► Lee, CT, TEX Miller, and BD Inouye.  Consumer effects on the vital rates of their resource can determine the outcome of competition between consumers.  In press at The American Naturalist.


Current competition theory does not adequately address the fact that competitors may affect the survival, growth, and reproductive rates of their resources. Ecologically important interactions in which consumers affect resource vital rates range from parasitism and herbivory to mutualism. We present a general model of competition that explicitly includes consumer-dependent resource vital rates. We build on the classic MacArthur model of competition for multiple resources, allowing direct comparison with expectations from established concepts of resource-use overlap. Consumers share a stage-structured resource population but may use the different stages to different extents, as they do the different independent resources in the classic model. Here, however, the stages are dynamically linked via consumer-dependent vital rates. We show that consumers' effects on resource vital rates result in two important departures from classic results. First, consumers can coexist despite identical use of resource stages, provided each competitor shifts the resource stage distribution toward stages that benefit other species. Second, consumers specializing on different resource stages can compete strongly, possibly resulting in competitive exclusion despite a lack of resource stage-use overlap. Our model framework demonstrates the critical role that consumer dependent resource vital rates can play in competitive dynamics in a wide range of biological systems.


Lee, CT, and BD Inouye. Mutualism between consumers and their shared resource can promote competitive coexistence.  The American Naturalist 175: 277–288.


Competitive coexistence depends on dynamic interactions between competitor and resource populations, including mutualism between the resource and each competitor. We add mutualism to a well-known model of resource competition, and show that it can powerfully stabilize competitive coexistence in the absence or presence of resource heterogeneity. We use a transition matrix approach to describe lottery competition, while allowing each of two competitors to affect the population dynamics of their shared resource. For example, two plant-defending ant species may compete for nesting space within ant-adapted (myrmecophytic) plants. We show that mutualism between consumers and a resource species can stabilize competitive coexistence of the consumers by allowing each competitor to influence resource dynamics in a way that benefits the other. The effect of this novel coexistence mechanism depends on a mutualism's biological details: for example, altering myrmecophyte fecundity affects competing ant species differently than does altering plant survival. Finally, we consider a heterogeneous resource (e.g., two types of nest site), and show how niche partitioning can stabilize coexistence in the absence of resource dynamics. When resource heterogeneity is dynamic (e.g., small and large plants of the same species), niche partitioning also provides new routes for additional stabilization via mutualism.


Lee, CT, and S Tuljapurkar. Quantitative, dynamic models to integrate environment, population, and society. In Kirch, PV, ed. Soils, Dryland Agriculture, and Social Complexity in Ancient Hawai’i:  A Model System for Human Ecodynamics. Forthcoming from SAR Press, Santa Fe, New Mexico.


From an agricultural standpoint, the inhabitants of pre-European-contact Hawai’i faced tremendous amounts of spatial and temporal environmental heterogeneity.  Even within dryland farming areas, variation in climate and soil properties is substantial.  In this chapter we use integrative dynamic models to clarify the consequences of this variability for dryland agricultural productivity and for the demography and well-being of dryland agriculturalists.  Agroecosystem modeling takes us from rainfall and temperature variability to soil nutrient status and dryland crop yield (Lee, Tuljapurkar, and Vitousek 2006).   Next, we describe a quantitative model for human demography that explicitly links food supply to human survival and fertility, thus relating crop production to population growth and health, as well as agricultural surplus (Lee and Tuljapurkar 2008).  Coupling the two models and applying them to the Kohala dryland field system, we demonstrate the potential consequences of partitioning the region into smaller administrative units over time, and interpret the results in terms of social inequality and hierarchical control (Ladefoged, Lee, and Graves 2008).  Our modeling approach incorporates intricate feedbacks and spatial and temporal heterogeneity in ways not possible without a dynamic perspective, and can be modified to apply to other locations and cultures, provided some data on the ecosystem, agricultural practices, and demography. 


Lee, CT, CO Puleston, and S Tuljapurkar. 2009.  Population and prehistory III: Food-dependent demography in variable environments. Theoretical Population Biology 76: 179-188.  


