ch 11 population growth

Life tables

Stable age distribution: when the age structure of a population doesnot change over time; occurs when survival and fecundity of eachage class stays constant over time For example, survivorship to the second year (l2) is calculated as

more survivorship?

Survivorship is the probability of surviving from birth to any later ageclass (lx); survivorship in the first age class is always set at 1. pop growth with Rnaught Ro = sum of lx times bx survivorship always zero at birth , but .5 after year one, then for year 2 nobody survive after age 3 so survivorship of age 4 is zero

In the geometric growth model, what does a λ value of 0.97 mean?

The population has decreased from one year to the next because the number of deaths has exceeded the number of births. but NOT that The population has decreased in size by 97 percent from one year to the next.

In population growth equations, dN⁄dt represents the _____.

change in population size at any particular point in time

Another useful measure of survival is the probability of surviving from birth to any later age class, which we call survivorship and denote as llx

lx , using the survival rate ( s x ) from one age class to the next age class Survivorship in the first age class is always set at 1 because all individuals in the population are initially alive. Survivorship at any given age class is the product of the prior year's survivorship and the prior year's survival rate. For example, survivorship to the second year is calculated as l2=l1(aka 1) * s1(.5) for x age classs 0-->lx for age 1 is 0.5

review: Source sink models and landscape more realistic than just talking basic ?

metapopulation, sources help vs extinction, Source sink include HABITAT INFO , sink extinction risk w o source Highest dens middle range for many spp Nyc largest by pop not land mass Pop longtime to get to million Billion 10-13 yrs, billion in 1804? Took one mil years reaching bil, took 123 for 2 bil, doubled in 40 years Grew so fast: 3 reasons, , food, medicine, Industrial energy Agriculture medicine increase longevity and third reason is ENERGY from industrial rev Pop model think 8-12, demog populations Darwin said apply to all org for getting growth rate

On this graph dNdt represents the _____. At low population sizes, dNdt is _____ and _____ as Nincreases

slope of the line; low, increases

If a population has an age structure pyramid with about the same number of people in the younger age classes as it has in the middle age classes, it means that the population _____.

will remain relatively stable

In the logistic growth equation, when the population size is low, the fraction N⁄K) approaches _____, and the term (1-N⁄K) approaches _____.

zero; one

If the intrinsic rate of growth for the prey population is 0.4 and the capture efficiency is 0.1, then: 16 prey are added to the population and 8 prey are consumed by predators

0.4(40) - (0.1*2.4*40)=16-8 so start 40 predators

You are studying the population growth of dragonflies in a wetland ecosystem, assuming ideal growth conditions. In this ecosystem, dragonflies breed only once per year over about 2 weeks. When you begin your study, you document that there are 250 dragonflies in the wetland. At the end of three reproductive cycles you calculate an annual growth rate of 0.67 in the population. What is the size of the population after three reproductive cycles?

(.67^3)*250=75 indivusls after three reproductive cycles Nt=No(lambda^t)

considering the trajectory of both populations simultaneously, which is called a joint population trajectory.

-once reaching prey isocline preds start increasing?, preds decrease when hitting pred isocline both start decreasing when hitting isocline Beginning with the lower right region, predators and prey both increase, and their joint population trajectory moves up and to the right. In the upper right region, prey are still abundant enough that predators can increase, upper right start lowering prey, predators consume when enough , prey decreasing p > r% c in upper right?->consuming them faster than prey repro In the upper left region, the continued decline in prey causes the predator population to decline, (think blue like decreasing pred in prey isocline) In the lower left region, the continued decline in predators allows the prey population to start increasing, which causes the trajectory to move down and to the right and completes the cycle. Together, the trajectories in the four regions define a counterclockwise cycling of predator and prey populations.

age structure of a population and predict future population growth, we need to collect data on individuals of different ages

A cohort life table follows a group of individuals born at the same time and then quantifies their survival and fecundity until the death of the last individual. In contrast, a static life table quantifies the survival and fecundity of all individuals in a population—spanning all ages—during a single time interval. As we will see, the two types of life tables are used in different situations and have different advantages and disadvantages.

