few that remain? Using stable population dynamics to aid reintroduction planning of an iteroparous species

Restoration of depleted populations is an important method in biological conservation. Reintroduction strategies frequently aim to restore stable, increasing, self-sustaining populations. Knowledge of asymptotic system dynamics may provide advantage in selecting reintroduction strategies. We introduce interactive software that is designed to identify strategies for release of females that are immediately aligned with stable population dynamics from species represented by 2-, 3-, 4-, and 5-stage life history strategies. The software allows managers to input a matrix of interest, the desired number of breeding females, and the desired management timeline, and calls upon stable population theory to give release strategies that are in concert with both stable population status and the management goals. We demonstrate how the software can aid in assessing various strategies ahead of a hypothetical restoration. For the purpose of demonstration of the tool only, we use published vital rates of an ungulate species, but remark that the selection of species for demonstration is not central to the use of this tool. Adaption of this tool to real-life restorations of any 2-, 3-, 4-, or 5-stage iteroparous species may aid in understanding how to minimize undesirable recovery complications that may naturally arise from transient population dynamics. The software is freely available at: https//cwhl.vet.cornell.edu/tools/stapopd.

Landscape heterogeneity is key to forecasting outcomes of plant reintroduction

Conservation and restoration projects often involve starting new populations by introducing individuals into portions of their native or projected range. Such efforts can help meet many related goals, including habitat creation, ecosystem service provisioning, assisted migration, and the reintroduction of imperiled species following local extirpation. The outcomes of reintroduction efforts, however, are highly variable, with results ranging from local extinction to dramatic population growth; reasons for this variation remain unclear. Here, we ask whether population growth following plant reintroductions is governed by variation at two scales: the scale of individual habitat patches to which individuals are reintroduced, and larger among-landscape scales in which similar patches may be situated in landscapes that differ in matrix type, soil conditions, and other factors. Quantifying demographic variation at these two scales will help prioritize locations for introduction and, once introductions take place, forecast population growth. This work took place within a large-scale habitat fragmentation experiment, where individuals of two perennial forb species were reintroduced into eight replicate ~50-ha landscapes, each containing a set of five ~1-ha patches that varied in their degree of isolation (connected by habitat corridors or unconnected) and edge-to-area ratio. Using data on individual growth, survival, reproductive output, and recruitment collected one to two years after reintroduction, we developed models to forecast population growth, then compared forecasts to observed population sizes, three and six years later. Both the type of patch (connected and unconnected) and identity of the landscape to which individuals were reintroduced had effects on forecasted population growth rates, but only variation associated with landscape identity was an accurate predictor of subsequently observed population growth rates. Models that did not include landscape identity had minimal forecasting ability, revealing the key importance of variation at this scale for accurate prediction. Of the five demographic rates used to model population dynamics, seed production was the most important source of forecast error in population growth rates. Our results point to the importance of accounting for landscape-scale variation in demographic models and demonstrate how such models might assist with prioritizing particular landscapes for species reintroduction projects.

Effects of territorial status and life history on Sandhill Crane (Antigone canadensis) population dynamics in south-central Wisconsin, USA

Population growth rate in long-lived bird species is often most sensitive to changes in adult survival. Sandhill Cranes (Antigone canadensis (Linnaeus, 1758)) have long life spans, small broods, and delayed first reproduction. Only territorial adult Sandhill Cranes participate in breeding, and territory acquisition reflects the interplay between the availability of suitable territories and the variation in mortality of adult birds occupying those territories. We estimated vital rates of a population at equilibrium using long-term resightings data (2000–2014; n = 451 marked individuals) in a multistate mark–resight model and used a stage-structured projection matrix to assess how strongly territorial adult survival affects population growth rate. Elasticity analysis indicated territorial birds surviving and retaining territories had a 2.58 times greater impact on population growth compared with the next most important transition rate (survival of nonterritorial adults remaining nonterritorial). Knowing how changes in vital rates of various stage classes will differentially impact population growth rate allows for targeted management actions including encouraging growth in recovering populations, assessing opportunity for recreational harvest, or maintaining populations at a desired level. This study also highlights the value of collecting demographic data for all population segments, from which one can derive reproductive output or growth rate.

