Population Projection Matrices Research Articles

Variety is the spice of life: nongenetic variation in life histories influences population growth and evolvability.

Individual vital rates are key determinants of lifetime reproductive success, and variability in these rates shapes population dynamics. Previous studies have found that this vital rate hetero- geneity can influence demographic properties including population growth rates, however, the explicit effects of the amount of variation within and the covariance between vital rates that can also vary throughout the lifespan on population growth remains unknown. Here, we explore the analytical consequences of nongenetic heterogeneity on long-term population growth rates and rates of evolution by modifying traditional age-structured population projection matrices to incorporate variation among individual vital rates. The model allows vital rates to be permanent throughout life ("fixed condition") or to change over the lifespan ("dynamic condition"). We reduce the complexity associated with adding individual heterogeneity to age-structured models through a novel application of matrix collapsing ("phenotypic collapsing"), showing how to col- lapse in a manner that preserves the asymptotic and transient dynamics of the original matrix. The main conclusion is that nongenetic individual heterogeneity can strongly impact the long-term growth rate and rates of evolution. The magnitude and sign of this impact depends heavily on how the heterogeneity covaries across the lifespan of an organism. Our results emphasize that nongenetic variation cannot simply be viewed as random noise, but rather that it has consistent, predictable effects on fitness and evolvability.

Balancing: A solution to our distorted indices of transient dynamics

AbstractBecause populations are at the mercy of random disturbances large and small, they rarely, if ever, converge on predicted long‐term behaviors. Therefore, when employing matrix population models, ecologists study the dynamics of populations that depart from stable distributions. Necessary for such studies are indices of transient dynamics that measure the size of short‐term population fluctuations. These indices advance our understanding of population dynamics by revealing that population growth rate in a single timestep can far exceed the stable population growth rate. Despite their value, indices of transient behavior possess two major shortcomings: they are scale dependent and easily distorted by outsized population classes. Distortion occurs whenever immature classes, due to their sheer size, carry greater weight in the calculation of population size than mature classes. Beluga sturgeon (Huso huso), for example, have an immature age class (eggs) that is several orders of magnitude larger than its mature age classes. To remove the undue influence of outsized classes, I use balancing, which rescales classes by the stable population distribution and makes the indices of transient dynamics scale invariant. I apply balancing to 1800 population projection matrices for various species across the Animal Kingdom, using reactivity and the Henrici metric of non‐normality as indices of transient dynamics. I found that balancing profoundly changes the picture of which populations have the greatest or least potential transient dynamics. Using a population projection matrix for northern pike (Esox lucius), I demonstrate how balancing influences pseudospectra contour plots that are used to infer transient dynamics.

The abundance and persistence of Caprinae populations

Stable or growing populations may go extinct when their sizes cannot withstand large swings in temporal variation and stochastic forces. Hence, the minimum abundance threshold defining when populations can persist without human intervention forms a key conservation parameter. We identify this threshold for many populations of Caprinae, typically threatened species lacking demographic data. Doing so helps triage conservation and management actions for threatened or harvested populations. Methodologically, we used population projection matrices and simulations, with starting abundance, recruitment, and adult female survival predicting future abundance, growth rate (λ), and population trend. We incorporated mean demographic rates representative of Caprinae populations and corresponding variances from desert bighorn sheep (Ovis canadensis nelsoni), as a proxy for Caprinae sharing similar life histories. We found a population’s minimum abundance resulting in ≤ 0.01 chance of quasi-extinction (QE; population ≤ 5 adult females) in 10 years and ≤ 0.10 QE in 30 years as 50 adult females, or 70 were translocation (removals) pursued. Discovering the threshold required 3 demographic parameters. We show, however, that monitoring populations’ relationships to this threshold requires only abundance and recruitment data. This applied approach avoids the logistical and cost hurdles in measuring female survival, making assays of population persistence more practical.

