Academic Appointments

All Publications

  • How the demographic transition affects kinship networks: A formal demographic approach DEMOGRAPHIC RESEARCH Jiang, S., Zuo, W., Guo, Z., Caswell, H., Tuljapurkar, S. 2023; 48: 899-930
  • Hurricanes affect diversification among individual life courses of a primate population. The Journal of animal ecology Diaz, A. A., Steiner, U. K., Tuljapurkar, S., Zuo, W., Hernández-Pacheco, R. 2023


    Extreme climatic events may influence individual-level variability in phenotypes, survival and reproduction, and thereby drive the pace of evolution. Climate models predict increases in the frequency of intense hurricanes, but no study has measured their impact on individual life courses within animal populations. We used 45 years of demographic data of rhesus macaques to quantify the influence of major hurricanes on reproductive life courses using multiple metrics of dynamic heterogeneity accounting for life course variability and life-history trait variances. To reduce intraspecific competition, individuals may explore new reproductive stages during years of major hurricanes, resulting in higher temporal variation in reproductive trajectories. Alternatively, individuals may opt for a single optimal life-history strategy due to trade-offs between survival and reproduction. Our results show that heterogeneity in reproductive life courses increased by 4% during years of major hurricanes, despite a 2% reduction in the asymptotic growth rate due to an average decrease in mean fertility and survival by that is, shortened life courses and reduced reproductive output. In agreement with this, the population is expected to achieve stable population dynamics faster after being perturbed by a hurricane ( ρ = 1.512 $$ \rho =1.512 $$ ; 95% CI: 1.488, 1.538), relative to ordinary years ρ = 1.482 ; 1.475 , 1.490 $$ \left(\rho =1.482;1.475,1.490\right) $$ . Our work suggests that natural disasters force individuals into new demographic roles to potentially reduce competition during unfavourable environments where mean reproduction and survival are compromised. Variance in lifetime reproductive success and longevity are differently affected by hurricanes, and such variability is mostly driven by survival.

    View details for DOI 10.1111/1365-2656.13942

    View details for PubMedID 37190852

  • Reproductive dispersion and damping time scale with life-history speed. Ecology letters Jiang, S., Jaggi, H., Zuo, W., Oli, M. K., Coulson, T., Gaillard, J. M., Tuljapurkar, S. 2022


    Iteroparous species may reproduce at many different ages, resulting in a reproductive dispersion that affects the damping of population perturbations, and varies among life histories. Since generation time ( T c $$ {T}_c $$ ) is known to capture aspects of life-history variation, such as life-history speed, does T c $$ {T}_c $$ also determine reproductive dispersion ( S $$ S $$ ) or damping time ( τ $$ \tau $$ )? Using phylogenetically corrected analyses on 633 species of animals and plants, we find, firstly, that reproductive dispersion S $$ S $$ scales isometrically with T c $$ {T}_c $$ . Secondly, and unexpectedly, we find that the damping time ( τ $$ \tau $$ ) does not scale isometrically with generation time, but instead changes only as T c b $$ {T}_c^b $$ with b < 1 $$ b<1 $$ (also, there is a similar scaling with S $$ S $$ ). This non-isometric scaling implies a novel demographic contrast: increasing generation times correspond to a proportional increase in reproductive dispersion, but only to a slower increase in the damping time. Thus, damping times are partly decoupled from the slow-fast continuum, and are determined by factors other than allometric constraints.

    View details for DOI 10.1111/ele.14080

    View details for PubMedID 35925997

  • Mutations and the Distribution of Lifetime Reproductive Success JOURNAL OF THE INDIAN INSTITUTE OF SCIENCE Tuljapurkar, S., Zuo, W. 2022
  • Distributions of LRS in varying environments. Ecology letters Tuljapurkar, S., Zuo, W., Coulson, T., Horvitz, C., Gaillard, J. 2021


    The lifetime reproductive success (LRS) of individuals is affected by random events such as death, realized growth or realized reproduction, and the outcomes of these events can differ even when individuals have identical probabilities. Another source of randomness arises when these probabilities also change over time in variable environments. For structured populations in stochastic environments, we extend our recent method to determine how birth environment and birth stage determine the random distribution of the LRS. Our results provide a null model that quantifies effects on LRS of just the birth size or stage. Using Roe deer Capreolus capreolus as a case study, we show that the effect of an individual's birth environment on LRS varies with the frequency of environments and their temporal autocorrelation, and that lifetime performance is affected by changes in the pattern of environmental states expected as a result of climate change.

