Introduction to Ecology
Introduction to Ecology EVE 101
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This 15 page Class Notes was uploaded by Raven Connelly on Tuesday September 8, 2015. The Class Notes belongs to EVE 101 at University of California - Davis taught by Thomas Schoener in Fall. Since its upload, it has received 77 views. For similar materials see /class/187320/eve-101-university-of-california-davis in Evolution And Ecology at University of California - Davis.
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EVEl 01 Lecture 6 Part I Page 1 Lecture 6 Outline Singlespecies population growth Readings Molles Chapters 1011 Part I I Introduction elements of population growth 11 Types of population growth 0 A Exponential geometric Density independent PG 0 B Logistic Density dependent PG 0 C Examples of exponential and logistic population growth 0 D Mechanisms of density dependence 111 Simple models of population growth 0 A Background 0 B Exponential C Logistic PG and density dependence 0 D Allee effect reverse density dependence Part 11 IV Demography 0 A Age structured population growth 0 B Life tables and estimating population growth rates V Reproductive strategies revised January 17 2008 Molles 4th edition pages 2008 Catherine A Toft EVE101 Lecture 6 Part I Page 2 Lecture 6 Single species population growth Part I Molles Chapter 11 I Introduction Elements of population growth We are now going to take a step quotbackquot and stop focusing on the individual Instead we will focus on the population a group of individuals and look at the sum of all individuals39 behavior physiology survival and reproduction collectively A population is a group of individuals and population quot growthquot is the change in numbers of individuals with time at a given place This change in numbers of individuals with time is the result of the collective births and deaths there and immigration to and emigration from that place This definition allows us the flexibility to talk about positive quotgrowthquot increase in numbers of individuals with time or negative quotgrowthquot 2 decrease in numbers of individuals with time Population growth is also referred to as population quotbehaviorquot or quotdynamicsquot First we consider a population to be mostly closed with only a little immigration or emigration so we can concentrate on the birth and death terms of population growth In other words the contribution of birth and death of individuals will outweigh that of individuals coming into immigration or leaving emigration the population from an unknown quotoutsidequot world In more advanced courses in ecology you will learn about the concept of metapopulation Ch 102 which is a group of local populations connected by some degree of immigration and emigration In studying the metapopulation we focus away from the local birth and death processes assuming that we understand them well and focus instead on the movement of individuals between populations immigration and emigration When do we need to the metapopulation scale also called landscape scale Molles Ch 21 We need to consider a larger spatial scale when there is marked spatial heterogeneity in birth and death rates For example within a species a local population might be increasing at a fast rate birthsgtgt deaths in one area and another local population might be declining births lt deaths somewhere else To understand the dynamics of the entire global population we have to consider all the local populations separately and consider dispersal among them If there is not much spatial heterogeneity we can learn what we need to know about a certain species by studying a fairly average local population and in doing so we can focus n birth and death processes instead of immigration and emigration We will concentrate on local processes in EVE 101 Everything we ve talked about in the unit on individual ecology leads to population growth Assimilating energy from food getting mates surviving predation elements and so on all lead to the positive term in population growth that is to having offspring Alternatively old age and death from hazards during feeding and reproduction predation death from elements etc all lead to the negative term in population growth We can ask then What is the rate at which new individuals are produced and what is the rate at which individuals die 2008 Catherine A Toft EVE101 Lecture 6 Part I Page 3 Thus Birth minus death is the basic equation for population quotgrowthquot rates Note again that quotgrowthquot could be positive growth rategt0 where birthgtdeath 0 where birth 2 death or negative growth ratelt0 where deathgtbirth 11 Basic types of population growth We can isolate two simple descriptive patterns in population growth 39 A exponential logarithmic or geometric the per capita growth rate is constant ie density independent 39 B logistic asymptotic or sigmoidal the per capita growth rate varies with population density ie density dependent A Exponential or geometric population growth Lecture handout Molles Ch 111 pp 255 259 There is a constant per capita per individual population growth rate birth minus death This means that the per capita growth rate does not change with the density of the population ie numbers of individuals already there In a few more pages we will