Effects of removing woody cover on long-term population dynamics of a rare annual plant (Agalinis auriculata): A study comparing remnant prairie and oldfield habitats

Worldwide, grasslands are becoming shrublands/forests. In North America, eastern red cedar (Juniperus virginiana) often colonizes prairies. Habitat management can focus on woody removal, but we often lack long-term data on whether removal leads to population recovery of herbaceous plants without seeding. We undertook a long-term study (17 years) of numbers of the rare annual plant Agalinis auriculata in a gridwork of 100 m2 plots in adjacent prairie and oldfield sites in Kansas, USA. We collected data before and after removal of Juniperus virginiana at the prairie. Plant population sizes were highly variable at both sites and over time. High numbers of plants in a plot 1 year were often followed by low numbers the following year, suggesting negative density-dependence. Plant numbers were lowest with extensive woody cover and with low precipitation. After woody plant removal, A. auriculata increased dramatically in abundance and occupancy in most years; increases were also seen at the oldfield, suggesting later survey years were overall more favorable. Synthesis and applications: Removal of woody plants led to increased numbers of a rare annual prairie plant, without seeding. Multiple years of data were essential for interpretation given extreme temporal variability in numbers. The largest prairie population was 7 years following tree removal, showing that positive effects of management can last this long. This species also fared well in oldfield habitat, suggesting restoration opportunities. Given that land managers are busy, time-efficient field methods and data analysis approaches such as ours offer advantages. In addition to general linear models, we suggest Rank Occupancy-Abundance Profiles (ROAPs), a simple-to-use data visualization and analysis method. Creation of ROAPs for sites before and after habitat management helps reveal the degree to which plant populations are responding to management with changes in local density, changes in occupancy, or both.

Inferring transient dynamics of human populations from matrix non-normality

In our increasingly unstable and unpredictable world, population dynamics rarely settle uniformly to long-term behaviour. However, projecting period-by-period through the preceding fluctuations is more data-intensive and analytically involved than evaluating at equilibrium. To efficiently model populations and best inform policy, we require pragmatic suggestions as to when it is necessary to incorporate short-term transient dynamics and their effect on eventual projected population size. To estimate this need for matrix population modelling, we adopt a linear algebraic quantity known as non-normality. Matrix non-normality is distinct from normality in the Gaussian sense, and indicates the amplificatory potential of the population projection matrix given a particular population vector. In this paper, we compare and contrast three well-regarded metrics of non-normality, which were calculated for over 1000 age-structured human population projection matrices from 42 European countries in the period 1960 to 2014. Non-normality increased over time, mirroring the indices of transient dynamics that peaked around the millennium. By standardising the matrices to focus on transient dynamics and not changes in the asymptotic growth rate, we show that the damping ratio is an uninformative predictor of whether a population is prone to transient booms or busts in its size. These analyses suggest that population ecology approaches to inferring transient dynamics have too often relied on suboptimal analytical tools focussed on an initial population vector rather than the capacity of the life cycle to amplify or dampen transient fluctuations. Finally, we introduce the engineering technique of pseudospectra analysis to population ecology, which, like matrix non-normality, provides a more complete description of the transient fluctuations than the damping ratio. Pseudospectra analysis could further support non-normality assessment to enable a greater understanding of when we might expect transient phases to impact eventual population dynamics.

Measurement error of state variables creates substantial bias in results of demographic population models

Integral projection and matrix population models are commonly used in ecological and conservation studies to assess the health and extinction risk of populations. These models use one (or more) measurable state variable(s), such as size or age, to predict individual performance, which, ideally, is the sole determinant of an individual's expected fate. However, even if ecologists successfully identify and measure the observable state variable(s) that best predicts individual fate, we are rarely, if ever, able to perfectly measure state for many species, especially those with size structure, where total plant biomass or starch stores, for example, may be the best predictors of fate. Here, we used a series of simulations to test how this imperfect quantification of actual state ("measurement error") leads to inaccurate prediction of state-dependent fates and influences the predictions of structured population models. We simulated 10 yr of best practice field data collection using known vital rate functions and incorporated measurement error of different magnitudes and types (completely random, temporal, and individual based) for two size-structured life histories. We found that even for conservative error rates, most types of measurement error increased the median predicted population growth rate by 1-2% growth per year. However, the magnitude of this error differed substantially with life history strategy and error type, with some scenarios resulting in >8% median overestimation of population growth rate. This effect arises largely from the well-known econometrics problem of "regression dilution" (overestimation of the intercept and underestimation of the slope of a regression when the predictor variable is measured with error), which in our simulations typically results in overly optimistic predictions of small or young individuals' vital rates. Our results suggest that the problem of measurement error for state variables, present in many demographic studies but virtually unacknowledged in the ecological literature, may lead to substantial misestimation of population behavior, resulting in erroneous inferences about not only growth, but also extinction risk and other aspects of population dynamics.

