Ecology study guide
Ecology study guide BIOL 4410
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Guide Ecology Study for Exam 2 - • Chapter 10 -- Population dynamics (pages 226-248) • Demography -- Life tables (lecture, Tuesday 9/27) • Demography -- Fertility tables (lecture, Thursday 9/29) • Application 1 -- Human demography (lecture, Tuesday 10/4) • Chapter 11 -- Population dynamics revisited (pages 249-269) This study guide contains the following • Highlighted Lecture and Book notes (in OneNote) • Example problems Link to OneNote, which has additional study materials (link at the end of this study guide) Introduction to Populations Chapter 7 • Population ecology: The study of the relationships between populations of organisms and their biotic and abiotic environments • Rationale: Before, we studied the adaptations of individuals to their environments, which allow them to survive and reproduce and form populations. • Now, we will study properties of these populations, remembering that they result from the evolved properties of individuals. • Population: A collection of individual organisms of the same species in a defined area • Most (large) species Species are well defined, based on various definitions of species. • One common definition is the Biological Species Concept, where individuals are of the same species if they interbreed in nature and produce viable offspring. • Whether organisms breed in captivity is irrelevant under this concept. Lions and tigers produce viable hybrid offspring in captivity, but not in What about brown nature despite bears in Russia and overlapping ranges, so are distinct species. Alaska? 1 AREA. Often arbitrary, set by researcher. “Populations” of Clematis fremontii var. reihlii . What is an individual? • At first glance, an individual should be at least as well- defined as a species. • For pioneers in wildlife biology, entomology, fisheries biology, etc., this was clear. 2 In principle, the individual fish can be counted, but what about the corals? (Ras Mohammed reef off Israel’s Sinai Peninsula) And how many plants are present here? (Bering Strait, Siberia) 3 Ecologists distinguish two kinds of individuals • 1. Unitary organisms: Zygote develops through a fixed series of stages, with a common form at each stage. (e.g., same number of eyes, legs, wings, etc.) – All vertebrates, insects, and mobile marine invertebrates (crustaceans, cephalopods, etc.) 2. Modular organisms: Zygote produces a module, which then produces more modules like itself, as building blocks. Here, body size and form are variable, depending on kind, number, and arrangement of modules, and the overall form typically branched, immobile. – Both vegetative and reproductive modules possible. – Higher plants, 19 phyla of marine invertebrates (corals, bryozoans, hydroids, sponges), many protists and fungi 4 • There are parallels between different kinds of modular plants and animals. • Here modular organisms that separate into unconnected parts as they grow. • Duckweed (top) • Hydra (bottom) Top: Freely branching organisms on a “stalk”:Japanese honeysuckle (left) and a hydroid colony. Bottom: Organisms that spread laterally: strawberries (left) and hydroid. Animals Plants 5 • Tightly packed colonies of modules • A tussock of spotted saxifrage, Saxifraga bronchialis • A segment of the hard coral, Turbinaria reniformis • Modules on a persistent, largely dead support. • Oak tree in which support is mainly dead woody tissues from previous modules • Gorgonian coral in which support is mainly heavily calcified tissues from earlier modules 6 Genet: The entire genetic individual from one zygote. Ramet: Asexually produced individual, capable of independent life • The root connections between trees may disappear over time, though they are still the same genetic individual, from the same seed. Genets or clones of aspen trees in the Coconino National Forest, AZ, can be distinguished by timing of bud break, flowering, or leaf fall. 7 Advantages of modular growth • Outgrow biological threats such as competitors and predators, as well as physical threats such as fire, wind throw, etc. • Avoid risky sexual reproduction, such as in prairies and marshes • Body size and form match immediate environment • Nearly immortal, though cells and tissues at any one time are relatively young • Dominate many communities, such as forests, grasslands, reefs • Tasmanian botanists have found the world's oldest living plant--a vast, low- World’s oldest plant? growing, one-of-a-kind shrub born Science 25 July 1997: Vol. 277, p. 483 43,000 years ago: Lomatia tasmanica (Proteaceae family), or King's holly. • It is more than 3X as old as the previous record holder, a 13,000-year- old box huckleberry in Pennsylvania, and ranges over 1.2 square km. • Discovered in 1934, it is the only one of its species. "We're trying to keep the exact location secret,”, but it lives in a rainforest in the protected World Heritage Area in southwest Tasmania. • It has shiny, dissected green leaves, 10 to 20 cm long with red flowers that bloom at the leaf tips; and about 200 stems. This specimen is sterile, propagating only by rhizomes. 