go into what this means in detail For now notice that in the arithmetic plot on the left the population size gets larger by a larger amount in each time step the plot curves upward quotfaster than linearlyquot This is because of the effect of quotcompoundingquot in the way money left in a bank account earns interest the money added to the account new individuals born in the previous time step earns interest give birth at the same per capita rate making even more new individuals in the next time step Geometric or exponential Both categories of population growth are defined by a constant per capita population growth rate Geometric population growth occurs in discrete steps such as in annual plants with non overlapping adult generations or in populations with highly seasonal periodic reproduction Exponential population growth better fits continuous population growth with adults of varying ages and reproduction occurring continuously or nearly so such as happens in the human population The per capita rate of increase in geometric population growth is traditionally given the symbol Greek quotlamdaquot A or capitol R either of which is also called the quotnet rate of increasequot The per capita rate of increase in exponential population growth is traditionally given the symbol quotlittlequot or lower case r which is also called the intrinsic rate of increase or biotic potential 2008 Catherine A Toft EVE101 Lecture 6 Part I Page 4 When the per capita rate of increase is constant the total population growth rate not per capita is ever increasing if r is positive the population size is compounding logarithmicly Thus the logarthmic plot on the right p 17 lecture handout shows a straight line with a slope that is the per capita population growth rate births minus deaths in contrast to the quotarithmeticquot plot on the left If the per capita growth rate is positive births gt deaths in exponential logarithmic population growth there is no upper limit to population size If the per capita growth rate is negative then the population heads toward extinction there is a lower limit to population size and that is zero negative individuals are not defined see your lecture handout Because the per individual contribution to births and deaths is constant on average it does not depend on population density so we call this type of population growth density independent We therefore could consider this type of per capita population growth rate to be the biotic potential of this population Unlimited positive births gt deaths population growth is obviously not realistic forever of course Most organisms have the quotbioticquot potential for exponential or geometric growth as was first observed by the famous demographer Thomas Malthus a fact which greatly interested Charles Darwin and triggered his understanding of the process of natural selection The ways in which organisms quotfailquot to reach this potential was a basis for Darwin39s theory of natural selection and it is a basis for much of what ecologists study today ENVIRONMENTAL NOTE If only politicians and economists could reach the same insights they continue to View healthy economies as only those that growth continuously When economic growth slows we lament this as a quotrecessionquot We hear politicians using the oxymoron quotsustainable growthquot No one ever extols the Virtue of a steady state economy growth rate 0 which is the only kind that can be sustained indefinitely all the services39 in an economy must ultimately depend on the number of 39goods ie resources Read on to find out how natural populations are regulated Examples of exponential or geometric population growth Examples in lecture Molles Figs 113 117 115 1126 Examples of exponential population growth are usually new introductions of immigrations to an uncolonized place for example rabbits in Australia muskrats in Europe tule elk on Grizzly Island in California reindeer on St Paul Island and collared dove in Great Britain A few individuals found a population and population density is very low We see population growth regionally as an expanding population Population gets dense in one location and the individuals in the population disperse to new empty areas Fig 101 p232 103 105 p 234 142 p 329 in Molles Importantly no population can sustain exponential unlimited growth forever because eventually there are no new places to expand to and resources overall become limiting 2008 Catherine A Toft EVE101 Lecture 6 Part I Page 5 Examples of longer term exponential population growth include populations that were depressed for some reason and are now 39 39 r 39 y in r r 39 size such as that of the Scotch pine Pinus sylvestrus which was depressed after the last ice age Fig 106 see also Fig 1017 And then there is the infamous example of the human population Homo sapiens The human population The world population of humans has approximated exponential growth for much of its history showing no decrease in per capita population growth rate with increasing density of humans worldWide at least not so far The human population growth over a long period of time is actually not a perfect exponential because the per capita growth rate is not a constant Typically the per capita population growth rate has increased with increasing density because of