Overview of Population Ecology - Basic Models General objectives and questions addressed Historical trends Key people Key terms Some example data sets Basics of exponential and geometric growth Basics of limited growth and density dependence Equilibrium concepts and stability Survivorship and life histories What regulates populations? Survey of recent papers - topic coverage Example paper - Akcakaya, H. R. 1992. Population cycles of mammals: Evidence for a ratio-dependent predation hypothesis. Ecol. Monog. 62: 119-142. General objectives of population ecology: Deterrmine the relative impact of alternative factors (biotic, abiotic) on the changes in size of populations. Determine conditions under which populations maintain relatively constant numbers of individuals - why are some populations highly variable in size and others not What are the relative effects of alternative life history patterns on population dynamics What are the effects of population structure (age, size, space, etc. ) on population dynamics Provide basis for linking population dynamics of several species Main historical trends: A variety of paradigms have been described in the historical development of population biology (den Boer and Reddingius, and see S. Kingsland for alternative views): Mechanistic view (Lotka, Volterra) - populations as differential equations - treating them as made up of many, many individuals, each with small effect on the aggregate - a mechanistic view that grew out of physical models. In this view, one can still break down populations (as Lotka did extensively for age structure) but maintain the same assumptions about large sizes within each age group. Regulation or engineering view (Nicholson) - population density was in balance, e.g. adjusted to prevailing conditions, positing a "controlling factor" or "density geoverning factor" (now thought of as a density dependent factor) which produced a balance. There is an inherent equilibrium, with a stabilizing feedback driving population densities back to this equilibrium following perturbations - a cybernetic view, in which population regulation is taken for granted. Systems view (von Bertalanffy) - there are general principles, laws and models that apply to systems with many components, irrespective of the details of these components, which are applicable to the hierarchical levels in ecology. These laws are not necessarily derivable from a reductionist view. Natural History view (Andrewartha and Birch) - population dynamics is the result of a complex interplay between the properties of the organisms themselves and the variables in the environment. A view of populations made up of many small interaction groups, with which most individauls interact across their lifespan. So distribution and abundance determined by variations in localized environmental factors which determine the organisms growth and survival in these localized groups. An Alternative (not in den Boer and Reddingius) Individual-Based View - here we take the reductionist view that the properties of populations can be derived from the complex of interactions between individuals, environment, and other species. Thus it is not just localized interaction groups which determine population dynamics, but the entire complex of individual characteristics which vary through the population. It is a view in which it is possible for rare individuals to have significant impacts on population-level phenomena. People (a few): H. G. Andrewartha - density independent view of population regulation L. C. Birch - density independent view of population regulation L. C. Cole - population cycles and randomness G. F. Gause - early experiments for lab population growth (Paramecia) G. E. Hutchinson - Limnological examples, Diversity issues P. H. Leslie - matrix age structured models A. J. Lotka - mechanical view of populations, age structure results A. J. Nicholson - competition, classic blowflies population data M. Verhulst - logistic equation (also called Verhulst-Pearl, but Verhulst was first) V. Volterra - Harvesting populations - 2 species predator prey models L. Von Bertalanffy - systems view of populations Some references: Papers to read: Akcakaya, H. R. 1992. Population cycles of mammals: Evidence for a ratio-dependent predation hypothesis. Ecol. Monog. 62: 119-142. Chitty, D. 1960. Population processes in the vole and their relevance to general theory. Can. J. Zol. 38:99-113. Ehrlich, P. R. and L. C. Birch. 1967. The "balance of nature" and "population control". Am. Nat. 101:97-107 Hallam, T. G. 1986. Population Dynamics in a homogeneous environment. Biomathematics 17:61-94. Krebs, C. J., M. S. Gaines, B. L. Keller, J. H. Myers and R. H. Tamarin. 1973. Population cycles in small rodents. Science 179: 35-41. References: Berryman, A. A. 1981. Population Systems: A General Introduction. Plenum, NY. Den Boer, P. J. and J. Reddingius. 1996. Regulation and Stabilization Paradigms in Population Ecology. Chapman and Hall, London. Gotelli, N. J. 1995. A Primer of Ecology. Sinauer, Sunderland, MA Gutierrez, A. P. 1996. Applied Population Ecology: A Supply-Demand Approach. Wiley, NY. Hastings, A. 1997. Population Biology: Concepts and Models. Springer, NY. Hutchinson, G. E. 1978. An Introduction to Population Ecology. Yale, New Haven. Kingsland, S. E. 1985. Modeling Nature: Episodes in the History of Population Ecology. Univ. of Chicago, Chicago. Roughgarden, J. 1998. A Primer of Theoretical Ecology. Prentice Hall, NY. Tanner, J. T. 1978. A Guide to the Study of Animal Populations. Univ. of Tennessee, Knoxville. Wilson, E. O. and W. H. Bossert. 1971. A Primer of Population Biology. Sinauer, Sunderland, MA. Some Terms: Allee effect - negative growth rate of a population at low population densities Carrying capacity - population density at which the population per capita growth rate is zero Density dependence - in general, any limitation on a process due to the density of the population, so a density dependent growth rate would correspond to the case in which per capita growth rate was a function of density Density independence - in general, the process of concern is not affected by population density, so a density independent grwoth rate would correspond to the case in which per capita growth rate was not a function of density. Equilibrium - situation in which the growth rate = 0 Functional response - the rate of prey capture per predator as a function of prey density Life history - the pattern of births and deaths for a population Linearization - approximating a general non-linear function in a small region by a linear function Numerical response - the per capita growth rate of the predator population as a function of prey density Resilience - time constant for return to equilibrium following a perturbation Stable equilibrium (Local asymptotic stability) - following a small perturbation in population density from an equilibrium, the population moves back towrads equilibrium density. Exponential growth Unlimited growth - during early phases of epidemic, introduction to a new habitat, per capita growth rate is constant Geometric growth - discrete time analog of exponential growth Logistic growth Simplest density dependent growth in which per capita growth rate is linear in population density Appropriate discrete analog is not what is typically called the discrete logistic, but rather is the hyperbolic form x(n+1)=aX(n)/(b+x(n)) Discrete logistic x(n+1)= rx(n) (1-x(n)) exhibits diverse dynamical characteristics not possible in continuous logistic Equilibrium concepts Locally stable equilibrium is only one possibility. Also have global stability (approach the equilibrium from any initial condition), dynamic stability (limit cycles), resilience, persistence, structural stability Population regulation Major controversies arose between those with a view in which nature is in balance (e.g. there are density dependent regulating factors) and those with a view that it is density independent factors which govern population regulation. Thus some view populations as persistyent, and others view them as winking in and out on a regular basis. This was also driven by different views of what was trying to be explained: balance or fluctuations in populations. Much of this arose before there was a large theoretical literature on spatial effects on populations, in particular the effect of underlying spatial heterogeneity in habitats and the effect on population persistence over larger spatial extents (the metapopulation view) Topics from 1990's search on population dynamics, and animal population dynamics in 4 ecology journals: Summary: Reintroduction 1 Food effects 3 Spatial effects 5 Soil populations 1 Landscape effects 2 Cannibalism 1 Social effects 1 Models and theory 4 Clonal aspects 1 Mark-recapture 2 Immigration effects 1 Density dependence 1 Total: 22