The population dynamics of preindustrial societies depend intimately on their surroundings, and food is a primary means through which environment influences population size and individual well-being. Food production requires labor; thus, dependence of survival and fertility on food involves dependence of a population's future on its current state. We use a perturbation approach to analyze the effects of random environmental variation on this nonlinear, age-structured system. We show that in expanding populations, direct environmental effects dominate induced population fluctuations, so environmental variability has little effect on mean hunger levels although it does decrease population growth. Growth rate determines the time until population limitation by space. Limitation introduces a tradeoff between population density and well-being, so population effects become more important than direct effects of environment: environmental fluctuation increases mortality, releasing density dependence and disproportionately raising average well-being for survivors. We discuss social implications of these findings for the long-term fate of populations as they transition from expansion into limitation, given that conditions leading to high well-being during growth depress well-being during limitation.


Lee, CT, and S Tuljapurkar.  2008.  Population and prehistory I: Food-dependent population growth in constant environments.  Theoretical Population Biology 73: 473-482.


We present a demographic model that describes the feedbacks between food supply, human mortality and fertility rates, and labor availability in expanding populations, where arable land area is not limiting.  This model provides a quantitative framework to describe how environment, technology, and culture interact to influence the fates of preindustrial agricultural populations.  We present equilibrium conditions and derive approximations for the equilibrium population growth rate, food availability, and other food-dependent measures of population well-being.  We examine how the approximations respond to environmental changes and to human choices, and find that the impact of environmental quality depends upon whether it manifests through agricultural yield or maximum (food-independent) survival rates. Human choices can complement or offset environmental effects: greater labor investments increase both population growth and well-being, and therefore can counteract lower agricultural yield, while fertility control decreases the growth rate but can increase or decrease well-being. Finally we establish equilibrium stability criteria, and argue that the potential for loss of local stability at low population growth rates could have important consequences for populations that suffer significant environmental or demographic shocks.


Donahue, MJ, and CT Lee. 2008. Colonization.  pp. 672-278 in SE Jorgensen and BD Fath (Editor-in-Chief), General Ecology. Vol. 1 of Encyclopedia of Ecology, 5 vols. Oxford: Elsevier.  


Colonization is the arrival of individuals to areas of suitable habitat that are currently uninhabited. Populations are established by the successful colonizers that survive and reproduce. Colonization is a spatial process central to several fundamental concepts in ecology, including species coexistence, disturbance and recovery, succession, metapopulations, biodiversity, invasive species, and speciation. We consider the influence of colonization on each of these processes around the central theme of colonization–extinction balance. At the smallest scale, individual recruitment (colonization) and mortality (extinction) determine the density and persistence of a population. At a slightly larger scale, small disturbances of a competitive dominant can open space allowing good colonizers to coexist with dominant competitors via competition–colonization tradeoff. Large disturbances may result in a landscape with communities in different successional stages and, therefore, higher regional biodiversity. On continental scales, colonization–extinction balance sheds light on patterns of biodiversity through ‘island biogeography theory’. We consider the influence of colonization on disease dynamics, range expansion, and spatial spread, with particular emphasis on anthropogenic effects that enhance colonization rates. Over a longer timescale, colonization of new niche space may lead to niche expansion or speciation.


Morris, WF, CA Pfister, S Tuljapurkar, CV Haridas, CL Boggs, MS Boyce, EM Bruna, DR Church, T Coulson, DF Doak, S Forsyth, J-M Gaillard, CC Horvitz, S Kalisz, BE Kendall, TM Knight, CT Lee, and ES Menges. 2008. Longevity can buffer plant and animal populations against changing climatic variability. Ecology 89 (1): 19-25.  


Both means and year-to-year variances of climate variables such as temperature and precipitation are predicted to change. However, the potential impact of changing climatic variability on the fate of populations has been largely unexamined. We analyzed multiyear demographic data for 36 plant and animal species with a broad range of life histories and types of environment to ask how sensitive their long-term stochastic population growth rates are likely to be to changes in the means and standard deviations of vital rates (survival, reproduction, growth) in response to changing climate. We quantified responsiveness using elasticities of the long-term population growth rate predicted by stochastic projection matrix models. Short-lived species (insects and annual plants and algae) are predicted to be more strongly (and negatively) affected by increasing vital rate variability relative to longer-lived species (perennial plants, birds, ungulates). Taxonomic affiliation has little power to explain sensitivity to increasing variability once longevity has been taken into account. Our results highlight the potential vulnerability of short-lived species to an increasingly variable climate, but also suggest that problems associated with short-lived undesirable species (agricultural pests, disease vectors, invasive weedy plants) may be exacerbated in regions where climate variability decreases.