8 The largest creature on earth? Giant Sequoia “General Sherman” Volume 55,040 ft , DBH 27.1 ft, Height 274 ft Maybe not? • “Tree-killing mushroom largest living thing ever found” Greenville News, 08/05/2000 • Armillaria ostoyae covers 2200 acres • Malheur National Forest, Oregon 9 Makgadikgadi grasslands in Botswana, southern Africa, after rains. Complications of modular growth • For the organisms: Physiology and growth are not regulated by central organs (e.g., heart, brain) but rather in a distributed fashion, which provides flexible responses to environment • We exploit this, for example, with hedges and topiary such as here, with a modular dragon! • For us: Taxonomy must be based on single modules (e.g., leaves, flowers), not total form. 10 Life History Diversity Life history patterns vary within and among species. The differences may be due to genetic variation or environmental conditions. Generalizations about life history traits of a species can be made. The life history strategy of a species is the overall pattern in the average timing and nature of life history events. It is determined by the way the organism divides its time and energy between growth, reproduction and survival A typical life history for a unitary organism 11 Life history traits • Maturity - age at first reproduction • Parity - # of episodes of reproduction • Fecundity - # of offspring produced per reproductive episode • Senescence (aging or termination of life) • In general, because time, energy and other resources are limited, there are tradeoffs between these variables. Figure 7.3 Life History Strategy 12 Life History Diversity Life history traits influenced by genetic variation are usually more similar within families than between them. Natural selection favors individuals whose life history traits result in their having a better chance of surviving and reproducing. How and why have particular life history patterns evolved? The theoretical ideal: Life histories are optimal (maximization of fitness). Life history strategies are not necessarily perfectly adapted to maximize fitness, particularly when environmental conditions change. Classifications of life cycles I. Based on expected lifetime • Annuals - live one year. – Senescence or aging genetically determined – (many insects, other inverts, plants, some verts) • Perennials - live more than one year – Senescence or aging not genetically determined – Different age classes coexist in population – (most vertebrates, higher plants, many inverts) • Biennials (Biannuals) - live two years then die 13 • Desert in bloom. • In desert areas where rain is rare and unpredictable, a dense and spectacular flora of short-lived annuals commonly develops after rains. • They often complete their life cycles in little more than a month, producing dormant seeds to wait for the next rains. Classifications of life cycles (cont.) • II. Based on frequency of reproduction • Semelparity (semelparous) - breeding only once in a lifetime, often in a massive, single, – suicidal effort – (Many insects and other invertebrates, salmon, many plants including annuals, biennials, perennials) • Iteroparity (iteroparous) - breeding more than once – Usually show restraint, balancing benefits from increased current reproduction with costs of decreased future reproduction (most vertebrates & perennial plants) 14 Some life histories for perennial species: seasonal breeder, continuous breeder, semelparous breeder. Variation in life histories • Moreau (1940s) noted that songbirds in the tropics lay fewer eggs (usually 2 or 3) than their relatives at high latitudes (4 - 10) • David Lack first suggested that this and other variation within and between species may be adaptive. • He related life history traits to fitness, showed that they vary with the environment much as morphological traits do, and suggested experimental tests. • Cole's paradox showed that annual and perennial habits may yield similar outcomes. 15 concepts Mindlessmastery Plant intelligence Anthony Trewavas roots, tissue cell numbers andtypes, canall vary hugely. Monoecious plants canchange orcenturies,plantshavebeenregardedas frommaletofemaleandbackagain.Environ- Traditional definitions of intelligence passive creatures. Their development is mental influences on the parent can show use movement as a criterion. But F thoughttobepredetermined, withonly their effects three, four, eventwenty genera- temporaryinterruptionsinresponsetostress. tionsdowntheline.Buttheprimaryvariation are the adaptive behaviours shown Because plants lack obvious visible move- comesfrommodulardevelopment,therepet- by individual plants also ‘intelligent’? ment,theyseemtobebereftofbehaviourand itive programme that generates enormous intelligence. Yet they dominate every land- numbersofleaves,buds,flowersandroots.A competitive neighbours using near-infrared scape,representing99%ofthebiomassofthe plant canconsist of one bud, one leaf anda light,predicttheconsequencesoftheiractivi- Earth. There