advances in human culture aiding use of resources and developing human knowledge for example in areas such as medicine Thus the human population has actually grown at a rate faster than exponential Ecologists and demographers in particular Raymond Pearl thought that the human population had reached the inflection point of the logistic curve the place where the total population growth rate is maximum ie where the slope of the logisitic curve is at its maximum in the middle of this century Based on this assumption they projected a steady state size of the human population to be about 2 3 billion Unfortunately they were wrong The human population passed the 3 billion mark in 1960 with no suggestion whatsoever of an inflection In Winter 2008 there are 664 billion humans on the planet Fig 1126 p 269 in Molles The human population still seems to be growing approximately exponentially with a current doubling time of just over 40 years Lately the per capita population growth has decreased a little as a consequence of education and improving quality of life world wide However improving quality of life means a higher per capita consumption of resources so although the population39s growth rate in units of numbers of humans added per unit time is less the per capita impact on the planet s resources remains if anything greater Links for further information include 39 The US Census Bureau httpwwwcensusgovipcwwwpopclockworldhtml 39 Museum of Natural History in Paris France has an outstanding web site exhibit on the growth of the human population If you go to one site I recommend this one httpwww nnnexnn 39 We will see that most organisms DO NOT withhold their reproduction so as not to overrun the environment including humans Virtually all organisms will reproduce exponentially at slower or faster rates until they begin to encounter some limit imposed from outside either by 2008 Catherine A Toft EVE101 Lecture 6 Part I Page 6 resources or predation amp disease As we proceed we will learn how this regulation of populations takes place First and foremost be aware that self regulating individuals in a population cannot be favored by natural selection quotfor the good of the speciesquot or for the quotgoodquot of the environment This can never happen Why Definition of population regulation 1 the upper limit to population size imposed from outside this population or 2 any process by which a populations is limited in size 3 strictest of all the mechanisms by which the per capita population growth rate is density dependent decreases with increasing size of the population B Logistic sigmoidal population growth Lecture handout Molles Ch 112 3 pp 259 66 Logistic growth in contrast is population growth that slows down as the population size gets large When plotted as numbers of individuals against time logistic population growth appears as a S shaped or quotsigmoidalquot curve This type of population growth is almost exponential at small enough population sizes Then as population density increases the per individual contribution to births and deaths gets smaller and rate of population growth slows Eventually the population39s growth slows to zero and population size is unchanging with time because births 2 deaths We term this maximum population size the population39s carrying capacity This is densitydependent population growth That is the percapita individual population growth rate depends on the population density In the plot of N against time the higher the density the slower the rate of growth hence the quotflatterquot slope to the population quotcurvequot in the phase after early exponential type population growth Eventually the growth rate of the population decreases to zero and we observe the flat or asymptotic region of the population size plot We will look at more plots of per capita population growth when we use the population growth model below The reason for the densitydependence in births and death rates is virtually always some form of resource limitation there is not enough to go around Thus when we use the term quotdensity dependencequot in talking about per capita rates of population growth we mean that per capita population growth rate decreases with increasing density Examples of logistic growth Lecture Molles Figs 118 1115 We can follow new introductions deer in Tasmania yeast or paramecium in a laboratory culture Figs 119 10 or populations depressed by another form of regulation Kaibab deer after predators were eliminated African buffalo after rinderpest was eliminated Fig 1112 over an entire region and see the way the population eventually levels off because resources become limiting The per capita population growth rate is densitydependent meaning that as 2008 Catherine A Toft EVEI 01 Lecture 6 Part I Page 7 population density increases the per capita population growth rate decreases How this is accomplished varies but in general the birth rate decreases or the death rate increases or both As you can imagine density dependent processes are not pretty Sometimes the population overshoots the resources there and crashes Later we will try to understand these dynamics C Mechanisms for densitydependent population growth First let s make a list of the factors that can produce density dependent effects on population growth The list is