Time to cut: population models reveal how to mow invasive common ragweed cost-effectively

Roadsides are an important habitat for invasive common ragweed, Ambrosiaartemisiifolia L., by facilitating seed dispersal. Reducing the size of roadside populations is therefore essential for confining this highly allergenic species. Here, we aim to determine the cost-effectiveness of mowing regimes varying in frequency and timing, by analysing population-level effects and underlying demographic processes. We constructed population models of A.artemisiifolia parameterised by demographic data for four unmanaged reference populations across Europe in two years. We integrated the effects of four experimental mowing regimes along Austrian road sides on plant performance traits of five years and experimental data on seed viability after cutting. All four experimental regimes reduced the projected intrinsic population growth rates (r) compared to the unmanaged controls by reducing plant height and seed viability, thereby counteracting increased size-dependent fecundity. The prevailing 2-cut regime in Austria (cutting during vegetative growth, here in June and just before seed ripening, here in September) performed least well and the reduction in r was mainly due to reduced seed viability after the second cut. The efficacy of the two best experimental regimes (alternative schemes for 2 or 3 cuts) was mainly due to cutting just before female flowering (here in August) by decreasing final adult plant height dramatically and thereby reducing seed numbers. Patterns were consistent across reference populations and years. Whether regimes reduced r below replacement level, however, varied per population, year and the survival rate of the seeds in the soil bank. Our model allowed projecting effects of five theoretical mowing regimes with untested combinations of cuts on r. By plotting r-cost relationships for all regimes, we identified the most cost-effective schemes for each cutting frequency (1–3 cuts). They all included the cut just before female flowering, highlighting the importance of cutting at this moment (here in August). Our work features i) the suitability of a modelling approach for the demography of an annual species with a seed bank, ii) the importance of seed viability in assessing mowing effects, iii) the use of population models in designing cost-effective mowing regimes.

Weak interspecific interactions in a sagebrush steppe? Conflicting evidence from observations and experiments

Stable coexistence requires intraspecific limitations to be stronger than interspecific limitations. The greater the difference between intra- and interspecific limitations, the more stable the coexistence, and the weaker the competitive release any species should experience following removal of competitors. We conducted a removal experiment to test whether a previously estimated model, showing surprisingly weak interspecific competition for four dominant species in a sagebrush steppe, accurately predicts competitive release. Our treatments were (1) removal of all perennial grasses and (2) removal of the dominant shrub, Artemisia tripartita. We regressed survival, growth, and recruitment on the locations, sizes, and species identities of neighboring plants, along with an indicator variable for removal treatment. If our "baseline" regression model, which accounts for local plant-plant interactions, accurately explains the observed responses to removals, then the removal coefficient should be non-significant. For survival, the removal coefficients were never significantly different from zero, and only A. tripartita showed a (negative) response to removals at the recruitment stage. For growth, the removal treatment effect was significant and positive for two species, Poa secunda and Pseudoroegneria spicata, indicating that the baseline model underestimated interspecific competition. For all three grass species, population models based on the vital rate regressions that included removal effects projected 1.4- to 3-fold increases in equilibrium population size relative to the baseline model (no removal effects). However, we found no evidence of higher response to removal in quadrats with higher pretreatment cover of A. tripartita, or by plants experiencing higher pre-treatment crowding by A. tripartita, raising questions about the mechanisms driving the positive response to removal. While our results show the value of combining observations with a simple removal experiment, more tightly controlled experiments focused on underlying mechanisms may be required to conclusively validate or reject predictions from phenomenological models.

Time-lagged effects of weather on plant demography: drought and Astragalus scaphoides