    View details for DOI 10.1111/ele.13745

    View details for PubMedID 33904254

  • Skewed distributions of lifetime reproductive success: beyond mean and variance. Ecology letters Tuljapurkar, S., Zuo, W., Coulson, T., Horvitz, C., Gaillard, J. 2020


    Lifetime reproductive performance is quantified here by the LRS (lifetime reproductive success), the random number of offspring an individual produces over its lifetime. Many field studies find that distributions of LRS among individuals are non-normal, zero-inflated and highly skewed. These results beg the question, what is the distribution of LRS predicted by demographic models when the only source of randomness is demographic stochasticity? Here we present the first exact analysis of the probability distribution of LRS for species described by age+stage models; our analysis starts with estimated vital rates. We illustrate with three examples: the Hadza, human hunter-foragers (age-only), the evergreen tree Tsuga canadensis (stage-only) and Roe deer, Capreolus capreolus (age+stage). For each we obtain the exact distribution of LRS, but also calculate and discuss the first three moments. Our results point to important questions about how such LRS distributions affect natural selection, and life history evolution.

    View details for DOI 10.1111/ele.13467

    View details for PubMedID 32043827

  • Age distribution, trends, and forecasts of under-5 mortality in 31 sub-Saharan African countries: A modeling study. PLoS medicine Mejía-Guevara, I., Zuo, W., Bendavid, E., Li, N., Tuljapurkar, S. 2019; 16 (3): e1002757


    Despite the sharp decline in global under-5 deaths since 1990, uneven progress has been achieved across and within countries. In sub-Saharan Africa (SSA), the Millennium Development Goals (MDGs) for child mortality were met only by a few countries. Valid concerns exist as to whether the region would meet new Sustainable Development Goals (SDGs) for under-5 mortality. We therefore examine further sources of variation by assessing age patterns, trends, and forecasts of mortality rates.Data came from 106 nationally representative Demographic and Health Surveys (DHSs) with full birth histories from 31 SSA countries from 1990 to 2017 (a total of 524 country-years of data). We assessed the distribution of age at death through the following new demographic analyses. First, we used a direct method and full birth histories to estimate under-5 mortality rates (U5MRs) on a monthly basis. Second, we smoothed raw estimates of death rates by age and time by using a two-dimensional P-Spline approach. Third, a variant of the Lee-Carter (LC) model, designed for populations with limited data, was used to fit and forecast age profiles of mortality. We used mortality estimates from the United Nations Inter-agency Group for Child Mortality Estimation (UN IGME) to adjust, validate, and minimize the risk of bias in survival, truncation, and recall in mortality estimation. Our mortality model revealed substantive declines of death rates at every age in most countries but with notable differences in the age patterns over time. U5MRs declined from 3.3% (annual rate of reduction [ARR] 0.1%) in Lesotho to 76.4% (ARR 5.2%) in Malawi, and the pace of decline was faster on average (ARR 3.2%) than that observed for infant (IMRs) (ARR 2.7%) and neonatal (NMRs) (ARR 2.0%) mortality rates. We predict that 5 countries (Kenya, Rwanda, Senegal, Tanzania, and Uganda) are on track to achieve the under-5 sustainable development target by 2030 (25 deaths per 1,000 live births), but only Rwanda and Tanzania would meet both the neonatal (12 deaths per 1,000 live births) and under-5 targets simultaneously. Our predicted NMRs and U5MRs were in line with those estimated by the UN IGME by 2030 and 2050 (they overlapped in 27/31 countries for NMRs and 22 for U5MRs) and by the Institute for Health Metrics and Evaluation (IHME) by 2030 (26/31 and 23/31, respectively). This study has a number of limitations, including poor data quality issues that reflected bias in the report of births and deaths, preventing reliable estimates and predictions from a few countries.To our knowledge, this study is the first to combine full birth histories and mortality estimates from external reliable sources to model age patterns of under-5 mortality across time in SSA. We demonstrate that countries with a rapid pace of mortality reduction (ARR ≥ 3.2%) across ages would be more likely to achieve the SDG mortality targets. However, the lower pace of neonatal mortality reduction would prevent most countries from achieving those targets: 2 countries would reach them by 2030, 13 between 2030 and 2050, and 13 after 2050.