Demographic responses of an insular elephant population to removal as a management intervention

AbstractDisturbances that change population structure may evoke transient dynamics that can be assessed within a demographic resilience framework. Conservation management interventions are conceptually disturbances that can be evaluated through such a framework to inform management actions and goals. The Main Camp in Addo Elephant National Park in South Africa presents a case study. Here management reduced the size of the elephant (Loxodonta africana) population by ~26%. We compared population growth, modelled trends, constructed life tables and parameterized population projection matrices from data collected before, during and after the interventions. The interventions reduced population size and density, but co‐occurring droughts may have reduced subsequent population growth and stage‐specific survival. Transient dynamics followed the interventions and droughts and were associated with an unstable stage structure. The effect of adult survival on modelled asymptotic growth (its elasticity) was greater than a change in fertility. However, lowered juvenile survival contributed most to changes in transient growth. Management plans for elephant populations should consider the length of transients induced by interventions and environmental disturbances such as droughts. Our approach can benefit the assessment of population responses of elephants to disturbances such as poaching and persistent droughts elsewhere in Africa.

Novel passive detection approach reveals low breeding season survival and apparent lactation cost in a critically endangered cave bat.

Capture-mark-recapture/resight (CMR) methods are used for survival-rate studies, yet are often limited by small sample sizes. Advances in passive integrated transponder (PIT) technology have enabled passive detection or ‘resight’ of marked individuals using large antennas with greater read-ranges than previously possible. We used passively-detected resight data and CMR models to study survival rates of the southern bent-winged bat Miniopterus orianae bassanii, a critically endangered, cave-dwelling bat. Over three years, we used PIT-tagging to monitor 2966 individuals at the species’ largest breeding aggregation, using daily detection data (> 1.6 million detections) to estimate seasonal survival probabilities, structured by age, sex and reproductive status, and parameterise population projection matrices. This has hitherto been impossible using traditional CMR methods due to disturbance risk and low recapture rates. Bats exhibited lowest apparent seasonal survival over summer and autumn, particularly for reproductive females in summer (when lactating) and juveniles in autumn (after weaning), and high survival in winter. Lowest survival rates coincided with severe drought in summer–autumn 2016, suggesting that dry conditions affect population viability. Under all likely demographic assumptions, population projection matrices suggested the population is in deterministic decline, requiring urgent action to reduce extinction risk. Passively-collected resight data can now be used in combination with CMR models to provide extensive, robust information for targeted wildlife population management.

Incorporating vital rates and harvest into stochastic population models to forecast elk population dynamics

AbstractThe dynamics of ungulate populations across variable ecosystems and management strategies demonstrate disparate trajectories such that some populations are overabundant, while other populations are subject to recovery efforts. Understanding how variation in vital rates such as pregnancy and survival integrate to shape the trajectories of populations is, therefore, helpful for informed management, particularly given that our understanding of the dynamics of harvested ungulate populations is often limited. Age‐related variation in vital rates among elk (Cervus canadensis) suggest that suitable population matrix models require age‐specific vital rates that can be logistically and analytically challenging to obtain. Our goals were to use a large, long‐term data set on elk and hierarchical Bayesian models to estimate age‐specific pregnancy and annual survival rates and their process variances, use stochastic population projection matrices to understand the effects of additional mortality from harvest on population dynamics, and identify the influence of different combinations of vital rates on population trajectories. We found that median age‐specific pregnancy rates increased with age from yearlings (0.52, 90% credible interval [CrI] = 0.37, 0.65) to a plateau among prime ages (e.g., 9‐year‐old: 0.91, 90% CrI = 0.87, 0.94), followed by a decline for the oldest ages (e.g., 19‐year‐old: 0.10, 90% CrI = 0.03, 0.28). Annual survival rates plateaued among prime‐aged animals (e.g., 9‐year‐old: 0.94, 90% CrI = 0.92, 0.96), and declined for the oldest‐ages (e.g., 19‐year‐old: 0.21, 90% CrI = 0.04, 0.56). We found higher process variation in pregnancy rates than survival rates; annual pregnancy rates for a 7‐year‐old varied from 0.82 (90% CrI = 0.67, 0.92) to 0.98 (90% CrI = 0.95, 0.99), and annual survival rates varied from 0.94 (90% CrI = 0.85, 0.96) to 0.96 (90% CrI = 0.93, 0.99). Simulated population trajectories indicated that additional mortality due to harvest resulted in a shift in the age structure towards younger animals with lower probabilities of pregnancy. When we held calf survival between 0.48 and 0.50 and specified constant pregnancy rates, changes in age structure alone resulted in variation of the recruitment of female calves from 0.20 to 0.16. We found that populations with a low mean value of calf survival (0.25) and no additional mortality due to harvest had marginal demographic performance ( = 1.02) and could sustain no additional mortality from harvest and still increase. In contrast, productive populations with a high mean value of calf survival (0.75) required high harvests to abate population growth (e.g., harvest rate = 0.20, = 0.94). Finally, we found a temporally lagged effect of harvest on age structure such that a shift towards younger animals could persist for multiple years following a reduction in harvest, suggesting that harvest may have multi‐year lagged depressive effects on population growth rates above and beyond the direct effects on survival rates. Our work highlights the importance of considering the effect of varying age‐structure on population dynamics, suggests minimum combinations of vital rates required for increasing or decreasing elk population growth rates to general management objectives, and provides the framework required for future management‐specific recommendations using stochastic population projection matrices.