Temperature and precipitation determine the conditions where plant species can occur. Despite their significance, to date, surprisingly few demographic field studies have considered the effects of abiotic drivers. This is problematic because anticipating the effect of global climate change on plant population viability requires understanding how weather variables affect population dynamics. One possible reason for omitting the effect of weather variables in demographic studies is the difficulty in detecting tight associations between vital rates and environmental drivers. In this paper, we applied Functional Linear Models (FLMs) to long-term demographic data of the perennial wildflower, Astragalus scaphoides, and explored sensitivity of the results to reduced amounts of data. We compared models of the effect of average temperature, total precipitation, or an integrated measure of drought intensity (standardized precipitation evapotranspiration index, SPEI), on plant vital rates. We found that transitions to flowering and recruitment in year t were highest if winter/spring of year t was wet (positive effect of SPEI). Counterintuitively, if the preceding spring of year t - 1 was wet, flowering probabilities were decreased (negative effect of SPEI). Survival of vegetative plants from t - 1 to t was also negatively affected by wet weather in the spring of year t - 1 and, for large plants, even wet weather in the spring of t - 2 had a negative effect. We assessed the integrated effect of all vital rates on life history performance by fitting FLMs to the asymptotic growth rate, log(λt). Log(λt) was highest if dry conditions in year t - 1 were followed by wet conditions in the year t. Overall, the positive effects of wet years exceeded their negative effects, suggesting that increasing frequency of drought conditions would reduce population viability of A. scaphoides. The drought signal weakened when reducing the number of monitoring years. Substituting space for time did not recover the weather signal, probably because the weather variables varied little between sites. We detected the SPEI signal when the analysis included data from two sites monitored over 20 yr (2 × 20 observations), but not when analyzing data from four sites monitored over 10 yr (4 × 10 observations).

Less favourable climates constrain demographic strategies in plants

Correlative species distribution models are based on the observed relationship between species’ occurrence and macroclimate or other environmental variables. In climates predicted less favourable populations are expected to decline, and in favourable climates they are expected to persist. However, little comparative empirical support exists for a relationship between predicted climate suitability and population performance. We found that the performance of 93 populations of 34 plant species worldwide – as measured by in situ population growth rate, its temporal variation and extinction risk – was not correlated with climate suitability. However, correlations of demographic processes underpinning population performance with climate suitability indicated both resistance and vulnerability pathways of population responses to climate: in less suitable climates, plants experienced greater retrogression (resistance pathway) and greater variability in some demographic rates (vulnerability pathway). While a range of demographic strategies occur within species’ climatic niches, demographic strategies are more constrained in climates predicted to be less suitable.

Conservation implications of physiological carry-over effects in bats recovering from white-nose syndrome

Although it is well documented that infectious diseases can pose threats to biodiversity, the potential long-term consequences of pathogen exposure on individual fitness and its effects on population viability have rarely been studied. We tested the hypothesis that pathogen exposure causes physiological carry-over effects with a pathogen that is uniquely suited to this question because the infection period is specific and time limited. The fungus Pseudogymnoascus destructans causes white-nose syndrome (WNS) in hibernating bats, which either die due to the infection while hibernating or recover following emergence from hibernation. The fungus infects all exposed individuals in an overwintering site simultaneously, and bats that survive infection during hibernation clear the pathogen within a few weeks following emergence. We quantified chronic stress during the active season, when bats are not infected, by measuring cortisol in bat claws. Free-ranging Myotis lucifugus who survived previous exposure to P. destructans had significantly higher levels of claw cortisol than naïve individuals. Thus, cryptic physiological carry-over effects of pathogen exposure may persist in asymptomatic, recovered individuals. If these effects result in reduced survival or reproductive success, they could also affect population viability and even act as a third stream in the extinction vortex. For example, significant increases in chronic stress, such as those indicated here, are correlated with reduced reproductive success in a number of species. Future research should directly explore the link between pathogen exposure and the viability of apparently recovered populations to improve understanding of the true impacts of infectious diseases on threatened populations.

Implications of different population model structures for management of threatened plants

Population viability analysis (PVA) is a reliable tool for ranking management options for a range of species despite parameter uncertainty. No one has yet investigated whether this holds true for model uncertainty for species with complex life histories and for responses to multiple threats. We tested whether a range of model structures yielded similar rankings of management and threat scenarios for 2 plant species with complex postfire responses. We examined 2 contrasting species from different plant functional types: an obligate seeding shrub and a facultative resprouting shrub. We exposed each to altered fire regimes and an additional, species-specific threat. Long-term demographic data sets were used to construct an individual-based model (IBM), a complex stage-based model, and a simple matrix model that subsumes all life stages into 2 or 3 stages. Agreement across models was good under some scenarios and poor under others. Results from the simple and complex matrix models were more similar to each other than to the IBM. Results were robust across models when dominant threats are considered but were less so for smaller effects. Robustness also broke down as the scenarios deviated from baseline conditions, likely the result of a number of factors related to the complexity of the species' life history and how it was represented in a model. Although PVA can be an invaluable tool for integrating data and understanding species' responses to threats and management strategies, this is best achieved in the context of decision support for adaptive management alongside multiple lines of evidence and expert critique of model construction and output.