    View details for DOI 10.1371/journal.pmed.1002757

    View details for PubMedID 30861006

    View details for PubMedCentralID PMC6413894

  • Advancing front of old-age human survival. Proceedings of the National Academy of Sciences of the United States of America Zuo, W., Jiang, S., Guo, Z., Feldman, M. W., Tuljapurkar, S. 2018; 115 (44): 11209–14


    Old-age mortality decline has driven recent increases in lifespans, but there is no agreement about trends in the age pattern of old-age deaths. Some argue that old-age deaths should become compressed at advanced ages, others argue that old-age deaths should become more dispersed with age, and yet others argue that old-age deaths are consistent with little change in dispersion. However, direct analysis of old-age deaths presents unusual challenges: Death rates at the oldest ages are always noisy, published life tables must assume an asymptotic age pattern of deaths, and the definition of "old-age" changes as lives lengthen. Here we use robust percentile-based methods to overcome some of these challenges and show, for five decades in 20 developed countries, that old-age survival follows an advancing front, like a traveling wave. The front lies between the 25th and 90th percentiles of old-age deaths, advancing with nearly constant long-term shape but annual fluctuations in speed. The existence of this front leads to several predictions that we verify, e.g., that advances in life expectancy at age 65 y are highly correlated with the advance of the 25th percentile, but not with distances between higher percentiles. Our unexpected result has implications for biological hypotheses about human aging and for future mortality change.

    View details for PubMedID 30327342

  • Susceptibility of wild and colonized Anopheles stephensi to Plasmodium vivax infection MALARIA JOURNAL Mohanty, A., Nina, P., Ballav, S., Vernekar, S., Parkar, S., D'souza, M., Zuo, W., Gomes, E., Chery, L., Tuljapurkar, S., Valecha, N., Rathod, P. K., Kumar, A. 2018; 17: 225


    As much as 80% of global Plasmodium vivax infections occur in South Asia and there is a shortage of direct studies on infectivity of P. vivax in Anopheles stephensi, the most common urban mosquito carrying human malaria. In this quest, the possible effects of laboratory colonization of mosquitoes on infectivity and development of P. vivax is of interest given that colonized mosquitoes can be genetically less divergent than the field population from which they originated.Patient-derived P. vivax infected blood was fed to age-matched wild and colonized An. stephensi. Such a comparison requires coordinated availability of same-age wild and colonized mosquito populations. Here, P. vivax infection are studied in colonized An. stephensi in their 66th-86th generation and fresh field-caught An. stephensi. Wild mosquitoes were caught as larvae and pupae and allowed to develop into adult mosquitoes in the insectary. Parasite development to oocyst and sporozoite stages were assessed on days 7/8 and 12/13, respectively.While there were batch to batch variations in infectivity of individual patient-derived P. vivax samples, both wild and colonized An. stephensi were roughly equally susceptible to oocyst stage Plasmodium infection. At the level of sporozoite development, significantly more mosquitoes with sporozoite load of 4+ were seen in wild than in colonized populations.

    View details for PubMedID 29871629

  • Demographic and clinical profiles of Plasmodium falciparum and Plasmodium vivax patients at a tertiary care centre in southwestern India MALARIA JOURNAL Chery, L., Maki, J. N., Mascarenhas, A., Walke, J. T., Gawas, P., Almeida, A., Fernandes, M., Vaz, M., Ramanan, R., Shirodkar, D., Bernabeu, M., Manoharan, S. K., Pereira, L., Dash, R., Sharma, A., Shaik, R. B., Chakrabarti, R., Babar, P., White, J., Mudeppa, D. G., Kumar, S., Zuo, W., Skillman, K. M., Kanjee, U., Lim, C., Shaw-Saliba, K., Kumar, A., Valecha, N., Jindal, V. N., Khandeparkar, A., Naik, P., Amonkar, S., Duraisingh, M. T., Tuljapurkar, S., Smith, J. D., Dubhashi, N., Pinto, R. G., Silveria, M., Gomes, E., Rathod, P. K. 2016; 15