“Realistic Choice of Annual Matrices Contracts the Range of λS Estimates” under Reproductive Uncertainty Too

Our study is devoted to a subject popular in the field of matrix population models, namely, estimating the stochastic growth rate, λS, a quantitative measure of long-term population viability, for a discrete-stage-structured population monitored during many years. “Reproductive uncertainty” refers to a feature inherent in the data and life cycle graph (LCG) when the LCG has more than one reproductive stage, but when the progeny cannot be associated to a parent stage in a unique way. Reproductive uncertainty complicates the procedure of λS estimation following the defining of λS from the limit of a sequence consisting of population projection matrices (PPMs) chosen randomly from a given set of annual PPMs. To construct a Markov chain that governs the choice of PPMs for a local population of Eritrichium caucasicum, an short-lived perennial alpine plant species, we have found a local weather index that is correlated with the variations in the annual PPMs, and we considered its long time series as a realization of the Markov chain that was to be constructed. Reproductive uncertainty has required a proper modification of how to restore the transition matrix from a long realization of the chain, and the restored matrix has been governing random choice in several series of Monte Carlo simulations of long-enough sequences. The resulting ranges of λS estimates turn out to be more narrow than those obtained by the popular i.i.d. methods of random choice (independent and identically distributed matrices); hence, we receive a more accurate and reliable forecast of population viability.

Quantifying patch-specific seed dispersal and local population dynamics to estimate population spread of an endangered plant species.

AimHabitat loss and fragmentation impose high extinction risk upon endangered plant species globally. For many endangered plant species, as the remnant habitats become smaller and more fragmented, it is vital to estimate the population spread rate of small patches in order to effectively manage and preserve them for potential future range expansion. However, population spread rate has rarely been quantified at the patch level to inform conservation strategies and management decisions. To close this gap, we quantify the patch‐specific seed dispersal and local population dynamics of Minuartia smejkalii, which is a critically endangered plant species endemic in the Czech Republic and is of urgent conservation concern.LocationŽelivka and Hrnčíře, Czechia.MethodsWe conducted demographic analyses using population projection matrices with long‐term demographic data and used an analytic mechanistic dispersal model to simulate seed dispersal. We then used information on local population dynamics and seed dispersal to estimate the population spread rate and compared the relative contributions of seed dispersal and population growth rate to the population spread rate.ResultsWe found that although both seed dispersal and population growth rate in M. smejkalii were critically limited, the population spread rate depended more strongly on the maximal dispersal distance than on the population growth rate.Main conclusionsWe recommend conservationists to largely increase the dispersal distance of M. smejkalii. Generally, efforts made to increase seed dispersal ability could largely raise efficiency and effectiveness of conservation actions for critically endangered plant species.

Population projections from holey matrices: Using prior information to estimate rare transition events

Population projection matrices are a common means for predicting short- and long-term population persistence for rare, threatened and endangered species. Data from such species can suffer from small sample sizes and consequently miss rare demographic events resulting in incomplete or biologically unrealistic life cycle trajectories. Matrices with missing values (zeros; e.g., no observation of seeds transitioning to seedlings) are often patched using prior information from the literature, other populations, time periods, other species, best guess estimates, or are sometimes even ignored. To alleviate this problem, we propose using a multinomial-Dirichlet model for parameterizing transitions and a Gamma for reproduction to patch missing values in these holey matrices. This formally integrates prior information within a Bayesian framework and explicitly includes the weight of the prior information on the posterior distributions. We show using two real data sets that the weight assigned to the prior information mainly influences the dispersion of the posteriors, the inclusion of priors results in irreducible and ergodic matrices, and more biologically realistic inferences can be made on the transition probabilities. Because the priors are explicitly stated, the results are reproducible and can be re-evaluated if alternative priors are available in the future.