is a clear conflict betweenthe flower,ormillionsofthem;thesameistrueof ties,andifnecessarytakeavoidingaction.The commonlyheldviewandthesuccessofplant roots.Wesimplydonotunderstandthisorga- shape, growthanddirectionof the stemare life.Onlynowarewebeginningtoexposethe nizationalplasticity,butplasticityisforesighalteredtomaintainanoptimalpositionrela- remarkable complexity of plant behaviour. Plantscontinuouslyscreenatleast15dif- tivetosunlight;leafpositionsareadjustedto Arevolutionissweepingawaythedetritusof ferentenvironmental variableswithremark- optimize light collection. Whencompetitive passivity, replacing it with anexciting dyn- ablesensitivity— a footprintonthesoilora neighboursapproachthestiltpalm,theentire amic—theinvestigationofplantintelligence local stone, for example, are perceived and plant simply moves away by differential isbecomingaseriousscientificendeavour. actedupon. Weeitherknoworcanguessthe growthoftheproprootssupportingthestem. From their evolutionary beginnings, receptorsformostofthesesignals,whichare The rhizomes of individual clonal herbs photosynthesizing plants eschewed move- transducedinfractions of a secondthrough (prostrate stems that carry buds and roots) ment because light was freely available. But largenumbersofsmallGTPases,secondmes- can select a habitat by growing into and colonizationofthelandmeantthatessential sengers anda thousandproteinkinases. The foraginginareasthatare free ofcompetitors resources were distributed as a spatial and flowofinformationiscontinuous.Integrated and/orhaverichresourceconditions.Manyof B temporalmosaic, andcompetitionfor them responses are constructed after reference tothe buds change fate anddevelopintoleaves O becamemorefierce.Forthesessileplant,new thebankofinternalinformationthatspecifies insteadof rhizomes, but a searchcapacity is Y formsofbehaviourevolvedtoallowefficient theplant’secologicalniche. maintained as other rhizomes of the same E A foraging inthe local environment. Growth But coordinatedresponses require com- plant elect togrow intopoorer soils where R (andembryogenesis)continuedthroughout munication, and research in this area has theythinout,growmorerapidlyanddisperse. C the life cycle but insteadof a predetermined exploded. Internally, plant cells andtissuesRootstrackthree-dimensionalhumidityand P programme,developmentwasadaptedplas- communicatewitheachotherusingproteins; mineral gradients in soil with explosive A ticallytorespondtochangingenvironmental nucleic acids; many hormones; mineral, growthresponseswhenresource-richpatches K A resourcesandcharacteristics. chemical, hydraulic, mechanical, oxidative areencountered,butdeliberateevasiveaction F Theshapesandformsofstems,leavesand and electrical signals; peptides; various istakenwhencompetitors’rootsapproach. lipids; sugars; wall fragments; and other Thedodder,aparasiticplant,assessesthe complexcarbohydrates. Quitehowindivid- exploitabilityofanewhostwithinanhouror ualplantcellsaccommodatethisprodigious twoof its initial touchcontact. If these are amount of informationis not understood. deemedtobe insufficient, the plantcontin- Butevenanatomicallyuniformcellsexhibit ues searching for other, more profitable, enormously different responses toa single hosts. But if the decisionis made toexploit signal. A huge reservoir of individual cell the host, the dodder coils about it with a behaviours canbe coordinated toproduce particular number of coils (and eventually manyvarietiesoforganismbehaviour. suckers)thatdependsontheassessedfuture Buthowisthislinkedto‘intelligence’?As return. Severaldayslater, thedodder begins humans, we recognize intelligence by the totakeitshost’sresources. diagnostic of movement — but this is not a How is suchintelligent behaviour com- complete definition, as the chess-playing puted without a brain? Cellular calcium computer that beat Garry Kasparov made mediates most plant signals, and calcium veryclear. The functionofintelligentbehav- wavesinsidecellsoffercomputationalpossi- iourinanyorganismis,ofcourse,toincrease bilities. The challenge is set — remarkable fitness. Ifintelligenceisdefinedasadaptivelyyearsofdiscoverylieahead. ■ variablebehaviourduringthelifeoftheindi- AnthonyTrewavasisintheInstituteofCelland vidual, then, inplants, behaviouralplasticitMolecularBiology,UniversityofEdinburgh, bytheindividualiswhereintelligenceshould EdinburghEH93JH,UK. beapparent.Butsimplylookingforintelligent behaviour in ordinary greenhouse-grown FURTHER READING plants is unlikely to be productive. Chal- Silvertown, J. & Gordon, D. A.ev. Ecol. Syst. 20, lenging environmental circumstances are 349–366 (1989). requiredtoelicitintelligentresponsesbyany Sultan, S.ends Plant Sci. 5, 537–543 (2000). organism.Imaginativeconstructionofsitua- Bazzaz, F. A.nts in Changing Environments tionsinwhichplantchoiceandintentioncan (Cambridge Univ. Press, Cambridge, 2000). Theparasiticdoddercoilsaroundahaplesshost. betestedarenowprovidingrevelations. Stenhouse, D.e Evolution of Intelligence The growing shoot cansense its nearest (Allen & Unwin, London, 1974). NATURE |VOL415|21FEBRUARY200|www.nature.com 841 © 2002 Macmillan Magazines Ltd Population dynamics and demography - Chapter 9 - Emergent properties of populations • Density – Crude: # per unit area – Ecological: # per area of "suitable" habitat. • Dispersion – Random, spaced (regular) or clumped (aggregated) • Demography – Rates of birth, death, immigration and emigration – Derived measures such as growth rate, life expectancy, age structure, etc. • Other – Gene frequencies – sex ratio 1 Review: Measuring dispersion: three possible patterns Random - no attraction or repulsion to sites or individuals Regular - usually from competition for food, etc. Aggregated - to favored sites or to one another Review: Measuring total density • Some plants and animals are counted in their entirety (census) • O.herwise, we can estimate the total by – Plot and plotless sampling, scaled up to full population – Mark-release-recapture methods, • Can yield crude, first approximations to total density, • Or, with multiple captures and releases, more accurate estimates of density along with all factors that influence it: birth death, immigration and emigration rates. 2 * Estimating total density Plot Study - example: Mark – Recapture - example: Suppose you set up 100 traps and catch 20 3 mice, which you mark then release. 7 A few days later you open the traps again and 5 4 catch 30 mice, of which 10 are marked with dye. 9 How many mice are in the entire population? Counts in 10m x 10m plots2 1st estimate: 20 (number caught first night) with an average of 5.6/100M 2nd estimate: 40 (total caught in 2 nights) Best or 560 per hectare estimate, given date: 60, if we assume the proportion with marks in the recapture (10/30) = Plotless study - example: proportion with marks in the population (20/N) Pick random spots and navigate them. When you get there measure how far from that spot to the actual ‘thing’ you are measuring (plant or animal) and get the distance measurements. This determines density. Sometimes researchers will individually mark animals, with paint, fur dye, ear tags, leg bands, etc., for more accurate estimation of population processes, including demography, dispersal, reproduction, etc. 3 Measuring density (cont.) • Relative density – When estimates of true density are not needed. Instead, collect samples with constant but unknown relationship to density – Effort • # of lynx and hare pelts purchased by Hudson Bay Company • # of fish captured per boat per day – Traps • # of small mammals/100 trap-nights • # of moths per light trap – Area based samples • # of fecal pellets per unit area by plot or plotless sampling • # of bird vocalizations per transect Why do we study population dynamics? • Why? – Is a quantitative science • How? – Start with idealized, simplified model, because • 1. Heuristic (teaching) role: illustrate key points • realistic, but more complex models • 3. Sometimes describe behavior of complex Chinook Salmon run on the Columbia River models well • More generally, a mathematical model reveals all assumptions, is easy to check, solve, and modify. • In building more complex models, generally seek compromise between simplicity and realism. 4 Why population modeling • We derive models for population growth, competition, predation, and disease, all in discrete generations, and therefore using only algebra, and show how to find equilibria and stability properties. • We also teach demography, to better understand human population growth, and to follow (and copy) the * analyses carried out by Example: Will this biologists charged with endangered Australian managing game or marsupial increase in endangered species. number over time, if measured birth and death rates remain the same? No worries, mate! Density-independent growth of a semelparous annual (simplest case): Assumptions 1. All live one year, reproduce at same time, then die – All individuals are the same age. – Time is discrete, integer valued, not continuous. – Algebra is sufficient to solve all models. 2. All individuals have same reproductive abilities, each produces λ surviving offspring before it dies. – No differences in intrinsic properties (health, size, genes) – Or in extrinsic properties (territory, habitat, status) 3. The population is closed. – No immigration or emigration, only births and deaths matter 4. Density independent growth – Each individual has the same fertility and survival whether density is low or high 5 Density-independent growth of a semelparous annual (simplest case): Solution • N i # of individuals in the population at year i – N = λ N 1 0 2 – N =2λ N = 1 [λ N ] =0λ N 0 – …. – N =tλ N t-1 λ [λ t-N 0 = λ N 0 • N 0s the initial condition, λ is the parameter, and t is the variable. More general models have more of each. • The solution depends only on λ, which is called – Finite rate of increase – Multiplicative growth factor per generation – 1 + annual compound interest rate • A population increases in proportion to its size: at a 10% annual rate of increase: a population of 100 adds 10 individuals in 1 year, while a population of 1000 adds 100 individuals in 1 year This is a model of geometric growth, sometimes also called exponential growth. It's solution has three graphs, depending on whether λ >1, λ =1, or λ <1. (Note λ (Lambda) is approximately = 1+r) Itt * * * 6 The human population is often held as an example of . exponential growth, though it is not a perfect example. This model was derived for annual species. How do we predict the population dynamics of perennials? We need to measure birth and death rates as they vary with age. This demographic approach seems hard bu. often simplifies to the geometric growth model above. 