    Malaria remains an important cause of morbidity and mortality in India. Though many comprehensive studies have been carried out in Africa and Southeast Asia to characterize and examine determinants of Plasmodium falciparum and Plasmodium vivax malaria pathogenesis, fewer have been conducted in India.A prospective study of malaria-positive individuals was conducted at Goa Medical College and Hospital (GMC) from 2012 to 2015 to identify demographic, diagnostic and clinical indicators associated with P. falciparum and P. vivax infection on univariate analysis.Between 2012 and 2015, 74,571 febrile individuals, 6287 (8.4%) of whom were malaria positive, presented to GMC. The total number of malaria cases at GMC increased more than two-fold over four years, with both P. vivax and P. falciparum cases present year-round. Some 1116 malaria-positive individuals (mean age = 27, 91% male), 88.2% of whom were born outside of Goa and 51% of whom were construction workers, were enroled in the study. Of 1088 confirmed malaria-positive patients, 77.0% had P. vivax, 21.0% had P. falciparum and 2.0% had mixed malaria. Patients over 40 years of age and with P. falciparum infection were significantly (p < 0.001) more likely to be hospitalised than younger and P. vivax patients, respectively. While approximately equal percentages of hospitalised P. falciparum (76.6%) and P. vivax (78.9%) cases presented with at least one WHO severity indicator, a greater percentage of P. falciparum inpatients presented with at least two (43.9%, p < 0.05) and at least three (29.9%, p < 0.01) severity features. There were six deaths among the 182 hospitalised malaria positive patients, all of whom had P. falciparum.During the four year study period at GMC, the number of malaria cases increased substantially and the greatest burden of severe disease was contributed by P. falciparum.

    View details for DOI 10.1186/s12936-016-1619-5

    View details for Web of Science ID 000388529700001

    View details for PubMedID 27884146

    View details for PubMedCentralID PMC5123287

  • Distinct genomic architecture of Plasmodium falciparum populations from South Asia. Molecular and biochemical parasitology Kumar, S., Mudeppa, D. G., Sharma, A., Mascarenhas, A., Dash, R., Pereira, L., Shaik, R. B., Maki, J. N., White, J., Zuo, W., Tuljapurkar, S., Duraisingh, M. T., Gomes, E., Chery, L., Rathod, P. K. 2016


    Previous whole genome comparisons of Plasmodium falciparum populations have not included collections from the Indian subcontinent, even though two million Indians contract malaria and about 50,000 die from the disease every year. Stratification of global parasites has revealed spatial relatedness of parasite genotypes on different continents. Here, genomic analysis was further improved to obtain country-level resolution by removing var genes and intergenic regions from distance calculations. P. falciparum genomes from India were found to be most closely related to each other. Their nearest neighbors were from Bangladesh and Myanmar, followed by Thailand. Samples from the rest of Southeast Asia, Africa and South America were increasingly more distant, demonstrating a high-resolution genomic-geographic continuum. Such genome stratification approaches will help monitor variations of malaria parasites within South Asia and future changes in parasite populations that may arise from in-country and cross-border migrations.

    View details for DOI 10.1016/j.molbiopara.2016.07.005

    View details for PubMedID 27457272

  • A Life-History Approach to the Late Pleistocene Megafaunal Extinction AMERICAN NATURALIST Zuo, W., Smith, F. A., Charnov, E. L. 2013; 182 (4): 524-531


    A major criticism of the "overkill" theory for the late Pleistocene extinction in the Americas has been the seeming implausibility of a relatively small number of humans selectively killing off millions of large-bodied mammals. Critics argue that early Paleoindian hunters had to be extremely selective to have produced the highly size-biased extinction pattern characteristic of this event. Here, we derive a probabilistic extinction model that predicts the extinction risk of mammals at any body mass without invoking selective human harvest. The new model systematically analyzes the variability in life-history characteristics, such as the instantaneous mortality rate, age of first reproduction, and the maximum net reproductive rate. It captures the body size-biased extinction pattern in the late Pleistocene and precisely predicts the percentage of unexpectedly persisting large mammals and extinct small ones. A test with a global late Quaternary mammal database well supports the model. The model also emphasizes that quantitatively analyzing patterns of variability in ecological factors can shed light on diverse behaviors and patterns in nature. From a macro-scale conservation perspective, our model can be modified to predict the fate of biota under the pressures from both climate change and human impacts.