Climate change both facilitates and inhibits invasive plant ranges in New England

Forecasting ecological responses to climate change, invasion, and their interaction must rely on understanding underlying mechanisms. However, such forecasts require extrapolation into new locations and environments. We linked demography and environment using experimental biogeography to forecast invasive and native species' potential ranges under present and future climate in New England, United States to overcome issues of extrapolation in novel environments. We studied two potentially nonequilibrium invasive plants' distributions, Alliaria petiolata (garlic mustard) and Berberis thunbergii (Japanese barberry), each paired with their native ecological analogs to better understand demographic drivers of invasions. Our models predict that climate change will considerably reduce establishment of a currently prolific invader (A. petiolata) throughout New England driven by poor demographic performance in warmer climates. In contrast, invasion of B. thunbergii will be facilitated because of higher growth and germination in warmer climates, with higher likelihood to establish farther north and in closed canopy habitats in the south. Invasion success is in high fecundity for both invasive species and demographic compensation for Apetiolata relative to native analogs. For A. petiolata, simulations suggest that eradication efforts would require unrealistic efficiency; hence, management should focus on inhibiting spread into colder, currently unoccupied areas, understanding source-sink dynamics, and understanding community dynamics should A. petiolata (which is allelopathic) decline. Our results-based on considerable differences with correlative occurrence models typically used for such biogeographic forecasts-suggest the urgency of incorporating mechanism into range forecasting and invasion management to understand how climate change may alter current invasion patterns.

Minimum area requirements for an at-risk butterfly based on movement and demography

Determining the minimum area required to sustain populations has a long history in theoretical and conservation biology. Correlative approaches are often used to estimate minimum area requirements (MARs) based on relationships between area and the population size required for persistence or between species' traits and distribution patterns across landscapes. Mechanistic approaches to estimating MAR facilitate prediction across space and time but are few. We used a mechanistic MAR model to determine the critical minimum patch size (CMP) for the Baltimore checkerspot butterfly (Euphydryas phaeton), a locally abundant species in decline along its southern range, and sister to several federally listed species. Our CMP is based on principles of diffusion, where individuals in smaller patches encounter edges and leave with higher probability than those in larger patches, potentially before reproducing. We estimated a CMP for the Baltimore checkerspot of 0.7-1.5 ha, in accordance with trait-based MAR estimates. The diffusion rate on which we based this CMP was broadly similar when estimated at the landscape scale (comparing flight path vs. capture-mark-recapture data), and the estimated population growth rate was consistent with observed site trends. Our mechanistic approach to estimating MAR is appropriate for species whose movement follows a correlated random walk and may be useful where landscape-scale distributions are difficult to assess, but demographic and movement data are obtainable from a single site or the literature. Just as simple estimates of lambda are often used to assess population viability, the principles of diffusion and CMP could provide a starting place for estimating MAR for conservation.

When stable-stage equilibrium is unlikely: integrating transient population dynamics improves asymptotic methods

BACKGROUND AND AIMS

Evaluation of population projection matrices (PPMs) that are focused on asymptotically based properties of populations is a commonly used approach to evaluate projected dynamics of managed populations. Recently, a set of tools for evaluating the properties of transient dynamics has been expanded to evaluate PPMs and to consider the dynamics of populations prior to attaining the stable-stage distribution, a state that may never be achieved in disturbed or otherwise ephemeral habitats or persistently small populations. This study re-evaluates data for a tropical orchid and examines the value of including such analyses in an integrative approach.

METHODS

Six small populations of Lepanthes rubripetala were used as a model system and the R software package popdemo was used to produce estimates of the indices for the asymptotic growth rate (lambda), sensitivities, reactivity, first-time step attenuation, maximum amplification, maximum attenuation, maximal inertia and maximal attenuation. The response in lambda to perturbations of demographic parameters using transfer functions and multiple perturbations on growth, stasis and fecundity were also determined. The results were compared with previously published asymptotic indices.

KEY RESULTS

It was found that combining asymptotic and transient dynamics expands the understanding of possible population changes. Comparison of the predicted density from reactivity and first-time step attenuation with the observed change in population size in two orchid populations showed that the observed density was within the predicted range. However, transfer function analysis suggests that the traditional approach of measuring perturbation of growth rates and persistence (inertia) may be misleading and is likely to result in erroneous management decisions.

CONCLUSIONS

Based on the results, an integrative approach is recommended using traditional PPMs (asymptotic processes) with an evaluation of the diversity of dynamics that may arise when populations are not at a stable-stage distribution (transient processes). This method is preferable for designing rapid and efficient interventions after disturbances, and for developing strategies to establish new populations.