Realistic Choice of Annual Matrices Contracts the Range of λS Estimates

In matrix population modeling the multi-year monitoring of a population structure results in a set of annual population projection matrices (PPMs), which gives rise to the stochastic growth rate λS, a quantitative measure of long-term population viability. This measure is usually found in the paradigm of population growth in a variable environment. The environment is represented by the set of PPMs, and λS ensues from a long sequence of PPMs chosen at random from the given set. because the known rules of random choice, such as the iid (independent and identically distributed) matrices, are generally artificial, the challenge is to find a more realistic rule. We achieve this with the a following a Markov chain that models, in a certain sense, the real variations in the environment. We develop a novel method to construct the ruling Markov chain from long-term weather data and to simulate, in a Monte Carlo mode, the long sequences of PPMs resulting in the estimates of λS. The stochastic nature of sequences causes the estimates to vary within some range, and we compare the range obtained by the “realistic choice” from 10 PPMs for a local population of a Red-Book species to those using the iid choice. As noted in the title of this paper, this realistic choice contracts the range of λS estimates, thus improving the estimation and confirming the Red-Book status of the species.

Seed bank as a persistent problem in matrix population models: From uncertainty to certain bounds

Errors in the construction of matrix population models may lead to erroneous conclusions from modeling case studies, and neglecting the seed bank as a stage in the stage-structured model is a kind of ‘persistent problem’ common to many models of plant species. The problem arises due to uncertainties in the seed-related parameters that cannot be reliably estimated from empirical data. We investigate the consequences that including a seed bank into the underlying life cycle graph may have on λ1, the dominant eigenvalue of the calibrated matrix in the “no-seeds” model. Vital rates of that model were calibrated on a time series of data of the 'identified individuals’ type gained in our former, 11-year case study on a local population of Androsace albana, a short-lived perennial inhabiting alpine heaths. The calibration has resulted in 10 successive population projection matrices expressed in rational numbers, with a variety of λ1s distant from 1 by various amounts in both directions. To include the seed bank, we propose an integer-valued formalism with the following three unknown S-related parameters: S(t), the number of dormant seeds able to germinate at the current year of observation, t; Sp(t), the number of seeds produced this year, and Sm(t), the total number of seeds lost this year for various reasons. These preserve the rational form of all the other vital rates and holding the calibration equations true in the integer numbers, too. Some observable traits of A. albana plants help establish certain finite ranges of the three S-related parameters, and they enable finding the ensuing ranges of model outcomes by merely enumerating all the feasible triples. In this way, we get answers to pertinent questions about the λ1 of the seed model vs. its “no-seeds” counterpart and give a mathematical explanation of what we have obtained. An important conclusion is that the seed bank can principally not change the population growth into decline, nor vice versa, within the feasible ranges of parameters.

An analysis of elasticity vector distribution specific to semelparous species using randomly generated population projection matrices and the COMPADRE Plant Matrix Database

The elasticity of population growth rate λ is a notable statistic in population projection matrix models and has been used by many empirical researchers. Silvertown and his collaborators published a paper in 1996 in which they mapped elasticity vectors of stasis, growth and fecundity for 84 plant species in a ternary plot and reported that the elasticity vector distribution of semelparous species (10 species) was located in the upper-left region of the ternary plot. To understand and clarify why the elasticity vectors of semelparous species were distributed in the upper-left region, we conducted three analyses. First, we used 68 matrices of semelparous species populations in the COMPADRE Plant Matrix Database and plotted their elasticity vectors in the ternary plot. Second, we constructed randomly generated population projection matrices for three archetypes, where several biological assumptions were made, and obtained their elasticity vector distributions. We showed that the high fecundity and/or immediate death after reproduction shifted the elasticity vector distribution to the upper-left region of the plot. Third, we examined the evolutionary change in the distribution using a population projection matrix model in which the trade-off between fecundity and adult survival was incorporated. The evolutionary trajectory derived from the trade-off model showed that the evolutionary consequence of semelparity was located in the upper-left more than was that of iteroparity in the ternary plot. Synthesizing the results derived from the three analyses, we concluded that the distinctive distribution of the elasticity vectors of semelparous species is the outcome of natural selection under the trade-off with low convexity, and the outcome of the resultant big-bang reproduction and immediate death after reproduction.