    View details for DOI 10.1086/671995

    View details for Web of Science ID 000327901800028

    View details for PubMedID 24021404

  • The Macroecology of Sustainability PLOS BIOLOGY Burger, J. R., Allen, C. D., Brown, J. H., Burnside, W. R., Davidson, A. D., Fristoe, T. S., Hamilton, M. J., Mercado-Silva, N., Nekola, J. C., Okie, J. G., Zuo, W. 2012; 10 (6)


    The discipline of sustainability science has emerged in response to concerns of natural and social scientists, policymakers, and lay people about whether the Earth can continue to support human population growth and economic prosperity. Yet, sustainability science has developed largely independently from and with little reference to key ecological principles that govern life on Earth. A macroecological perspective highlights three principles that should be integral to sustainability science: 1) physical conservation laws govern the flows of energy and materials between human systems and the environment, 2) smaller systems are connected by these flows to larger systems in which they are embedded, and 3) global constraints ultimately limit flows at smaller scales. Over the past few decades, decreasing per capita rates of consumption of petroleum, phosphate, agricultural land, fresh water, fish, and wood indicate that the growing human population has surpassed the capacity of the Earth to supply enough of these essential resources to sustain even the current population and level of socioeconomic development.

    View details for DOI 10.1371/journal.pbio.1001345

    View details for Web of Science ID 000305945600007

    View details for PubMedID 22723741

  • Insights into plant size-density relationships from models and agricultural crops PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA Deng, J., Zuo, W., Wang, Z., Fan, Z., Ji, M., Wang, G., Ran, J., Zhao, C., Liu, J., Niklas, K. J., Hammond, S. T., Brown, J. H. 2012; 109 (22): 8600-8605


    There is general agreement that competition for resources results in a tradeoff between plant mass, M, and density, but the mathematical form of the resulting thinning relationship and the mechanisms that generate it are debated. Here, we evaluate two complementary models, one based on the space-filling properties of canopy geometry and the other on the metabolic basis of resource use. For densely packed stands, both models predict that density scales as M(-3/4), energy use as M(0), and total biomass as M(1/4). Compilation and analysis of data from 183 populations of herbaceous crop species, 473 stands of managed tree plantations, and 13 populations of bamboo gave four major results: (i) At low initial planting densities, crops grew at similar rates, did not come into contact, and attained similar mature sizes; (ii) at higher initial densities, crops grew until neighboring plants came into contact, growth ceased as a result of competition for limited resources, and a tradeoff between density and size resulted in critical density scaling as M(-0.78), total resource use as M(-0.02), and total biomass as M(0.22); (iii) these scaling exponents are very close to the predicted values of M(-3/4), M(0), and M(1/4), respectively, and significantly different from the exponents suggested by some earlier studies; and (iv) our data extend previously documented scaling relationships for trees in natural forests to small herbaceous annual crops. These results provide a quantitative, predictive framework with important implications for the basic and applied plant sciences.

    View details for DOI 10.1073/pnas.1205663109

    View details for Web of Science ID 000304881700052

    View details for PubMedID 22586097

  • A general model for effects of temperature on ectotherm ontogenetic growth and development PROCEEDINGS OF THE ROYAL SOCIETY B-BIOLOGICAL SCIENCES Zuo, W., Moses, M. E., West, G. B., Hou, C., Brown, J. H. 2012; 279 (1734): 1840-1846


    The temperature size rule (TSR) is the tendency for ectotherms to develop faster but mature at smaller body sizes at higher temperatures. It can be explained by a simple model in which the rate of growth or biomass accumulation and the rate of development have different temperature dependence. The model accounts for both TSR and the less frequently observed reverse-TSR, predicts the fraction of energy allocated to maintenance and synthesis over the course of development, and also predicts that less total energy is expended when developing at warmer temperatures for TSR and vice versa for reverse-TSR. It has important implications for effects of climate change on ectothermic animals.

    View details for DOI 10.1098/rspb.2011.2000

    View details for Web of Science ID 000301981300023

    View details for PubMedID 22130604

  • Rensch's Rule in Large Herbivorous Mammals Derived from Metabolic Scaling AMERICAN NATURALIST Sibly, R. M., Zuo, W., Kodric-Brown, A., Brown, J. H. 2012; 179 (2): 169-177


    Rensch's rule, which states that the magnitude of sexual size dimorphism tends to increase with increasing body size, has evolved independently in three lineages of large herbivorous mammals: bovids (antelopes), cervids (deer), and macropodids (kangaroos). This pattern can be explained by a model that combines allometry, life-history theory, and energetics. The key features are that female group size increases with increasing body size and that males have evolved under sexual selection to grow large enough to control these groups of females. The model predicts relationships among body size and female group size, male and female age at first breeding, death and growth rates, and energy allocation of males to produce body mass and weapons. Model predictions are well supported by data for these megaherbivores. The model suggests hypotheses for why some other sexually dimorphic taxa, such as primates and pinnipeds (seals and sea lions), do or do not conform to Rensh's rule.