7 This introduces a new topic: Demography • Study of the "vital rates" of a population, of births, deaths, immigration and emigration, often by age, location, social class, etc. • X = age interval or class (by year or other interval) – (= stage of development, especially in poikilotherms) – (= size class, in modular organisms such as trees) • N = # of individuals in age (stage, etc.) class X at time t – (= raw data) • C x, tProportion of individuals in the population that are in age class x at time t – (# in age class X )/(# in all ages classes at t) • Age distribution = Set of all C x, tlues at time t Age distributions of three countries 8 Mortality • Life table: An age-specific summary of the mortality rates in a population. We use three related measures, each calculated for every age X. • Age-specific survival rate – S x the proportion of individuals age X that survive to become age X+1 • Age-specific mortality rate – Q x the proportion of individuals age X that DON'T survive to become age X+1 • Survivorship – definition, L = 1.0.) newborns (age 0) that survive to age X (By 0 • All three measure the same process in the same population, so it is natural that any one measure can be calculated from the others. Comments on survival measures • The shape of survivorship curve is an emergent property of a population, which reflects how, and how well, individuals are adapted to their environment. This is true also for the fecundity curve, and the two curves influence each other. *• If the age specific survival S is the same at every age, then the L curve is exponential decay x x • Life tables introduced to ecology in 1921 by Raymond Pearl, and are now used to ask – are there differences in survivorship between sexes – between sites or times – under different management or experimental plans – where in the life do significant mortality risks occur – or, if births are also known, what are the prospects for a population, and how should it best be managed. 9 Pearl recognized three "typical" survivorship curves on a log scale, showing the effects of positive-, zero-, and negative-ageing, respectively. * . Species with Type I, II, and III Survivorship Curves Some examples 10 Life tables can be calculated in several ways. • Cohort (= dynamic) life table: – Follow a cohort of individuals (of the same age), through life and record the fraction still alive at every age = Lx – Accurate but takes a lifetime, & rates may change. • Vertical (=static = snapshot) life table: – Measure age distribution Cx at a single time, and assume it equals the survivorship curve Lx. – Faster, but only accurate if both density and age distribution are constant. Proof by demonstration. • Dynamic-composite life table (= mixed life table): – Combine data from multiple cohorts and years. – Common compromise, but may still be wrong Cohort life tables on wild populations are rare. A cohort life table takes a lifetime (of the organism) to measure, and Survivorship curve for the 1978 is obtained only for species of cohort of Cactus finches on Daphne Island, Galapagos interest, as with Cactus finches on Daphne Island, Galapagos, by Note this trend Peter and Rosemary Grant 11 A vertical or snapshot life-table is based on the current distribution in the population. It is easy to measure, and often wrong. Classic example of a mixed life- table (with multiple cohorts and years) for Dall mountain sheep * Demography continued – Chapter 9 Survival, reproduction, and their joint effects on populations Fecundity tables • Age specific summary of birth rates in a population) – physiological natality (maximum possible) – realized natality (actual observed, in given density, population, environment, etc.) – in human studies, demographers also distinguish number of pregnancies from number of live births. *• Note that I use fecundity, fertility and natality interchangeably (demographers are more careful), and count only live births. • Fx= Fertility at age (stage) X. – (= Ave. # of offspring produced by an individual age X, while in age class X), OR – (= Ave. # of female offspring produced by a female age X, while in age class X. 1 Comments on fecundity tables • There is no classification of fecundity curves, though they reflect age at maturity, parity, senescence • F values can be estimated by cohort, static or mixed studies, with all the same comments. • Sometimes we aggregate age classes, to yield total (crude) birth and death rates in the population: • Crude