Ladefoged, TN, CT Lee, and MW Graves. 2008.  Modeling life expectancy and surplus production of dynamic pre-contact territories in leeward Kohala, Hawai'i. Journal of Anthropological Archaeology 27(1): 93-110.


Hawaiian territoriality evolved in response to the ecodynamics of changing populations set within shifting socio-political structures. Modeling agricultural surplus production and life expectancy of various prehistoric and protohistoric territorial configurations in the leeward Kohala dryland field system identifies the costs and benefits associated with dynamic territorial units. The results of the modeling indicate that if people lived autonomous lives within their territories the 18-km long landscape containing the field system would have been optimally divided into 14 territories. The archaeological and ethnohistorical data suggest that at European contact the area was divided into 32 generally smaller territorial units. This configuration, while lowering average life expectancy and increasing levels of spatial variability in surplus production, maximized average yearly surplus and reduced its temporal variability. Dividing the field system into 32 units provided opportunities for elite managers to monitor production and control the redistribution of resources. The modeling and archaeological data suggest selection occurred differentially among social units, with certain segments of society having enhanced fitness in terms of agricultural resources at the expense of others, while maximizing the potential for surplus generation and possible redistribution.


Tuljapurkar, S, CT Lee, and M Figgs. 2007. Demography and food in early Polynesia. Pages 35-51 in Kirch, PV, and J.-L. Rallu, eds. The Growth and Collapse of Island Societies: Archaeological and Demographic Perspectives from the Pacific. Honolulu: University of Hawai’i Press. 


The study of  prehistoric populations relies on heterogeneous and incomplete data – archeological, ethnographic, ecological, historical – which need to be interpreted and integrated using conceptual and analytical models. For the island populations of Polynesia, Kirch (1984, 1994) provides a synthetic summary and model of demographic and cultural evolution over a millennium. This synthesis frames history in a temporal demographic sequence: founding immigrants begin a period of exponential numerical increase in time and of spatial spread; then follows a confrontation with Malthusian limits which is manifest in expansion into marginal areas and in the slowing or cessation of population increase; the latter period is marked by the evolution of sociocultural hierarchies in the form of chiefdoms.  This temporal story rests on assumptions concerning the relationship between agriculture and long run population dynamics, including the productivity of agriculture in prehistory, the nature of marginal areas, Malthusian limits and carrying capacity.  This paper examines these and related concepts from demographic, ecological and comparative perspectives. First, we examine briefly and critically Malthusian limits and carrying capacity, and then the concepts of marginal areas and sustainability. Second, we consider the problem of demographic reconstruction based on the limited data available for prehistoric populations. We present a new data-driven method that uses data tabulated by Weiss (1973) on various prehistoric populations to generate a new family of model life tables. The success of this approach suggests that we may be able to reduce reliance on mortality models for contemporary populations. Finally, we discuss an ecologically based approach to the interaction between agricultural practices and soil dynamics.  Sowing, fertilizing, and cropping alter the cycle of nutrient flow from the atmosphere and the soil into plants and back again.  We propose a quantitative model of this cycle and its dynamics, and discuss its use in studying the relationship between agriculture and demography in prehistory. We argue that such an approach can provide robust insights into the dynamic processes that underlie population change and population-environment relationships in prehistory.


Lee, CT, S Tuljapurkar, and P Vitousek. 2006. Risky business: spatial and temporal variation in preindustrial dryland agriculture.  Human Ecology 34 (6): 739-763.


Traditional dryland agriculture in the Pacific island was often labor-intensive and risky, yet settlement and farming in dry areas played an important role in the development of Polynesian societies. We investigate how temporal and spatial climatic fluctuations shape variation in agricultural production across dryland landscapes. We use a model that couples plant growth, climate, and soil organic matter dynamics, together with data from Kohala, Hawai'i, to understand how temperature, rainfall, nitrogen availability, and cropping activity interact to determine yield dynamics through time and space. Due to these interactions, the statistical characterization of rainfall alone is a poor characterization of agricultural yield. Using a simple linear model of human population dynamics, we show that the observed yield variation can affect long-term population growth substantially. Our approach to analyzing spatial and temporal fluctuations in food supply, and to interpreting the population consequences of these fluctuations, provides a quantitative evaluation of agricultural risk and human carrying capacity in dry regions.



