Inferring forest fate from demographic data: from vital rates to population dynamic models

As population-level patterns of interest in forests emerge from individual vital rates, modelling forest dynamics requires making the link between the scales at which data are collected (individual stems) and the scales at which questions are asked (e.g. populations and communities). Structured population models (e.g. integral projection models (IPMs)) are useful tools for linking vital rates to population dynamics. However, the application of such models to forest trees remains challenging owing to features of tree life cycles, such as slow growth, long lifespan and lack of data on crucial ontogenic stages. We developed a survival model that accounts for size-dependent mortality and a growth model that characterizes individual heterogeneity. We integrated vital rate models into two types of population model; an analytically tractable form of IPM and an individual-based model (IBM) that is applied with stochastic simulations. We calculated longevities, passage times to, and occupancy time in, different life cycle stages, important metrics for understanding how demographic rates translate into patterns of forest turnover and carbon residence times. Here, we illustrate the methods for three tropical forest species with varying life-forms. Population dynamics from IPMs and IBMs matched a 34 year time series of data (albeit a snapshot of the life cycle for canopy trees) and highlight differences in life-history strategies between species. Specifically, the greater variation in growth rates within the two canopy species suggests an ability to respond to available resources, which in turn manifests as faster passage times and greater occupancy times in larger size classes. The framework presented here offers a novel and accessible approach to modelling the population dynamics of forest trees.

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.

Climate drivers and animal host use determine kelp performance over decadal scales in the kelp Pleurophycus gardneri (Laminariales, Phaeophyceae)

Primary producers respond to climate directly and indirectly due to effects on their consumers. In the temperate coastal ocean, the highly productive brown algae known as kelp have both strong climate and grazer linkages. We analyzed the demographic response of the kelp Pleurophycus gardneri over a 25-year span to determine the interaction between ocean climate indicators and invertebrate infestation rates. Pleurophycus hosts amphipod species that burrow in the stipe, increasing mortality. Although kelp performance is generally greater with more negative values of the Pacific Decadal Oscillation (PDO) and colder seawater temperatures, Pleurophycus showed the opposite pattern. When we compared the 1990s, a period of positive values for the PDO and warmer sea surface temperatures, with the following decade, a period characterized by negative PDO values, we documented a contradictory outcome for proxies of kelp fitness. In the 1990s, Pleurophycus unexpectedly showed greater longevity, faster growth, greater reproductive effort, and a trend toward decreased amphipod infestation compared with the 2006-2012 period. In contrast, the period from 2006 to 2012 showed opposite kelp performance patterns and with a trend toward greater amphipod infestation. Pleurophycus performance metrics suggest that some coastal primary producers will respond differently to climate drivers, particularly if they interact strongly with grazers.

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.

Implications of clonality for ageing research

Senescence, an organismal performance decline with age, has historically been considered a universal phenomenon by evolutionary biologists and zoologist. Yet, increasing fertility and survival with age are nothing new to plant ecologists, among whom it is common knowledge that senescence is not universal. Recently, these two realities have come into a confrontation, begging for the rephrasing of the classical question that has led ageing research for decades: “why do we senesce?” to a more practical “what are the mechanisms by which some organisms escape from senescence?” Plants are amenable to examining this question because of their rich repertoire of life history strategies. These include the existence of permanent seed banks, vegetative dormancy and ability to produce clones, among others. Here, I use a large number of high resolution demographic models from 181 species that reflect life history strategies and their trade-offs among herbaceous perennials, succulents and shrubs measured under field conditions worldwide to examine whether senescence rates of ramets from clonal plants differ from those of whole plants reproducing either strictly sexually, or with a combination of sexual and clonal mechanisms. Contrary to the initial expectation from the mutation accumulation theory of senescence, ramets of clonal plants were more likely to exhibit senescence than those species employing sexual reproduction. I discuss why these comparisons between ramets and genets are useful, as well as its implications and future directions for ageing research.

