Presentation on theme: "Population Regulation"— Presentation transcript:
1Population Regulation For all these questions about population growth and modelsdescribing it, the common observation in nature is thatmost populations of plants and animals seem to remainfairly constant in size from year to year…An important question in ecology is what mechanisms“regulate” or “control” population size?If those populations seem to be in equilibrium, are theynear K? What keeps a population near K?
2The most straightforward chain of argument goes… Increased NResources Become LimitingCompetition Among Individuals for ResourcesCompetition has Effects on Birth and Death RatesDoes this “regulate” or just limit population size?
3What is regulation?The ‘engineering-style’ definition:The amplitude of any perturbation to a variable at itsset point will be decreased by regulation to restore thevariable to its set point.A practical example:The thermostat in your house is set to a specifictemperature (“the set point”). Should temperature in yourhouse increase, the thermostat turns on your central airconditioning to bring the house temperature back down (orvice versa when it becomes to cold and the furnace isturned on).
4The idea that populations are “regulated” was highly controversial…There were two opposed schools…David Lack (e.g.1954) argued that population size wasregulated by food, predators, and disease, i.e. by bioticfactors.Andrewartha & Birch, at around the same time, claimedthat numbers were determined by factors extrinsic to thepopulation acting on it. For example, r is strongly affectedby weather.
5The data used by Andrewartha & Birch came from studies of thrips (Thrips imaginis) growing in roses. They were ableto predict population size from past size and weather in theprevious fall and current spring fairly well. They foundlittle evidence of density-dependence.
6Here are observed and predicted numbers at peak for a number of years, using only previous numbers and weatherfactors...
7They also showed that r was strongly affected by temperature and moisture, key variables in climatic pattern.Climate rcool & dry 0.01cool & moist 0.03warm & dry 0.01moderate & moist 0.1
8Does this mean that thrips are “regulated” entirely in a density-independent way? The possibility caused a longcontroversy. For this case, it was largely settled in 1961 byF.E. Smith…What would indicate density-dependence?1) What happens to per capitagrowth rate as the populationapproaches K? Per capita growthrate declines. So should thechange per unit time in lnN.Here’s what Smith found inAndrewartha & Birch’s data…(Oct. to Nov. is growth to peak)
92) Smith’s 2nd argument came from variance in population size and growth. A basic principle in statistics is that thevariance of a sum of two independent variables shouldbe the sum of the variances of the individual variables, i.e.Var (X + Y) = Var (X) + Var (Y)Look at population growth…ln N(t + 1) = ln N(t) + ln N(t)but in the data the varianceis much smaller as the meanN(t) (or ln N(t)) approachesits annual peak. Again, here’sthe figure showing that...
10For the negative relationship between numbers and the change in numbers as the peak density is approached tobe as strong as this, there must have been a stronglynegative covariance between the variables (ln N(t) andΔln N(t). That is exactly what would be expected inlogistic growth. Growth rate (or Δln N(t)) shoulddecrease as population size increases.
11The argument developed, in part, because of the kinds of species studied by supporters of the two points of view...Supporters of Andrewartha & Birch studied insects, forwhich growth and mortality are strongly affected byweather.Supporters of Lack generally were working with vertebratespecies, where behaviour (territory defense) and interactions(competition and predation) often apparently limit populationsize.
12Actually, this long lasting argument should never have occurred. Darwin expressed clearly how both abiotic(density-independent) and biotic (density-dependent) factorsinteract to determine population size and growth…“Climate plays an important part in determining theaverage number of species, and periodical seasons ofextreme cold or drought seem to be the most effectiveof all checks…The action of climate seems at first to bequite independent of the struggle for existence; but inso far as climate chiefly acts in reducing food, it bringson the most severe struggle between the individuals,whether of the same or distinct species, which subsiston the same kind of food.”
13There are many other examples of apparently density-independent dynamics in populations (many are studies of insects!).In a grain weevil, for example, the intrinsic rate of increase (r) varies 10-fold with minor changes in humidity and temperature in environmental chambers.Wouldn’t we expect insect growth, then, to be sensitive to environmental variation (drought, heavy rainfall, extreme cold or heat) in the real world?In the end, what we consider to be the critical factor depends on the organism we are studying.
14When density-dependence occurs, and affects r, those effects are manifest throughchanges in birth rate anddeath rate. Here is what theseparate relationships look likein abstract form...IntensecompetitionResources limitedPlentiful resourcesfor each individual
15The result of changes in both birth and death rates is an equilibrium population size, K. At size K, birth and deathrates are equal, i.e.b = dPopulation size K is called a stable point.