death rate: total # of deaths per unit time/total # alive (e.g., 10 deaths per year/1000 alive) • Crude birth rate: total # of births per unit time/total # alive (e.g., 30 births per year/1000 alive) • Interest rate: Crude birth rate - crude death rate (e.g., 30 births - 10 deaths = +20 /1000 or 2%/yr) We can combine age-specific birth and death schedules for predictions. Suppose our population has the following: * 2 * If we repeat this process over a number of generations, three patterns emerge • In a closed population, if the Lxand F vxlues are constant (density independent), then in time three patterns will emerge: • I. The population will achieve a stable age distribution (SAD), at which point (and not before!) • II. the total density (individuals of all ages) will grow geometrically, N 1 λ N 0 and N = λ Nt t 0 • III. The density in each age class will also grow geometrically, and at the same annual rate λ. • These results were proven mathematically, but are most easily demonstrated by example. 3 In a closed population, the age-specific birth and death rates determine the population density and age structure. * Recall, a population will grow or shrink if λ>1 or λ<1, but we can’t easily calculate λ for age- structured populations. What to do? * But we can calculate a related growth rate from age-specific birth and death schedules • R 0 Net reproductive rate (NRR) = Average # of female offspring produced by a female in her lifetime = multiplicative factor per generation = R, the multiplicative growth factor per year, only for annuals • R 0 (Prob. of surviving from birth to age 0 x fecundity at age 0) + (Prob. of surviving from birth to age 1 x fecundity at age 1) + (Prob. of surviving from birth to age 2 x fecundity at age 2) +… • R 0 L x0F + 0 x 1 + L1x F 2 …..2 • Clearly, population growth will be down, constant, or up, respectively depending on whether R <1,0R =1,0or R >1. 0 * Example of the calculation of both NRR and generation time T. Here R 02.1 and T = 4.1 yrs, so the population will double every 4 years. Note: T can be defined several ways: 1) average age at parenthood (cohort) as here, or 2) the average parental age at birth (static analysis) 5 • Suppose you were managing this endangered species, and measured these survivorship Lx and age specific fertilityxF (here M xere) curves • Will a closed population with these vital rates grow on its own? • If not, what actions will be most helpful? No worries, mate! review 6 Leadbetter’s possum can recover with current birth and death schedules Demography of the Yellow- stone Grizzly population Yellowstone National Park’s grizzly bears are long-lived and both critical and difficult to study. Here are long-term demographic data from Knight and Eberhardt (1985) showing age specific survival and fertility, for 3 year age-intervals. 0.9 In the long-term, will births exceed deaths, so that 0.8 0.7 the population will increase? 0.6 0.5 0.4 Survival 0.3 0.2 0.1 0 1 2 3 4 5 6+ 0.8 0.7 0.6 0.5 0.4 Fertility 0.3 0.2 0.1 0 1 2 3 4 5 6+ 7 * Review these slides Predicted demographics, from the field data on Yellowstone’s Grizzly bear populations. Here: R = 0.9995. What does it all mean? Projections without demographic stochasticity (left), and with it, for 1 and 25 simulations. How accurate are these data? What are sources of error? Are there limits to these simulations? What other factors could managers consider, in their planning for the long- term health of this population? 8 The relationship between annual and long- term growth rates • The growth rate over a generation of T years, R , is equal 0 to the annual growth rate λ compounded for T years. N = R N but also N = λ N T T 0 0 T 0 Therefore, R 0 λ , and taking logs of both sides yields Log eR )0= T Log (e), or Log eR )0T = Log (e) • But λ = 1 + r, where r is the annual compound interest rate, and Log (λ) = r, approximately, so that we have a relationship between annual e interest rate, family size, and generation time. • r = Log (R ) / T, or, in words, e 0 • Annual interest rate = log (family size)/generation time • Clearly, generation time has stronger influence on r. The relationship between annual growth rates and doubling times • We are interested in how long it takes for N to grow to N = 2 N given R. 0 T 0, • 2 N 0 R NTd 0.Cancel the common term and take natural logs. • Log e2) = T Ldg (λe, or • Since Log (e) =0.7 and Log (λ)e= r, t.e annual interest rate, we get • T d 0.7 / r • Therefore, a population growing at 10%/yr (that is, with r = 0.1) will double in size in Td=7 years. 