Modelling time to population extinction when individual reproduction is autocorrelated

In nature, individual reproductive success is seldom independent from year to year, due to factors such as reproductive costs and individual heterogeneity. However, population projection models that incorporate temporal autocorrelations in individual reproduction can be difficult to parameterise, particularly when data are sparse. We therefore examine whether such models are necessary to avoid biased estimates of stochastic population growth and extinction risk, by comparing output from a matrix population model that incorporates reproductive autocorrelations to output from a standard age-structured matrix model that does not. We use a range of parameterisations, including a case study using moose data, treating probabilities of switching reproductive class as either fixed or fluctuating. Expected time to extinction from the two models is found to differ by only small amounts (under 10%) for most parameterisations, indicating that explicitly accounting for individual reproductive autocorrelations is in most cases not necessary to avoid bias in extinction estimates.

Matrix models for size-structured populations: unrealistic fast growth or simply diffusion?

Matrix population models are widely used to study population dynamics but have been criticized because their outputs are sensitive to the dimension of the matrix (or, equivalently, to the class width). This sensitivity is concerning for the population growth rate (λ) because this is an intrinsic characteristic of the population that should not depend on the model specification. It has been suggested that the sensitivity of λ to matrix dimension was linked to the existence of fast pathways (i.e. the fraction of individuals that systematically move up a class), whose proportion increases when class width increases. We showed that for matrix population models with growth transition only from class i to class i + 1, λ was independent of the class width when the mortality and the recruitment rates were constant, irrespective of the growth rate. We also showed that if there were indeed fast pathways, there were also in about the same proportion slow pathways (i.e. the fraction of individuals that systematically remained in the same class), and that they jointly act as a diffusion process (where diffusion here is the movement in size of an individual whose size increments are random according to a normal distribution with mean zero). For 53 tree species from a tropical rain forest in the Central African Republic, the diffusion resulting from common matrix dimensions was much stronger than would be realistic. Yet, the sensitivity of λ to matrix dimension for a class width in the range 1-10 cm was small, much smaller than the sampling uncertainty on the value of λ. Moreover, λ could either increase or decrease when class width increased depending on the species. Overall, even if the class width should be kept small enough to limit diffusion, it had little impact on the estimate of λ for tree species.

A method for detecting positive growth autocorrelation without marking individuals

In most ecological studies, within-group variation is a nuisance that obscures patterns of interest and reduces statistical power. However, patterns of within-group variability often contain information about ecological processes. In particular, such patterns can be used to detect positive growth autocorrelation (consistent variation in growth rates among individuals in a cohort across time), even in samples of unmarked individuals. Previous methods for detecting autocorrelated growth required data from marked individuals. We propose a method that requires only estimates of within-cohort variance through time, using maximum likelihood methods to obtain point estimates and confidence intervals of the correlation parameter. We test our method on simulated data sets and determine the loss in statistical power due to the inability to identify individuals. We show how to accommodate nonlinear growth trajectories and test the effects of size-dependent mortality on our method's accuracy. The method can detect significant growth autocorrelation at moderate levels of autocorrelation with moderate-sized cohorts (for example, statistical power of 80% to detect growth autocorrelation ρ² = 0.5 in a cohort of 100 individuals measured on 16 occasions). We present a case study of growth in the red-eyed tree frog. Better quantification of the processes driving size variation will help ecologists improve predictions of population dynamics. This work will help researchers to detect growth autocorrelation in cases where marking is logistically infeasible or causes unacceptable decreases in the fitness of marked individuals.

Separating intrinsic and environmental contributions to growth and their population consequences

Among-individual heterogeneity in growth is a commonly observed phenomenon that has clear consequences for population and community dynamics yet has proved difficult to quantify in practice. In particular, observed among-individual variation in growth can be difficult to link to any given mechanism. Here, we develop a Bayesian state-space framework for modeling growth that bridges the complexity of bioenergetic models and the statistical simplicity of phenomenological growth models. The model allows for intrinsic individual variation in traits, a shared environment, process stochasticity, and measurement error. We apply the model to two populations of steelhead trout (Oncorhynchus mykiss) grown under common but temporally varying food conditions. Models allowing for individual variation match available data better than models that assume a single shared trait for all individuals. Estimated individual variation translated into a roughly twofold range in realized growth rates within populations. Comparisons between populations showed strong differences in trait means, trait variability, and responses to a shared environment. Together, individual- and population-level variation have substantial implications for variation in size and growth rates among and within populations. State-dependent life-history models predict that this variation can lead to differences in individual life-history expression, lifetime reproductive output, and population life-history diversity.