16Now let’s compare the birth rate that would be observed when population “regulation” is density-independent versusdensity-dependent...Birth rate is not a function of density when “regulation” isdensity-independent. In fact, this shouldn’t be called “regulation”.
17And the death rate under each situation... Similarly, when “regulation” is density-independent thereis no relationship between death rate and population size ordensity (and no ‘regulation).
18Density-independent birth and death rates tell us that crowding is not important in populations “regulated” inthat way.Where population growth is density-independent, there isno tendency for the population to return to an equilibriumvalue, or K.In fact, K is not defined under those conditions. There is nounique density where b = d, and therefore no equilibrium.So, what might a graph of population size over time looklike for a density-independent population? ...
19Is there an equilibrium evident? No. Is there a pattern evident? Not with respect to populationsize.
20Organisms showing density-dependent “regulation” of population size…appear to have a carrying capacity Kare limited by resourcesHowever, even these species may show changes inpopulation size near K.What we observe in some species could be described as“loose” regulation, and the population is not necessarilykept close to K. One cause may be environmental variationaltering the effective K. We’ll return to this idea at the end.
21In many species, under real environmental conditions there is no clear regulation of population size because atthe densities occurring in nature birth and death rates areeffectively density-independent.In these species, patterns of population change areopportunistic. Populations grow rapidly (exponentially)when conditions are good.Exponential growth is followed by large crashes innumbers when conditions worsen.This is the pattern usually seen in insects and weedy plantswith annual life cycles.
22In some species, population regulation is apparent, and population size fluctuates around K because birth and deathrates are density-dependent.The logistic model you have seen and used is one (andliterally the simplest) model of density-dependence. Thegrowth rate (effective r) decreases as N increases, due to adecrease in the birth rate and/or an increase in the death rate.The effective r decreases to 0 at population size K.remember dN/dt = rN(K – N/K)effective r = r(K – N/K)Although many other species fit this pattern, it was firstdescribed and widely fits data for vertebrate species.
23Here are a couple of examples to show you that the model does apply to other populations, as well:An experiment where aphids were introduced onto individualpea plants, and population growth on those pea plants wasfollowed. (Interval between ticks on the x-axis is 2 days.)
24These are willows in England after myxamatosis essentially wiped out the population of rabbits that had eaten mostseedlings. Thus, here it is not a new population, but one thatis starting from small numbers due to removal of predation.
25Finally, logistic growth in an ant colony in Brazil. The ants weren’t counted directly, but the size of the colony is directlyproportional to the number of craters that surround nestentrances.
26In plants, population regulation incorporates a “second level”. In a densely planted population, there ismortality, but the survivingindividuals grow. Individualplant weight increases asdensity decreases. The processis called self-thinning. Thisfigure demonstrates it forhorseweed (Erigeron canadensis)
27The “trajectory” of plant self-thinning is well established. The slope of a plot of log individual plant weight againstlog plant density is -3/2. Therefore, self-thinning is calledthe -3/2 power law. Since plants all follow the same law,plots for much different species follow parallel lines...
28Finally,…In still other species, regulation by density-dependentbirth and death rates is present, but the regulation is “loose”.When this occurs, population size may depart substantiallyfrom K (or K may vary substantially).Such loose regulation occurs when birth and death rateshave a range of possible values at any population size. Herewe cannot establish a single-valued function relating either/or birth and death rate to density.This is called “density-vague” regulation.
29Here is what you might see as a population trajectory. With density-vague regulation, it may reflect continuous variationin K… or it may reflect density-vague responses in birthand death rates.
30How can such variation occur in a regulated population? Here is an abstract view of the ranges of birth and deathrates possible plotted over a range of population sizes…K might be any valuein the indicated range,i.e. anywhere withinthe ~diamond shapedbox, depending onpopulation size.
31References:Andrewartha, H.G. and L.C. Birch (1954) The Distribution andAbundance of Animals. Univ. Chicago Press, ChicagoDavidson, J. and H.G. Andrewartha (1948) The influence of rainfall,evaporation and atmospheric temperature on fluctuations in the sizeof a natural population of Thrips imaginis (Thysanoptera). J. Anim.Ecol. 17:Lack, D. (1954) The Natural Regulation of Animal Numbers. OxfordUniv. Press, New York, N.Y.Smith, F.E. (1961) Ecology, 42:403-7.