    View details for DOI 10.1086/663686

    View details for Web of Science ID 000299000400006

    View details for PubMedID 22218307

  • Growth, mortality, and life-history scaling across species EVOLUTIONARY ECOLOGY RESEARCH Charnov, E. L., Zuo, W. 2011; 13 (6): 661-664
  • Human hunting mortality threshold rules for extinction in mammals (and fish) EVOLUTIONARY ECOLOGY RESEARCH Charnov, E. L., Zuo, W. 2011; 13 (4): 431-437
  • Energetic Limits to Economic Growth BIOSCIENCE Brown, J. H., Burnside, W. R., Davidson, A. D., DeLong, J. P., Dunn, W. C., Hamilton, M. J., Mercado-Silva, N., Nekola, J. C., Okie, J. G., Woodruff, W. H., Zuo, W. 2011; 61 (1): 19-26
  • Response to Comments on "Energy Uptake and Allocation During Ontogeny" SCIENCE Zuo, W., Moses, M. E., Hou, C., Woodruff, W. H., West, G. B., Brown, J. H. 2009; 325 (5945)
  • Energy Uptake and Allocation During Ontogeny SCIENCE Hou, C., Zuo, W., Moses, M. E., Woodruff, W. H., Brown, J. H., West, G. B. 2008; 322 (5902): 736-739


    All organisms face the problem of how to fuel ontogenetic growth. We present a model, empirically grounded in data from birds and mammals, that correctly predicts how growing animals allocate food energy between synthesis of new biomass and maintenance of existing biomass. Previous energy budget models have typically had their bases in rates of either food consumption or metabolic energy expenditure. Our model provides a framework that reconciles these two approaches and highlights the fundamental principles that determine rates of food assimilation and rates of energy allocation to maintenance, biosynthesis, activity, and storage. The model predicts that growth and assimilation rates for all animals should cluster closely around two universal curves. Data for mammals and birds of diverse body sizes and taxa support these predictions.

    View details for DOI 10.1126/science.1162302

    View details for Web of Science ID 000260605200047

    View details for PubMedID 18974352

    View details for PubMedCentralID PMC2891030

  • GeoSVM: an efficient and effective tool to predict species' potential distributions JOURNAL OF PLANT ECOLOGY Zuo, W., Lao, N., Geng, Y., Ma, K. 2008; 1 (2): 143-145

    View details for DOI 10.1093/jpe/rtn005

    View details for Web of Science ID 000265790100008

  • Revisiting a model of ontogenetic growth: Estimating model parameters from theory and data AMERICAN NATURALIST Moses, M. E., Hou, C., Woodruff, W. H., West, G. B., Nekola, J. C., Zuo, W., Brown, J. H. 2008; 171 (5): 632-645


    The ontogenetic growth model (OGM) of West et al. provides a general description of how metabolic energy is allocated between production of new biomass and maintenance of existing biomass during ontogeny. Here, we reexamine the OGM, make some minor modifications and corrections, and further evaluate its ability to account for empirical variation on rates of metabolism and biomass in vertebrates both during ontogeny and across species of varying adult body size. We show that the updated version of the model is internally consistent and is consistent with other predictions of metabolic scaling theory and empirical data. The OGM predicts not only the near universal sigmoidal form of growth curves but also the M(1/4) scaling of the characteristic times of ontogenetic stages in addition to the curvilinear decline in growth efficiency described by Brody. Additionally, the OGM relates the M(3/4) scaling across adults of different species to the scaling of metabolic rate across ontogeny within species. In providing a simple, quantitative description of how energy is allocated to growth, the OGM calls attention to unexplained variation, unanswered questions, and opportunities for future research.

    View details for DOI 10.1086/587073

    View details for Web of Science ID 000255212900009

    View details for PubMedID 18419571