Estimating von Bertalanffy parameters with individual and environmental variations in growth

Variation among individuals is an ubiquitous feature of natural populations. However, the relative roles of intrinsic individual differences and stochastic processes in generating variation remain poorly understood. For somatic growth, identifying the contribution of individual and stochastic processes to observed variation in size has important implications both for basic and applied biology. Here we propose and develop methods for estimating individual variation in growth using size-at-age data. We modify the von Bertalanffy growth model to explicitly incorporate individual, environmental, and stochastic variation and provide analytic expressions for the mean and variance of length-at-age in populations. We use a Bayesian statistical model to estimate individual variation from length-at-age data and apply the model to simulated data to test its efficacy. Although a first step towards understanding individual variation, we demonstrate that estimating individual variation from observational samples is possible and provide a platform for future analytical and statistical developments.

Loop analysis for pathogens: niche partitioning in the transmission graph for pathogens of the North American tick Ixodes scapularis

In population biology, loop analysis is a method of decomposing a life cycle graph into life history pathways so as to compare the relative contributions of pathways to the population growth rate across species and populations. We apply loop analysis to the transmission graph of five pathogens known to infect the black-legged tick, Ixodes scapularis. In this context loops represent repeating chains of transmission that could maintain the pathogen. They hence represent completions of the life cycle, in much the same way as loops in a life cycle graph do for plants and animals. The loop analysis suggests the five pathogens fall into two distinct groups. Borellia burgdorferi, Babesia microti and Anaplasma phagocytophilum rely almost exclusively on a single loop representing transmission to susceptible larvae feeding on vertebrate hosts that were infected by nymphs. Borellia miyamotoi, in contrast, circulates among a separate set of host types and utilizes loops that are a mix of vertical transmission and horizontal transmission. For B. miyamotoi the main loop is from vertebrate hosts to susceptible nymphs, where the vertebrate hosts were infected by larvae that were infected from birth. The results for Powassan virus are similar to B. miyamotoi. The predicted impacts of the known variation in tick phenology between populations of I. scapularis in the Midwest and Northeast of the United States are hence markedly different for the two groups. All of these pathogens benefit, though, from synchronous activity of larvae and nymphs.

Do persistently fast-growing juveniles contribute disproportionately to population growth? A new analysis tool for matrix models and its application to rainforest trees

Plants and animals often exhibit strong and persistent growth variation among individuals within a species. Persistently fast-growing individuals have a higher chance of reaching reproductive size, do so at a younger age, and therefore contribute disproportionately to population growth (lambda). Here we introduce a new approach to quantify this "fast-growth effect." We propose using age-size-structured matrix models in which persistently fast and slow growers are distinguished as they occur in relatively young and old age classes for a given size category. Life-cycle pathways involving fast growth can then be identified, and their contribution to lambda is quantified through loop analysis. We applied this approach to an example species, the tropical rainforest tree Cedrela odorata, that shows persistent growth variation among individuals. Loop analysis showed that juvenile trees reaching the 10-cm diameter class at below-median age contributed twice as much to lambda as slow juvenile growers. Fast growth to larger-diameter categories also contributed disproportionately to lambda. The results were robust to changes in parameter values and life-history trade-offs. These results show that the fast-growth effect can be strong in long-lived species. Persistent growth differences among individuals should therefore be accommodated for in demographic models and life-history studies.