Analysis of a multitrait population projection matrix reveals the evolutionary and demographic effects of a life history trade-off

It is increasingly recognized that incorporating life history trade-offs into evolutionary demography models requires trade-offs to be decomposed into fixed (a.k.a genetic) and individual (a.k.a dynamic) components. This is fundamental in order to understand how trade-offs are related to fixed and dynamic components of individual heterogeneities and generate variance in individual trajectories. Therefore, embedding such trade-offs into population projection matrices usually requires three categories: a life-history determining trait (e.g., age or stage), a fixed trait incorporating the genetic trade-off, and a dynamic trait modeling the individual component. This has proved a complex exercise until the recent advent of Multitrait Population Projection Matrices (MPPMs).11MPPM: Multitrait (i.e., multi-category) Population Projection Matrix. Recent developments of Trait-Level Analysis (TLA)22TLA: Trait-Level Analysis, a toolbox for MPPMs developed by Coste et al. (2017). tools for MPPMs now allow us to study the demographic and evolutionary consequences of each component of a life history trade-off. Here, we illustrate this by constructing and analyzing an evolutionary demography model that implements both dynamic and fixed components of the costs of reproduction, the trade-off between current/early reproduction and future/later fitness. In particular, we explain and describe the use of the TLA to measure the effects of this trade-off on individual fitness. Here, we focus on the variance of lifetime reproductive success between models implementing the individual costs and asymptotically-equivalent matrices from which they are absent. This allows us to show that dynamic costs decrease that variance and more so for slow organisms. Therefore, accounting for this component of the costs, instead of classically focusing solely on fixed costs of reproduction, is paramount in order to correctly assess the relative importance of the “neutral” and “adaptive” components of individual heterogeneity.

Sex differences in migration and demography of a wide-ranging seabird, the northern gannet

Marine vertebrates show a diversity of migration strategies, including sex differences. This may lead to differential demography, but the consequences of such between-sex variation are little understood. Here, we studied the migration of known-sex northern gannets Morus bassanus—a partial migrant with females ~8% heavier than males. We used geolocators to determine wintering areas of 49 breeding adults (19 females and 30 males) from 2 colonies in the northeast Atlantic (Bass Rock and Grassholm, UK). We also tested for sex-specific survival probabilities using capture-mark-recapture methods (n = 72 individuals Bass Rock, n = 229 individuals Grassholm; 2010-2018) and applied sex-specific population projection matrices (PPMs) to quantify population-level effects. Tracked gannets wintered in a range of large marine ecosystems (LMEs): Canary Current LME (CCLME; 69%), Celtic-Biscay Shelf LME (16%), Iberian Coastal LME (8%), North Sea LME (4%) or Mediterranean LME (2%). Migratory destination differed between the sexes: 90% of females vs. 57% of males wintered in the CCLME. Survival was similar between the sexes at Bass Rock (mean ± 95% CI = 0.951 ± 0.053 and 0.956 ± 0.047 for females and males, respectively). At Grassholm, there was evidence of slight sex differences in breeder survival: females had lower annual survival (0.882 ± 0.040) than males (0.946 ± 0.026). At Bass Rock, PPMs with no sex effect best fitted the observed population increase (1994-2014). Sex-specific PPMs fitted the population estimates for Grassholm (1995-2015). Our results reveal that female gannets are more likely to travel further than males to winter in the CCLME. This difference is unlikely due to morphological differences, unlike in other bird species. However, the reason for slightly higher over-winter female mortality at Grassholm is unclear.

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.