from The Science of Ecology by Ehrlich and Roughgarden 39 1 Resource depletion and fecundity 39 a The amount of food available determines the growth rate and body size of an individual and the number of offspring tissue devoted to reproduction is related to body size Most common in organisms with indeterminate growth many insects and other invertebrates fish amphibians reptiles ie grow after they reach a reproductive size 39 b The amount of food determines how much you can put into reproduction at any given time If not enough or less you produce fewer eggs or offspring or you wait a year 39 2 Resource depletion and survival In these cases individuals starve to death or poor nutrition makes it more likely to die of predation exposure or disease Here the principle of allocation comes in the more time foraging animals or more physiological effort invested in growth or resource uptake the less effort an individual will devote to defense against predators 3 Space depletion Animals increase territory size when they face lower food availability and this may mean not enough room for everyone to have a territory If you don39t have a territory you don39t reproduce a situation common in many birds In sessile organisms individuals simply take up space until none is left 4 Increased time in social interaction Individuals spend more time defending territories as population size increases and less time foraging and mating this situation is common in many fish 5 Intraspecific predation or other harassment Many insects frogs salamanders etc will eat the eggs of others of their own species The more dense the eggs and the adults etc the higher proportion will be eaten Cannibalism 6 Densitydependent interspecific predation For example predators may use search images The more common a particular prey species predators eat it disproportionately So in that population of prey predation is greater at higher densities 2008 Catherine A Toft EVEl 01 Lecture 6 Part I Page 8 7 Migration or dispersal The higher the population density the more likely individuals are to risk danger or starvation and they head for new areas ie the quotlemming effect quot Actually populations are remarkably quotviscousquot meaning that individuals chose to stay near conspecifics even if that means some degree of detrimental crowding Even though they are territorial they stay together crowded in a space and defend territories against each other They could spread out more but they don39t for a variety of reasons However if population density gets too high individuals will gradually emigrate spread out All of the above emphasize when populations go from medium to highest densities Let39s consider one effect at the very very low to low densities 8 reverse density dependent or the quot Alleequot effect When population sizes are too low individuals can39t find mates or they can39t engage in normal social interactions Populations pushed below a threshold can go extinct because populations can39t increase in size unless the density of individuals is at the threshold for example Eskimo curlew Carolina parakeet both species were driven to extinction 111 Simple models of population growth A Background Ch 111 3 Now we will go over some simple descriptive models of population growth to try to understand how populations behave By population behavior we mean the pattern of numbers of individuals through time WHY MODELS Ecology is a quantitative subject so we use mostly simple mathematical models to try to describe understand and predict ecological phenomena Use of models absolutely essential for population studies Populations behave on a time scale and spatial scale that humans cannot directly observe and so have no natural intuition for You do not go into the field with a pair of binoculars and watch a population you can watch only individuals It39s hard for the human mind to sum over all births deaths etc over long periods and large spatial scales Instead mathematical models compress time and space and allow us to look at the cumulative effects of all factors affecting population growth so that we can get intuition and understand the process We watch for example a population behave on a computer screen not in the field Note again we use quotsimplifying modelsquot we begin with the fewest possible elements in our model and add until we get the simplest representation that explains the patterns of population growth rule of parsimony 2008 Catherine A Toft EVEl 01 Lecture 6 Part I Page 9 B Exponential population growth Molles ch 111 lecture handout Symbols N number of individuals in a certain area population size N0 number of individuals at the start time t0 t one time unit r 2 per capita birth rate b minus per capita death rate d b d quotintrinsic rate of increase 2 per capita rate of population growth e 2 base of the natural logarithms Rate of change in the population during a given time period t dNdt rN r is a constant so you get exponential growth see Molles Fig 113 6 We also call little r the quotinstantaneous rate of growthquot because time t is a vanishingly small instant of time and the quotbiotic potentialquot because it is the maximum possible population growth ie under conditions of unlimited resources Population size after a given time t N N0 equot is the solution to dNdt rN That