Survival against the odds: ontogenetic changes in selective pressure mediate growth-mortality trade-offs in a marine fish

For organisms with complex life cycles, variation among individuals in traits associated with survival in one life-history stage can strongly affect the performance in subsequent stages with important repercussions on population dynamics. To identify which individual attributes are the most influential in determining patterns of survival in a cohort of reef fish, we compared the characteristics of Pomacentrus amboinensis surviving early juvenile stages on the reef with those of the cohort from which they originated. Individuals were collected at hatching, the end of the planktonic phase, and two, three, four, six and eight weeks post-settlement. Information stored in the otoliths of individual fish revealed strong carry-over effects of larval condition at hatching on juvenile survival, weeks after settlement (i.e. smaller-is-better). Among the traits examined, planktonic growth history was, by far, the most influential and long-lasting trait associated with juvenile persistence in reef habitats. However, otolith increments suggested that larval growth rate may not be maintained during early juvenile life, when selective mortality swiftly reverses its direction. These changes in selective pressure may mediate growth-mortality trade-offs between predation and starvation risks during early juvenile life. Ontogenetic changes in the shape of selectivity may be a mechanism maintaining phenotypic variation in growth rate and size within a population.

Sensitivity of the Early Life Stages of Macroalgae from the Northern Hemisphere to Ultraviolet Radiation†

The reproductive cells of macroalgae are regarded as the life history stages most susceptible to various environmental stresses, including UV radiation (UVR). UVR is proposed to determine the upper depth distribution limit of macroalgae on the shore. These hypotheses were tested by UV-exposure experiments, using spores and young thalli of the eulittoral Rhodophyceae Mastocarpus stellatus and Chondrus crispus and various sublittoral brown macroalgae (Phaeophyceae) with different depth distribution from Helgoland (German Bight) and Spitsbergen (Arctic). In spores, the degree of UV-induced inhibition of photosynthesis is lower in eulittoral species and higher in sublittoral species. After UV stress, recovery of photosynthetic capacity is faster in eulittoral compared to sublittoral species. DNA damage is lowest while repair of DNA damage is highest in eulittoral compared to sublittoral species. When the negative impact of UVR prevails, spore germination is inhibited. This is observed in deep water kelp species whereas the same UVR doses do not inhibit germination of shallow water kelp species. A potential acclimation mechanism to increase UV tolerance of brown algal spores is the species-specific ability to increase the content of UV-absorbing phlorotannins in response to UV-exposure. Growth rates of young Mastocarpus and Chondrus gametophytes exposed to experimental doses of UVR are not affected while growth rates of all young kelp sporophytes exposed to UVR are significantly lowered. Furthermore, morphological UV damage in Laminaria ochroleuca includes tissue deformation, lesion, blistering and thickening of the meristematic part of the lamina. The sensitivity of young sporophytes to DNA damage is correlated with thallus thickness and their optical characteristics. Growth rate is an integrative parameter of all physiological processes in juvenile plants. UV inhibition of growth may affect the upper distribution depth limit of adult life history stages. Juveniles possess several mechanisms to minimize UVR damage and, hence, are less sensitive but at the expense of growth. The species-specific susceptibility of the early life stages of macroalgae to UVR plays an important role for the determination of zonation patterns and probably also for shaping up community structure.

An algorithm for a decomposition of weighted digraphs: with applications to life cycle analysis in ecology

In the analysis of organism life cycles in ecology, comparisons of life cycles between species or between different types of life cycles within species are frequently conducted. In matrix population models, partitioning of the elasticity matrix is used to quantify the separate contributions of different life cycles to the population growth rate. Such partition is equivalent to a decomposition of the life cycle graph of the population. A graph theoretic spanning tree method to carry out the decomposition was formalized by Wardle [Ecology 79(7), 2539-2549 (1998)]. However there are difficulties in realizing a suitable decomposition for complex life histories using the spanning-tree method. One of the problems is the occurrence of life cycles that contain contradictory directions that defy biological interpretation. We propose an algorithmic approach for decomposing a directed, weighted graph. The graph is to be decomposed into two parts. The first part is a set of simple cycles that contain no contradictory directions and that consist of edges of equal weight. The second part of the decomposition is a subgraph in which no such simple cycles are obtainable. When applied to life cycle analysis in ecology, the proposed method will guarantee a complete decomposition of the life cycle graph into individual life cycles containing no contradictory directions.