Survivorship curves RISK CHILDHOOD AND CHILD BIRTH

A type I survivorship curve depicts a population that experiences low mortality early in life and high mortality later in life (e.g. bears,humans, elephants, whales) risky childhood, then puberty, then not risk til 50ish, dropdown bc of risk of child BIRTH A type II curve depicts a population that experiences CONSTANT mortality throughout its life span (e.g., squirrels, corals). A type III curve depicts apopulation with high mortalityearly in life and high survival laterin life (e.g., weeds). many trees die off, but trees that do establish can live long time Most populations exhibit asurvivorship curve that combinesfeatures of type I and III curves steep risk in childhood type 1 initial decrease kinda reflect type 3

Survivorship curves

A type I survivorship curve depicts a population that experiences lowmortality early in life and high mortality later in life (e.g. bears,humans, elephants, whales). A type II curve depicts a population that experiences constantmortality throughout its life span (e.g., squirrels, corals). A type III curve depicts apopulation with high mortalityearly in life and high survival laterin life (e.g., weeds). Most populations exhibit asurvivorship curve that combinesfeatures of type I and III curves. initial tiny dropdown at beginning type 1 curve, comms from childbirth and early childhood being risky before age 4, then after puberty good until 50 type 2 again steeper drop-off at first many seedlings type 3 just die initial tiny type 1 decrease resembles type 3 b4 leveling off

To understand the differences in survival among different age classes, we can graph survival over time, as illustrated in Figure 11.19. We can then categorize survivorship curves as type I, type II, or type III.

A type I survivorship curve depicts a population with low mortality early in life and high mortality late in life. Examples include humans, elephants, and whales. A type II survivorship curve occurs when a population experiences relatively constant mortality throughout its life span. Organisms with type II curves include squirrels, corals, and some species of songbirds. A type III survivorship curve depicts a population with high mortality early in life and high survival later in life. This is a common pattern in many species of insects and in plants such as dandelions and oak trees that produce hundreds or thousands of seeds

Geometric growth model part one time interval

According to the geometric growth model, the size of a population after one time interval is:

Geometric growth model part one time interval similar to Exponential growth model but adding discrete time periods general for both?

After two time intervals, the population size would be: size pop after one time interval w this model is: n1=n0(lambda) nt=n0(lambda)^t, just adding lambda for discrete time interval Although the exponential model has continuous data points that form a curve whereas the geometric model has discrete data points for each breeding season, the two models show the same GENERLA pattern in population growth, SAME CURVE SHAPE find identical growth curves compares the DIRECT relationships between λ and r by examining the values of λ and r when populations are decreasing, constant, or increasing BOTH GO TOGETHER When a population is constant, λ = 1 and r = 0 . only dif is r can be negative, while negative r means lambda less than one

a cohort life table comes from Peter and Rosemary Grant, who have studied several species of ground finches in the Galápagos Islands off the coast of Ecuador.

Grants were able to capture all the birds on the island and mark them with uniquely colored plastic leg bands. not super mobile finches away from islands Using 210 cactus finches (Geospiza scandens) that fledged in 1978, the researchers constructed a cohort life table for the population. In Figure 11.20, you can see the annual survival rates for these birds. As is the case for many species, the survival rate was low in the population's first year and then remained high for several subsequent years However, survival was quite variable throughout the life of the birds. This variation in survival reflects variation in the environment due to climatic changes during El Niño years El Niño years are wet years, the vegetation produces abundant food for the finches and this causes high survival. Following El Niño years are periods of several dry years. During this time, food becomes scarce for the finches and this causes low survival was in fact lower lower survive from enviro it is difficult to determine whether low survival at a particular age is due to the age of the individuals or due to the environmental conditions that occur during that year.

Density-dependence in animals more, natural neg dep

In the 1970s, common terns began to colonize Bird Island in Massachusetts. When nest sites became limiting, the population stopped growing and birds began colonizing nearby Ram Island. When nest sites on Ram Island became limiting, they colonized Penikese Island.

predator isocline

In this graph, we draw a vertical line at the point where N = m ÷ ac , which is the number of prey that causes the predator population to be stable. allows the predator population to increase because there is an increased abundance of prey to consume In the region to the left, the predator population decreases because there is not enough prey available. (Lower a and c)