is how many individuals you have after time t How does this work See Fig 113 p 256 You have some number N0 at the start of a time period and you want to know how many individuals you have at the end of the time period ie what is N You first have to estimate the per capita instantaneous intrinsic rate of increase r r b d which incorporates the per capita birth and death rates b and d You learn to do this later when we cover life tables in real life you can39t measure instantaneous rates but rather you count up births and deaths over a finite time interval the census period Because the population is growing exponentially you can compute mathematically how many individuals will be born or will die over that period t So you start with the original number No They give birth and die and offspring may also give birth and die and their offspring and so on over the time interval t We therefore multiply No the number you start with by the base of the natural logarithm raised to a power determined by the growth rate and the amount of time that has passed We raise the intrinsic growth rate r X the time t to this power of the natural logarithm because offspring born during the period t are themselves giving birth etc and 2008 Catherine A Toft EVEl 01 Lecture 6 Part I Page 10 quotcompoundingquot the production of new individuals in the same way that your bank account compounds interest giving you interest on the interest you earned etc This is why this form of population growth 1 is constant is called logarithmic population growth When you reduce the whole picture to rates in particular instantaneous rates you reduce time t to a very small number as t approaches 0 and use the science of calculus to predict population behavior C Logistic growth Ch 112 3 1 Basic Modellecture handout p 18 We will use a really simple minded totally descriptive but also very well studied equation to get a logistic curve Pianka39s book Evolutiona Ecology 5th edition has a very clear explanation on pg 187 on how the two scientists Verhulst and Pearl originally justified and derived this model First we postulate some population size N K which will be the upper limit of population density based on resource abundance We don39t care about the type of resources or the animal39s behavior we just pick a value K that describes the population s upper limit This is the asymptote of the sigmoidal logistic curve and it is called the carrying capacity of the environment quotCarrying capacityquot comes from Paul Erlington a wildlife biologist in this and other fields of ecology it was apparent that population size had some upper limit based resources available particularly during the worst time of the year during which the population goes through a quotbottleneckquot ie winter As N approaches K then NK approaches 1 and so 1 NK approaches 0 and K NK approaches 0 In other words these are all the possible ways to view the process of the population39s size approaching carrying capacity so that we can understand the effect on the population39s growth rate where ranal rmax 1 N K and r3 b0 1 NK d0 1 NK so that when N is high and close to K raml will become closer to zero as birth and death rates get closer to being equal The idea is that the per capita rate of growth of the population will slow down as the population nears K for various reasons we will talk about in a minute Now we can see that rmax your book uses rm m means maximum is the same thing as the quotplainquot r in the exponential growth model This rmax is the biotic potential because the per capita population 2008 Catherine A Toft EVEl l Lemm P3111 Pagell gym1h rate 1s maxn39mn39n wheh Individuals are me and lemmas are as ye1 m1de nanymg Capamty 1h Ellh r weeds pm is less than pm the clnser yhu get m x Let s 1mhhewa1 what 1h1s demiydependeme luuks hhe aha gmph and hewhehsny z DensnyDepen leme alnukmmmedetal 11ee1we hand ulpp 19 FDpula39J n Demw N snenanusare bmhsunly deathsunly andeveryvhngmbetween Numammhauhe exam s1upes ufthe bmhand death rate hhes 111216 1s a 1aee A1216 heyemss where 1m and paw pmm 1s the nanymg napamty K The hmue pmn lh rm 1s the gxeahestmffexeme between mks ani d M13112 gs 11 1415 p mun K The anm H 211th m the maxn39nmn e the bum puemah hh1y whehN 1s very sma11 e1hse m 2210 A1216 111216 1s oznnxcahenheATnn Fme Lemes Fan Page 12 at us maximum shave Lhs is pictured mLhB graph NltK then rmts whaUWlllN1mmasenrdecrease7L1kemse when NgtK rmts whatv W111 N thenmcrease Urdenrease7 We see thatwhenNltK ngta andwhenNgtK nltn se LhatN almys returns In K Ths pmpeny Dfxetummg t the same pmnt the same pupulaunn 5123 run matterwhat IS knuwn as an equmlm39um Ifwe leek at density dependence m the pnpulaunn s gmwvh me as a whale msmad e the per we getthts a the h m m n pletem agamstums mLhB luglsuc pt tptuw n ume We ean see that the maximum rate ngmunh efthe pnpulaunn dNdt Uncurs where the gmphnfthe Inglsuc Curvels steepest mm K12 D The Auee effect or reverse demity dependence leeture handnut e rm because the pupulanun IS almys at the maximum gmwvh me during expunenual n my n n m nh a function Dfpupulanun density N as we ean see mm the shave gmphs 92m camex m EVEI 01 Lecture 6 Part I Page 13 In that plot we see that that raml rmax occurs when N 0 there are no individuals at all and the density is at its lowest That