9 More comments on the growth of age- structured populations • Stable age distribution is related to the survivorship curve in a simple and important way. Learn. • Only two things are happening in the population: individuals reproduce (F )xand die (L ,xS ox D ) xff. All other measures are derived from these: • λ, R , r, T, Td 0 • Stable age distribution • Life expectancy: Average number of years left in life, defined for individuals of each age x. • Reproductive value: Average contribution made to the next generation, defined for individuals of each age x. 10 Application of ecology I. Human demography (Chapter 9) Mexico City Human population growth is often described as exponential, though it is not quite. In exponential growth (decay) the doubling time (halving time) is constant….. Another view: World population growth in billions Number of years to add each billion (year) All of Human History (1800) First Billion 123 (1930) Second Third 33 (1960) 14 (1974) Fourth Fifth 13 (1987) Sixth 12 (1999) 14 (2013) Seventh 15 (2028) Eighth Ninth 26 (2054) Sources: First and second billion: Population Reference Bureau. Third through ninth billion: United Nations, World Population Prospects: The 1998 Revision (medium scenario). 2 UN Projections of Human Population Size Estimates of the world carrying capacity: What do you think? How can we measure? An early but still relevant analysis . Population growth cannot continue indefinitely, and will stop because of or despite our plans * 4 Trends in urbanization, by region (%) • The world is becoming increasingly urban. By 2010, half of the world’s population lived in urban areas, (in towns > 2,000). 84 83 • World regions differ greatly in 75 75 levels of urbanization. 60 53 54 55 • In more developed regions and 47 41 in the Caribbean and Latin 30 37 38 America, over 70 percent of the population is urban, whereas in 15 17 Africa and Asia, u:der 40 percent of the population is urban. By 2030, however, the urban proportion of these two World Africa Asia Latin America/More regions will exceed 50 percent. Caribbean Developed Regions 1950 2000 2030 • By 2030, roughly 60 percent of the world’s population will be living in urban areas. Source: United Nations, World Urbanization Prospects: The 2001 Revision (medium scenario), 2002. Trends in largest cities worldwide • The largest cities in the world are growing rapidly, and shifting from the more to less 1960 2000 2015 developed regions. • In 1960 the three largest cities 27 were in more developed 26 countries; by 2000, only Tokyo 23 23 remained in the top three. 18 18 14 • In 1960, New York was the 11 largest city in the world, with 9 14 million people. London TokyNew Sao Mexico Tokyo Mumbai Dhaka Tokyo • By 2015, the largest city York PauloCity (Bombay) worldwide is projected to be Tokyo, with nearly double this population size: 27 million. 5 China commits to 11 megacities by 2025 They will contain 250 million people. The largest, Jing-Jin-Ji, would be the size of England, France and Estonia and support 130 million people (twice the population of France). Iftht were a country, it would be the 10 most populous on Earth. 6 Signs of a growing human population The economic center of the map is shifting once again – this time toward the East. • In 1,000 A.D., the economic center of the world was in central Asia, west of China. By 1900, it had shifted to northern Europe, due to the industrial revolution. • By 1950, it had reached its westernmostpoint, reflecting America’s dominance in manufacturing and agriculture. • In the past decade, it has From Urban World: Cities and the Rise of the shifted to northern Russia. By 2025, it may return to central Consuming Class, by the McKinsey Global Asia – just north of where it was Institute, calculated by weighting national a thousand years ago. GDP by each nation’s geographic center. 7 What are the causes for rapid population growth? - Obviously, more Stage 1 Stage 2 Stage 3 Stage 4 births than deaths Birth rate -But modernization? Natural increase -Industrialization? Death rate - Urbanization? Time µ Demographic transition theory - Public health? This pattern occurs worldwide, though slowly and not always for the stated reasons. Rates of birth, death, and natural increase per 1,000 population 40 35 30 25 Natural Increase 20 15 10 5 0 1936- 1946-1955-1960- 1965-1970-1975-1980- 1985-1990-1995-2000- 1938 1948 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 BirthrateDeathrate Source: United Nations, World Population Prospects: The 2002 Revision (medium scenario), 2003. 8 • Problem: The demographic transition took nearly 2 centuries in Western Europe • Overall, birth and death rates have been declining worldwide • But these changes have been in parallel, so population growth continues. Notes on Birth and Death Rates, worldwide Birth rates and death rates are declining around the world. Overall economic Average number of children per woman development, public health programs, and improvements 8.2 in food production and 7.0 6.9 distribution, water, and 6.7 6.6 6.3 7.0 sanitation have led to dramatic 6.0 5.8 declines in death rates. 5.5 5.1 4.3 3.5 And women now have fewer 3.3 3.0 children than they did in the 2.4 2.3 2.4 1950s. Still, if death rates are lower than birth rates, populations Bangla- Egypt India Indo- Iran Nepal PakistaTurkey Yemen will continue to grow. desh nesia 1950-192000-2005 Also, it is possible for absolute Source: United Nations, World Population Prospects: The numbers of births to increase 2002 Revision (medium scenario), 2003. even when birth rates decline. 