Age structure narrow base indicates

Age structure pyramids with broad bases(e.g., the 2012 Indian population) indicatea growing population, BROAD BASE , DEMOGRAPHIC CANNOT BE ANY WIDER THAN IT ALREADY IS, EVEN W PERFECT LIFE EXPECTANCY , DEMOGRAPHICCANNOT BE WIDER, older classes may be wider but die off .Pyramids with narrow bases (e.g., the2012 German population) indicate adeclining population .Pyramids with straight sides (e.g.,the 2012 U.S.population) indicatea stable population, baby boomers biggest for us rn avg life expectancy from 40 yrs to 67.2 globally pop increase rate starting to decrease, hovered about 1.8 til 80s, below 1 rn CDR num deaths per 1,000 , more youth adn fewer elderly than slower growing developed country , use CDR to build pyramid narrow base indicates declining population very few children mean in future this age group will not widen even if perfect life expectancy , India broader base so younger groups larger and will increase pop in future how large city would be housing all the 6.8 in world if housing all people with density of New York-->New York size of Texas city less carb emissions, 50% less emissions in dense city center(avg 30%), twice average in distant suburbs, cars outside major cities, heat contains in apartment tower eco footprints of nations exceed avail ecological capacity, we have 6 hectares for about 8 ha footprint , meaning we import some resources and energy stuff for survival

The logistic growth model

As the population increases from a verysmall size, the rate of increase grows untilreaching ½ the carrying capacity(corresponding to the inflection point).Rate of per capita increase can be modeledas Rate of per capita increase can be modeledas: (1/N) *(dN/dt) rate pop growth , half of K is highest rate change individuals in the population continuallydecline in their ability to contribute topopulation growth To model the slowing growth of populations at high densities, we use the logistic growth model. The logistic growth model builds on the derivative of the exponential growth model, but adds a term, ( 1 − N / K ) , dn/dt(rate change pop growth)=rN(1-N/K)-->N/K near zero when less indivs-->so the term inside the parentheses approaches 1. When this happens, the equation becomes nearly identical to the exponential growth model., math of this shows how math closely near exponential model at first However, when the number of individuals in the population approaches the carrying capacity, the term inside the parentheses approaches 0. As a result, the population's rate of growth approaches 0. When we plot the growth of a population over time using the logistic growth curve, we obtain a sigmoidal, or S-shaped curve, middle point on the curve, where the population experiences its highest growth rate, is known as the inflection point. Above the inflection point, the population growth begins to slow->at half pt or inflection

We can draw a horizontal line at the point where p = r% c , which is the number of predators associated with a stable prey population. Prey isocline using rate growth over capture rate eval to number predators

At any combination of predator and prey numbers in the region below the equilibrium isocline, there are relatively few predators and the prey population increases., yellow prey up, more prey and less preds , In the region above this line, the prey population decreases because predators remove them faster than they can reproduce. (C higher than r in blue)

Life tables

Life tables: tables that contain class-specific survival and fecunditydata. Because it is often difficult to ascertain paternity, life tables aretypically based on the number of female offspring per female x = age class nx = the number of individuals in eachage class immediately after thepopulation has producedoffspring sx = the survival rate from one age class to the next age class bx = the fecundity of each age clas taking all 6.9 people in one city, as dense as New York but size of Texas if as dense as London would stretch to more places

concepts

Population growth rate is influenced by the proportions ofindividuals in different age, size, and life history classes Populations have growth limits. Under ideal conditions, populations can grow rapidly.

The logistic growth model

Carrying capacity (K): the maximum population size that can besupported by the environment, due to places and food limits Although positive and negative density dependence both occur in nature, population modelers have focused more on the effects of negative density dependence.in mimicking nat pop growth number of individuals in the population is small relative to the carrying capacity, the fraction N K is close to 0, so the term inside the parentheses approaches 1. When this happens, the equation becomes nearly identical to the exponential growth model. However, when the number of individuals in the population approaches the carrying capacity, the term inside the parentheses approaches 0. As a result, the population's rate of growth approaches 0 the carrying capacity-->part of logistic model? Logistic growth model: a growth model that describes slowinggrowth of populations at high densities; it is represented by, equation logistic growth model builds on the derivative of the exponential growth model, but adds a term, ( 1 − N / K ) , that accounts for a decline in growth rate as the population approaches its carrying capacity: dn/dt = rN(1-N/K) NEED TO BUILD/MORE RESOURCES TO SUPPORT MORE starts exponential until inflection, red dot=fastest inflection point, slow b4 hitting K S-shape curve: the shape of the curvewhen a population is graphed over timeusing the logistic growth model. Inflection point: the point on asigmoidal growth curve at which thepopulation has its highest growth rate N approaching K means 1, so entire derivative is zero when there is no growth , this is later growth leveling off inflection point = K capacity div by k population modelers have focused more on the effects of negative density dependence-->PATTERNS OF POP GROWTH IN NEG MODELED W LOGISTIC, As a result, they have developed growth models that mimic the behavior of many natural populations: rapid initial growth followed by slower growth as populations grow toward their maximum size as the population increases from a very small size, the rate of increase grows because the number of reproductive individuals increases. After reaching one-half of the carrying capacity, which corresponds to the inflection point of the S-shaped curve, the rate of increase begins to slow because the reproductive individuals are each obtaining fewer resources. On a per capita basis, the rate of population increase continually declines. population size affects the rate of increase on a per capita basis, not the entire population rate of increase, but increase per person , individuals in the population continually decline in their ability to contribute to the growth of the population. slowing rate of growth as per capita resources become limited.