is of course unrealistic Instead we would want dNdt 0 when N 0 and we can fix that problem on the graph on the page 23 of your lecture handou We might expect some populations at low population size to grow somewhat slowly for example if individuals cannot find mates because they are too rare or if some kind of social structure exists to protect individuals from predators or to compete for territories and food and so on In this more realistic plot the problem is fixed The population does not hit its rmax until some I39m tusl intermediate but low population size before normal density dependence is felt such as competition for limited resources This quotnormalquot density dependence is called direct density dependence ra decreases as N increases and the opposite of that is reverse density dependence raincreases as N increases The dotted line separates the region of reverse density dependence at low values of N from the region of direct density dependence at all higher values of N If you make the above plot work for you you see that as soon as you get one individual the population starts to increase births gt deaths until it reaches rmax at some intermediate population size N gt 0 and N lt K However how realistic is this In some species one asexually reproducing individual or one pregnant female might well be able to found a population that is this one individual has offspring and at least some individuals survive to reproduce Where the Allee effect has been tested in natural populations ecologists have found that indeed in many species one individual can found a population even if it takes a while for the population to reach its rmax we ignore genetic effects in this course to concentrate on demographic effects but a number of species in the wild do show little adverse effects of low genetic diversity In other species however the rarity of individuals in the population might have a strong effect on whether any can survive or give birth This effect might be particularly strong in social species in which some kind of social structure is necessary for successful foraging for defense against predators or for parental care Humans would be a good example but there are many 2008 Catherine A Toft EVEl 01 Lecture 6 Part I Page 14 more including many birds fish and mammals as well as insects such as colonial solitary wasps Even in species that are not strongly social just the challenge of finding a mate when individuals are rare might be extremely important to per capita population growth rates when population density is very low If the density of the population is too low the population species might not be able to achieve births gt deaths and it could go extinct We can add an extinction threshold to the Allee effect as follows I39M tllzal Do you see why NE is now an extinction threshold To do so make the graph work for you pick different values of N on the x axis and see what ranal is is it postive ra gt0 births gt deaths negative ra lt 0 deaths gt births or zero ra 0 births 2 deaths The value of ra will determine the trajectory of the population size N We can represent the trajectory of the population size by focusing only on the x axis which is the value of N and use arrows to represent time n allu jlurium ztalule or unstable We can see the meaning of quotequilibriumquot here we define equilibrium as the variable of interest N always returning to the same value The carrying capacity K is a good example of a stable equilibrium if N gt K then ra lt 0 and N decreases to K If N lt K ragt0 and N increases to K 2008 Catherine A Toft EVEl 01 Lecture 6 Part I Page 15 Through time N always goes back to K This is what is meant by a stable equilibrium What are the other two equilibrium points Answer 0 and NE N 0 is a stable equilibrium in a closed population with no individuals no more births or deaths can occur to change N The popular way to phrase this stable equilibrium is quotExtinction is foreverquot The other equilibrium NE is a completely different type of equilibrium known as an unstable equilibrium If N 2 NE then ra 0 so the population stays at this size But in real life there will always be variability in births and deaths As soon as N leaves this one point N gt NE then ragt0 and N goes to K or N lt NE then ralt 0 and N goes to 0 The equilibrium NE is unstable because population size always moves away from this point except in the unlikely case that N is exactly equal to NE NT is not an equilibrium point but is simply the population size that separates reverse density dependence Allee effect from direct density dependence At N lt NT ra increases with N reverse density dependence and at N gt NT ra decreases with N direct density dependence or simply quotdensity dependencequot What are some examples of species with strong reverse density dependence and possibly an extinction threshold with NE significantly greater than 0 The most spectucular extinctions of vertebrate species in North America include some possibilities including the passenger pigeon Carolina parakeet Eskimo curlew and heath hen all birds The American bison nearly went extinct and perhaps its NE was greatly lowered by our treating this species as domesticated cattle Can you think of other examples 2008 Catherine A Toft
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