Boyce, MS, CV Haridas, CT Lee, and the NCEAS Stochastic Demography Working Group. 2006. Demography in an increasingly variable world. Trends in Ecology and Evolution 21: 141-148. 


Recent advances in stochastic demography provide unique insights into the probable effects of increasing environmental variability on population dynamics, and these insights can be substantially different compared with those from deterministic models. Stochastic variation in structured population models influences estimates of population growth rate, persistence and resilience, which ultimately can alter community composition, species interactions, distributions and harvesting. Here, we discuss how understanding these demographic consequences of environmental variation will have applications for anticipating changes in populations resulting from anthropogenic activities that affect the variance in vital rates. We also highlight new tools for anticipating the consequences of the magnitude and temporal patterning of environmental variability.



Lee, CT, and A Hastings.  2006.  Non-equilibrium genetic structure is robust to the shape of the dispersal distribution.  Evolutionary Ecology Research 8: 279-293. 


Questions: How does rare, long-distance dispersal affect spatial genetic structure on ecological temporal scales? What is the magnitude of its effect relative to the effects of the mean extent of dispersal and of fecundity?

Model features: One-locus, two-allele individual-based simulation of a sessile, annual organism, without mutation.

Key variables: The shape of the dispersal distribution is leptokurtic or platykurtic, with kurtosis varying by a factor of 3; the spatial variance of dispersal and fecundity vary by a factor of 5.

Conclusions: Effects of the shape of the dispersal distribution and of fecundity on within-population spatial genetic autocorrelation are small compared with the strong effect of dispersal variance. Additional processes such as spatial population expansion can increase the effect of long-distance dispersal for some time, and may contribute to studies showing a large impact of dispersal distribution shape. Analysis of different trajectories for populations not in mutation-drift equilibrium provides key information about biological mechanisms and explains why long-distance dispersal is important to some ecological processes and not others.



Chesson, P, and CT Lee.  2005.  Families of discrete kernels for modeling dispersal. Theoretical Population Biology 67 (4): 241-256.


Integer lattices are important theoretical landscapes for studying the consequences of dispersal and spatial population structure, but convenient dispersal kernels able to represent important features of dispersal in nature have been lacking for lattices. Because leptokurtic (centrally peaked and long-tailed) kernels are common in nature and have important effects in models, of particular interest are families of dispersal kernels in which the degree of leptokurtosis can be varied parametrically. Here we develop families of kernels on integer lattices with several important properties. The degree of leptokurtosis can be varied parametrically from near 0 (the Gaussian value) to infinity. These kernels are all asymptotically radially symmetric. (Exact radial symmetry is impossible on lattices except in one dimension.) They have separate parameters for shape and scale, and their lower order moments and Fourier transforms are given by simple formulae. In most cases, the kernel families that we develop are closed under convolution so that multiple steps of a kernel remain within the same family. Included in these families are kernels with asymptotic power function tails, which have provided good fits to some observations from nature. These kernel families are constructed by randomizing convolutions of stepping-stone kernels and have interpretations in terms of population heterogeneity and heterogeneous physical processes.



Lee, CT, MF Hoopes, J Diehl, W Gilliland, G Huxel, EV Leaver, K McCann, J Umbanhowar, and A Mogilner.  2001.  Non-local concepts and models in biology.  Journal of Theoretical Biology 210: 201-219. 


In this paper, we consider local and non-local spatially explicit mathematical models for biological phenomena. We show that, when rate differences between fast and slow local dynamics are great enough, non-local models are adequate simplifications of local models. Non-local models thus avoid describing fast processes in mechanistic detail, instead describing the effects of fast processes on slower ones. As a consequence, non-local models are helpful to biologists because they describe biological systems on scales that are convenient to observation, data collection, and insight. We illustrate these arguments by comparing local and non-local models for the aggregation of hypothetical organisms, and we support theoretical ideas with concrete examples from cell biology and animal behavior.