Population demography

Demography: the study of populations.In the 19th century, Charles Darwin and other scientists realized thatthe study of demography could apply to all organisms on Earth Growth rate: in a population, the number of new individuals that areproduced per unit of time minus the number of individuals that die **any pop rapid rate if they are given the right conditions. **We typically consider the growth rate on an individual, or per capita, basis **xonditions allowing for INDIVIDUAL max repro and min per cap death make **Ideal conditions also lower death rates because stressors, such as hunger and disease, are decreased. When this happens, a population achieves its highest possible per capita growth rate, which is called the intrinsic growth rate, denoted as r (little r =ideal) Intrinsic growth rate (r): the highest possible per capita growth ratefor a population Under ideal conditions, individuals experience maximum r (i.e.,maximum reproductive rates and minimum death rates) maximum reproductive rates--would mean keep having Kida back to back right during puberty, not really us under max repro rates, rats w resources could get pregnant , r not frequent due to lacking ideal conditions

Density-dependent limitations

Density dependent: factors that affect population size in relation to the population's density. Negative density dependence: when the rate of population growth decreases as population density increases-->.density itself the factor altering growth? really limited resources but not always decreasing? The most common factors that cause negative density dependence are limiting resources SHARED MORE AS DENSITY INCREASES (e.g., food, nesting sites, physical space). we may lack housing in city, or if not getting food population is small, there is an abundance of resources for all individuals, but as the population increases, such resources are divided among more individuals As a population's size increases, resources are divided among more individuals, and per capita resources decline to a level at which individuals find it difficult to grow and reproduce. Crowded populations can also generate STRESS, transmit DISEASE, and attract PREDATORS. disease when closer , disease bring neg dens dependence All these factors contribute to slowing, and finally halting, population growth.

Density-independent limitations

Density independent: factors that limit population size regardless of the population's density. Common factors include climactic events (e.g., tornadoes, floods, extreme temperatures, and droughts). natural disasters tornadoes, hurricanes, floods, and fires. and , other less dramatic changes in the environment, including extreme temperatures and droughts, can also limit populations. The apple thrip (Thrips imaginis) was a common insect pest in Australia that would occasionally increase to very large numbers and devastate apple trees and rose bushes researchers surveyed thrip PEST populations on rose bush flowers in an attempt to understand the causes of the large variations in population size. Example: The apple thrip was a common insect pest in Australia that would undergo large population fluctuations. Researchers predicted that these fluctuations were due to seasonal fluctuations in temperature. and rainfall-->so they included these factors in their population growth model. THRIP TEMP FLUCATUATIONS Their POP SIZE predictions (dotted line) matched closely with actual abundances (bars)., matched the actual number of thrips they counted in their surveys., predicted mean thrip per flower number The influence of rainfall, evaporation and atmospheric temperature on fluctuations in the size of a natural population of Thrips there are growth limits just from climate extreemes, pop not mattering expanding range=density independent, due to climate conditions and glob warming limits on how large a population can grow. Ecologists categorize these limits as being either density independent or density dependent., using these in growth models Bark beetles are native insects that consume the phloem tissues of trees, causing the trees to die. During the past several decades, bark beetles have killed billions of coniferous trees . As a result, temperature is a major determinant of population size and its effects on the beetle population are density-independent beetles have more generations per year under warmer temperatures, but they can die from unusually cold temperatures They concluded that bark beetle populations are likely to increase dramatically and cause more damage to conifer trees in the future. beetles that consume conifer trees are expanding their geographic range northward in North America, as a result of warmer winter temperatures, harming commercially needed pine and spruce bc density indep factors from global temp change that guide their growth and adjust their range