Averaging the population projection matrices: Heuristics against uncertainty and nonexistence

In matrix population models, the process of population “projection” through a number of time steps is fundamentally multiplicative, hence the arithmetic mean of the consecutive matrices is of doubtful meaning, while the geometric mean quite corresponds to the multiplication principle. The geometric mean of positive numbers does not bear any problem, but that of matrices does. The “population projection matrices” (PPMs) are rather nonnegative than positive, with the allocation of non-zeros that is predetermined by the life cycle graph (LCG) reflecting the development biology of a given species, and this graph is principally incomplete. The average matrix A should logically have the same fixed pattern of zeros as those to be averaged, and this causes the averaging matrix equation to be overdetermined as a system of element-wise algebraic equations for the unknown positive elements. Therefore, the exact solution to the problem of pattern-geometric averaging does generally not exist, while the classical (least-squares) approximation leads to a significant error. My heuristic approach to finding a better approximate A for the PPMs in the form of L = T(transition) + F(fertility) is to solve the problem in a combined way: the pattern-geometric approximation for the T part and the exact arithmetic mean for F (as population recruitment is an additive process). As a result, the approximation error decreases drastically due to matrix T being always substochastic, while the combined, TF-averaging, method turns out efficient even under ‘reproductive uncertainty’ in data, i.e., for the whole families of feasible matrices F in the sum L = T + {F}. I illustrate the method of TF-averaging with 5 matrices L(t) calibrated for each pair of consecutive years from a 6-year period of observation in a case study of Eritrichium caucasicum, a short-lived perennial herbaceous species. The approximate TF-average enables gaining the ‘age-specific traits from stage-specific models’ (Caswell, 2001, p. 116) that are characteristic of the entire period, and I discuss other motivations/advantages for/of pattern-geometric means in matrix population models.

Trait level analysis of multitrait population projection matrices

In most matrix population projection models, individuals are characterized according to, usually, one or two traits such as age, stage, size or location. A broad theory of multitrait population projection matrices (MPPMs) incorporating larger number of traits was long held back by time and space computational complexity issues. As a consequence, no study has yet focused on the influence of the structure of traits describing a life-cycle on population dynamics and life-history evolution.We present here a novel vector-based MPPM building methodology that allows to computationally-efficiently model populations characterized by numerous traits with large distributions, and extend sensitivity analyses for these models. We then present a new method, the trait level analysis consisting in folding an MPPM on any of its traits to create a matrix with alternative trait structure (the number of traits and their characteristics) but similar asymptotic properties. Adding or removing one or several traits to/from the MPPM and analyzing the resulting changes in spectral properties, allows investigating the influence of the trait structure on the evolution of traits.We illustrate this by modeling a 3-trait (age, parity and fecundity) population designed to investigate the implications of parity–fertilitytrade-offs in a context of fecundity heterogeneity in humans. The trait level analysis, comparing models of the same population differing in trait structures, demonstrates that fertility selection gradients differ between cases with or without parity–fertility trade-offs. Moreover it shows that age-specific fertility has seemingly very different evolutionary significance depending on whether heterogeneity is accounted for. This is because trade-offs can vary strongly in strength and even direction depending on the trait structure used to model the population.

Demographic shifts related to mycoheterotrophy and their fitness impacts in two Cephalanthera species

Evolutionary losses of photosynthesis in terrestrial plants all originate in photosynthetic ancestors. The adaptive context under which this transition happens has remained elusive because of the rarity of plants in which both photosynthetic and non-photosynthetic forms exist as a polymorphism. Here, we report on demographic patterns in photosynthetic ("green") and nonphotosynthetic ("albino") individuals within populations of two such species, Cephalanthera damasonium and C. longifolia, which also acquire nutrition from their mycorrhizal hosts (partial mycoheterotrophy). We hypothesized that demographic shifts in albinos relative to greens would include compensatory patterns with respect to fitness, such that maladaptive changes to survival or reproduction would be adaptively countered by changes to other parameters, such as growth probabilities. We tracked individuals in two populations of C. damasonium for 3 yr, and in one population of C. longifolia for 14 yr. We then analyzed vital rates for both phenotypes using general linear mixed models (GLMMs) and multi-state capture mark-recapture models (CMR), and used these models to develop size-classified, function-based population projection matrices. We estimated fitness as the deterministic population growth rate (λ) for each phenotype, and explored the impact of shifts in demographic patterns to albinism via life table response experiments (LTREs). Mortality differed between greens and albinos, but not similarly across species. Albinos generally sprouted less than greens, and flowered more when small but less at other times. Albinos typically had a higher probability of fruiting, although their lower flower numbers yielded lower numbers of fruits overall. Fitness did not differ significantly among phenotypes. Thus, we did not find significant evidence that albinism is adaptive or maladaptive; however, if in fact it is the latter, then we did find evidence of incomplete compensation for declines in survival and reproduction from growth transitions, particularly to small flowering size classes in C. damasonium, and to large vegetative size classes in C. longifolia. These patterns indicate some support for the idea that albinism may lead to the speciation of mycoheterotrophic plants.