9 Total fertility rates (ave # of births/woman) 10 Places With the Lowest Birth Rates Worldwide Average number of children per woman, 2000-2005 Hong Kong Special Administrative Region 1.00 Latvia 1.10 Bulgaria 1.10 Macao Special Adminstrative Region 1.10 Slovenia 1.14 Russian Federation 1.14 Spain 1.15 Ukraine 1.15 1.15 Armenia Czech Republic 1.16 Source: United Nations, World Population Prospects: The 2002 Revision (medium scenario), 2003. 10 Death Rates: Life expectancy is increasing, in most regions. • Infants born now can 76 expect to live 65 years — 67 70 71 up nine years since the 59 65 54 56 late 1960s. 44 49 • Asia has experienced the largest increase in life expectancy since the late 1960s: from 54 to 67 yrs. 0 Africa Asia LatinMore DevelopWorld • Life expectancy varies America/CariRegions widely by region. In more 1965-12000-2005 developed countries, life expectancy averages 76 Life Expectancy at Birth, in Years years, compared with only 49 years in Africa. Source: United Nations, World Population Prospects: The 2002 Revision (medium scenario), 2003. Life expectancy varies dramatically between (and within) countries 11 And is closely tied to wealth. Here, life expectancy vs. GDP (WHO data) 0 This relationship is true for the US also. Notes on Trends in Aging, by World Region Population Ages 65 and Older - Percent By 2025, over 20% of the population in more developed 21 regions will be > 65. 14 By 2025, one-tenth of the 11 world’s population will be > 10 10 7 6 65. 4 6 3 Asia will see the proportion of its elderly population almost World Africa Asia Latin More double, from about 6 percent America/ Developed in 2000 to 10 percent in 2025. Caribbean Regions In absolute terms, this 20002025 represents a stark increase in just 25 years: from about 216 millio. to nearly 475 million Source: United Nations, World Population Prospects: The 2002 older people. Revision (medium scenario), 2003. Still, population growth continues, especially in less developed countries. Why? Billions 10 9 8 7 6 5 4 3 Less Developed Countries 2 1 More Developed Countries 0 1950 1970 1990 2010 2030 2050 Source: United Nations, World Population Prospects: The 2002 Revision (medium scenario), 2003. 13 Limitations to population control. I. Access to birth control still a problem: Desire for Smaller Families . Women With Two Children Who Say They Want No More Children Percent 60 tracked 59 52 50 38 33 29 29 22 13 Bangladesh Egypt Guatemala Kenya Zimbabwe Late 1980sLate 1990s/Early 2000s Source: ORC Macro, Demographic and Health Surveys, 1988-2000. Limitations to population control. II. Adult Literacy by Region • Nearly all men and women in more developed regions can read and write. 90 85 88 83 • Literacy rates are lower in the 74 69 68 72 less developed regions. 51 • Women’s literacy rates vary 48 significantly by region: from 51 percent in Africa, to 68 percent in Asia, to 88 percent in Latin America and the Caribbean. World AfricaLatin AmericaAsia Arab States/ • Overall, more men than women Caribbean North Africa are literate. This is especially FemalMale striking in the Arab states and North Africa. Literacy Rates, by Sex, 2000 Percent Source: UNESCO Institute for Statistics (www.uis.unesco.org). 14 Limitations to population control. III. Cultural and demographic inertia Population Structures by Age and Sex, 2005, in millions Less Developed More Developed Regions Regions Age 80+ 75-79 70-74 65-69 Male Female Male Female 60-64 55-59 50-54 45-49 40-44 35-39 30-34 25-29 20-24 17-19 10-16 5-9 0-4 300 200 100 0 100 200 300 300 100 100 300 Source: United Nations, World Population Prospects: The 2002 Revision (medium scenario), 2003. Notes on world’s age distribution • Less developed countries have younger populations, due to past high levels of childrearing. The fraction younger than 15 years old can range from 33 - 50%, but is < 20% in developed countries. • In less developed regions, > 2 Women aged 15-49 and Fertility billion people are below the age 90 87 82 2 20; these are future parents! 79 79 77 1.8 80 75 73 69 70 1.6 60 1.4 • There is a lag between changes in the 1.2 rate of growth and the net increase in 50 40 1 population per year. 0.8 30 0.6 20 • From 1985-1995, the population 0.4 10 0.2 growth rate declined yet the net 0 0 increase in the world’s population 1980-1985- 1990- 1995-2000- 2005-2010- 2015- 1985 1990 1995 2000 2005 2010 2015 2020 peaked in 1985. Net population added Annual population growth rate 15 Population in Countries With Low Fertility Decline or Growth, 2002-2025 Percent Country (average number of children per woman) 12 China (1.8) South Korea (1.4) 6 3 Trinidad & Tobago (1.6) -8 Italy (1.2) -14 Russia (1.1) -17 Bulgaria (1.1) Source: United Nations, World Population Prospects: The 2002 Revision (medium scenario), 2003. Notes on Population in Countries With Low Fertility • All countries shown above have below “replacement level” childbearing —the level required for population to ultimately stop growing or declining. Yet, half will continue to grow and half are pro
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