Population doubling time found how:

Doubling time: the time required for a population to double in size; can be estimated by rearranging the exponential growth model: Nt=nnaught^rt-->e^rt=Nt/No, right term=2 When a population doubles, = 2. , aka Nt/N0 or e^rt = 2 t = loge2/r WHERE T IS DOUBLING TIME or r=loge for geometric: t = loge2/logelambda loge2=.69 human doubling time of just 37 years by 1987 , is predicted to increase to 49 years by 2024. By making this substitution in the equation, we get:

The logistic growth model

Example:Georgyi Gause raised two species ofprotists in test tubes and added a fixedamount of food each day. . Because the two species differ in many ways, Populations initially grew in size exponentially, buteventually stabilized at different carryingcapacities. Gause suspected that the cause of this maximum population size was the amount of available food. To test this hypothesis, he did the experiment again, but this time doubled the amount of food. Because the two species differ in many ways, their populations stabilized at different carrying capacities, Gause suspected that the cause of this maximum population size was the amount of available food. To test this hypothesis, he did the experiment again, but this time doubled the amount of food. With twice as much food available, however, the two species stabilized at population sizes that were twice as large as in the first experiment, still levels off though increase the carrying capacity of a population. This early experiment confirmed that logistic growth can happen in real organisms and that the increased availability of a limiting resource can increase the carrying capacity of a population., To test whether carrying capacities weredetermined by the amount of resources,he doubled the amount of food in eachtest tube. With twice as much food available,populations grew to sizes that were twiceas large as those in the first experimen get s shaped hit max even w same amt food, changed food, twice as large w food double carrying capacity tested as being based on food by Gause, found S shaped log growth but dif K reached w double food Above the inflection point, growth begins to slow. When the population reaches its carrying capacity, K, growth is zero We can further understand how the logistic growth model behaves by examining the effect of population size on the rate of increase As shown in Figure 11.15a, as the population increases from a very small size, the rate of increase grows because the number of reproductive individuals increases. inflection point of the S-shaped curve, the rate of increase begins to slow because the reproductive individuals are each obtaining fewer resources. On a per capita basis, the rate of population increase continually declines. EVEN FROM TIME ZERO? how population size affects the rate of increase on a per capita basis,(1/N)(dN/dT) As you can see in Figure 11.15b, individuals in the population continually decline in their ability to contribute to the growth of the population. less per cap ability to help grow pop

Density-dependence in animals negative density dependence occurs in what conditions?

Examples: Raymond Pearl introduced different densities of fruit flies into bottles with identical amounts of food. BOTTLES=IDENTICAL FOOD FOR BREEDING ADULTS As fly numbers increased, competition for food became more INTENSE and adults had fewer progeny and shorter lifespan. daily number of progeny produced per pair of adult flies decreased AND LIFE SPAN progeny produced per pair of adult flies w less food, more directly down from this graph negative density dependence occurs in nature. Consider the common tern natural neg dependence, in terns 1970s, the tern population on the eastern coast of North America began to expand into an area known as Buzzards Bay in Massachusetts. It first colonized Bird Island, where its numbers quickly grew from about 200 to 1,800 individuals by 1990, In the 1970s, common terns began to colonize Bird Island in Massachusetts. When nest sites became limiting, the population stopped growing and birds began colonizing nearby Ram Island. (density dependent nest sites) These data demonstrate that although the terns have a high intrinsic growth rate, a limited number of nesting sites on an island ultimately limits the population size. regardless of r will be constrianed When nest sites on Ram Island became limiting, they colonized Penikese Island. dense populations of deer and kangaroos are so limited by food availability that they move into farms, where they eat crops, and suburban areas, where they eat shrubs and other landscape plants. we see negative density dependence when density-independent and density-dependent factors regulate populations and maintain their abundances at a level close to the maximum number that can be supported by the environment

Comparing growth models

Exponential and geometric growth models are identical, except er takes the place of λ. Hence, or rearranged, exponential J shaped, geometric adds discrete dots When a population is decreasing, λ < 1 and r < 0. When a population is constant, λ = 1 and r = 0. When a population is increasing, λ > 1 and r > 0 PUT EQUATION e^r = lambda, or rearranged? constants/variables describing growth rate fluctuate together

Exponential growth model The first model applies to species that r?