COMADRE: a global data base of animal demography.

Summary The open‐data scientific philosophy is being widely adopted and proving to promote considerable progress in ecology and evolution. Open‐data global data bases now exist on animal migration, species distribution, conservation status, etc. However, a gap exists for data on population dynamics spanning the rich diversity of the animal kingdom world‐wide. This information is fundamental to our understanding of the conditions that have shaped variation in animal life histories and their relationships with the environment, as well as the determinants of invasion and extinction.Matrix population models (MPMs) are among the most widely used demographic tools by animal ecologists. MPMs project population dynamics based on the reproduction, survival and development of individuals in a population over their life cycle. The outputs from MPMs have direct biological interpretations, facilitating comparisons among animal species as different as Caenorhabditis elegans, Loxodonta africana and Homo sapiens.Thousands of animal demographic records exist in the form of MPMs, but they are dispersed throughout the literature, rendering comparative analyses difficult. Here, we introduce the COMADRE Animal Matrix Database, an open‐data online repository, which in its version 1.0.0 contains data on 345 species world‐wide, from 402 studies with a total of 1625 population projection matrices. COMADRE also contains ancillary information (e.g. ecoregion, taxonomy, biogeography, etc.) that facilitates interpretation of the numerous demographic metrics that can be derived from its MPMs. We provide R code to some of these examples. Synthesis: We introduce the COMADRE Animal Matrix Database, a resource for animal demography. Its open‐data nature, together with its ancillary information, will facilitate comparative analysis, as will the growing availability of databases focusing on other aspects of the rich animal diversity, and tools to query and combine them. Through future frequent updates of COMADRE, and its integration with other online resources, we encourage animal ecologists to tackle global ecological and evolutionary questions with unprecedented sample size.

Assessing local population vulnerability with branching process models: an application to wind energy development

Quantifying the impact of anthropogenic development on local populations is important for conservation biology and wildlife management. However, these local populations are often subject to demographic stochasticity because of their small population size. Traditional modeling efforts such as population projection matrices do not consider this source of variation whereas individual‐based models, which include demographic stochasticity, are computationally intense and lack analytical tractability. One compromise between approaches is branching process models because they accommodate demographic stochasticity and are easily calculated. These models are known within some sub‐fields of probability and mathematical ecology but are not often applied in conservation biology and applied ecology. We applied branching process models to quantitatively compare and prioritize species locally vulnerable to the development of wind energy facilities. Specifically, we examined species vulnerability using branching process models for four representative species: A cave bat (a long‐lived, low fecundity species), a tree bat (short‐lived, moderate fecundity species), a grassland songbird (a short‐lived, high fecundity species), and an eagle (a long‐lived, slow maturation species). Wind turbine‐induced mortality has been observed for all of these species types, raising conservation concerns. We simulated different mortality rates from wind farms while calculating local extinction probabilities. The longer‐lived species types (e.g., cave bats and eagles) had much more pronounced transitions from low extinction risk to high extinction risk than short‐lived species types (e.g., tree bats and grassland songbirds). High‐offspring‐producing species types had a much greater variability in baseline risk of extinction than the lower‐offspring‐producing species types. Long‐lived species types may appear stable until a critical level of incidental mortality occurs. After this threshold, the risk of extirpation for a local population may rapidly increase with only minimal increases in wind mortality. Conservation biologists and wildlife managers may need to consider this mortality pattern when issuing take permits and developing monitoring protocols for wind facilities. We also describe how our branching process models may be generalized across a wider range of species for a larger assessment project and then describe how our methods may be applied to other stressors in addition to wind.