Exponential growth model: a model of population growth in whichthe population increases continuously at an exponential rate; can bedescribed by the equation Nt = Noe^rt Nt = future population size; N0 = current population size r = intrinsic growth rate; t = time over which apopulation grows where e is the base of the natural log (e = 2.72 ) -changing growth due to growth rate specific to spp over time , creates Nt for future population thus pops need higher intrinsic growth rates or a larger number of reproductive individuals The rate of a population's growth at any pointin time is the derivative of this equation: dN/dt=rN gives growth UNDER curve for growth rate any time along line rate of growth at any point in time by taking the derivative of the exponential growth equation, where d N d t represents the change in population size per unit of time. rate of change in population size at any particular point in time depends on the population's intrinsic growth rate and the population's size at that point in time. J-shaped curve: the shape of exponentialgrowth when graphed sp that eproduce throughout the year, human use this growth model

To calculate the number of individuals that survive to the next age class,

For example, if we start with 20 individuals at age 0 and their survival rate is 50 percent, then we can calculate the number of 1-year-olds that we will have in the following year: Number surviving to next age class=( n x )×( s x ) Number surviving to next age class=20×0.5 Number surviving to next age class=10 For example, if 10 individuals will survive to be 1-year-olds and each 1-year-old can produce one offspring, then we can calculate the number of new offspring that this age class will produce, multiply the number of individuals that survive to the next age class—as shown in the orange-shaded region—by the fecundity of that age class. use num surviving and fecund for total new offspring , by the fecundity of that age class. In addition, we will have 10 individuals that are now 1 year old, 24 individuals that are 2 years old, and 40 individuals that are now 3 years old those already in pop? When we add up all the age classes, we find that these survival and fecundity rates have caused the population to grow from a total size of 100 to a new total size of 112 individuals 1 year later. As a result, the geometric growth rate of the population is N1 / NO=1.12 If we examine these values of λ , we can see that they initially fluctuate widely between 1.05 and 1.69. As the years pass, however, the values of λ settle down to 1.49. Provided that the survival and fecundity of each class stay constant over time, λ will stabilize at a single value and the proportion of individuals in each age class will also stabilize. When the proportion of individuals in each age class does not change over time, we say it has a stable age distribution.

Classify each statement according to whether it applies to the exponential or geometric growth model.

Geometric growth model GEOMETRIC INCLUDES The annual growth rate (λ) describes the ratio of the population size FROM YR TO YR Exponential growth model -includes e, the base of the natural log -and assumes continuous growth over a period of time Geometric growth model -includes λ, the ratio of population sizes from year to year -assumes growth at specific intervals over a period of time Different models of population growth account for different modes of reproduction. Species that reproduce continuously throughout a given period of time, such as humans, can grow exponentially. The exponential growth model calculates the population size at a given time (Nt) by multiplying the starting population size (N0) by an exponential term. This model raises e, the base of the natural log, by the product of the growth rate (r) and the interval of time (t). 𝑁𝑡=𝑁0𝑒𝑟𝑡 For species that REPRODUCE at DISCRETE times during the year, such as birds that lay eggs in spring, the geometric growth model describes changes in population size at regular intervals. Population growth in these species is measured by COMPARING the population size at a certain time of year to the population size at the SAME time the preceding year. The geometric growth model specifies this ratio using the Greek symbol lambda, λ. 𝑁𝑡=𝑁0λ𝑡

Huffaker . However, they can coexist in a spatial mosaic of suitable habitats that provided a ?to the prey.

Increased habitat complexity and created a habitat that allowed for predator/prey cycles->in metapop? From this, we can conclude that stable population cycles can be achieved when the environment is complex enough that predators cannot easily find scarce prey. bot line=complexity 10:1 ratio fem prey to preds in trays introduced to trays without predators, the prey population rapidly increased and ultimately leveled off at between 5,500 and 8,000 mites. In most experiments, Huffaker introduced 20 female prey per tray and then introduced two female predators 11 days later. Because both species reproduce parthenogenetically, no males were needed. When predators were added, the predator population increased rapidly and soon wiped out the prey population. Without any prey to feed on, though, predators quickly became extinct. This time it took longer for the predators to locate the prey, but eventually all the prey were consumed and then the predators went extinct. Huffaker hypothesized that if predator dispersal could be further impeded, the two species might be able to coexist. and not drive to extinction, He knew that the predatory mites disperse by walking, but the prey mites use a silk line that they spin to float on wind currents. placing a mazelike pattern of Vaseline barriers among the oranges to slow the dispersal of the walking predators. He also placed vertical wooden pegs throughout the trays for the prey mites to use as jumping-off points. wood pegs and vasseline barrier to slow dispersal This arrangement produced a series of three population cycles during the 8-month experiment, as depicted in Figure 13.10. The distribution of predators and prey throughout the trays continually shifted over time, model created by impeding predator dispersal When predators discovered an orange that had been colonized by prey, they began eating them. As this was happening, some of the prey recolonized other oranges, thereby staying one step ahead of their predators by recolonized other areas,. In short, Huffaker created a metapopulation in the laboratory. Huffaker's experiment demonstrates that predators and prey cannot coexist in the absence of suitable refuges for the prey and not enough dist or no barriers dispersal advantage , could go to nearby orange suitable habitats

Select the statements that explain why very small and very large populations experience slow population growth under the logistic growth model.

Limited resources are shared among many individuals in very large populations. WILL LIMIT REPRO OF INDIVS? Small populations have fewer individuals capable of producing offspring. CHANGE/UNIT TIME The logistic growth model estimates the change in the number of individuals per unit time using the intrinsic growth rate (r), current population size (N), and carrying capacity (K). 𝑑𝑁𝑑𝑡=𝑟𝑁(1−𝑁𝐾) The logistic growth curve is sigmoidal, or S‑shaped. When N is very small, the fraction 𝑁/𝐾 in the logistic growth model is close to zero and the population behaves as an exponentially‑expanding population. Because there are few individuals capable of producing offspring when the population is very small, initial growth is slow. The growth rate increases as N increases until the population approaches the carrying capacity of the environment. When N approaches K, the fraction 𝑁/𝐾 in the logistic growth model is close to one and the population stops growing. The increasingly large number of individuals must share limited resources, which cannot support infinite population growth. The intrinsic growth rate for a population is the maximum number of offspring that a single individual can produce under ideal circumstances. The population size does not affect the intrinsic growth rate, because this rate describes maximum fertility per capita. The logistic growth model also accounts for carrying capacity, or the number of individuals that an environment can support. The population size does not affect carrying capacity, which is estimated by environmental resources such as food, space, and water The population size does not affect the intrinsic growth rate OR K CAPACITY

Olaus Murie, who examined the survival of Dall mountain sheep (Ovis dalli) at a site in Alaska during the 1930s

Murie knew that the horns of the sheep contained annual growth rings that could be used to calculate the ages of the sheep researchers calculated the survival and survivorship of different age classes. He also knew that following a cohort of highly mobile sheep for 15 years in Alaska was not feasible, so he took a static approach by conducting a search of all sheep skeletons in the area that had died He found a total of 608 skeletons from sheep that had died in recent years and assigned an age to each individual based on the growth rings in its horns. Using these estimates, he created a static life table showing how many of the original 608 sheep died in each age class. show a low survival rate during the first year, followed by high survival for the next 7 years. After 7 years of age, the annual survival rate began to drop, with the exception of those at 12 years of age However, only four animals made it to 12 years, which gives us a poor estimate of the typical survival rate for 12-year-old sheep. Because these data were taken from the skeletons of sheep that presumably died over a relatively short period, we do not see the large variation in survival rate that we saw in the cohort life table of the cactus finch.

You are studying the demographics of a lizard population on a Pacific island. The population when you begin studying it is 374 individuals. If the population has an intrinsic growth rate of 0.21, how big will the population be in 5 years?

Nt=Noe^rt, 1,068 individuals using this formula

Life tables contain?

Number surviving to next age class = (nx-->number indivs) x (sx-->.5 is fifty surviving to be infant) life tables-->go into next category in next year with 10 new indivs, made nothing in year one bx= fecundity for ppl surviving to next class class specific survival and fecundity female offspring per female because hard to determine paternity and build tables from this Number of new offspring produced = (nx) x (sx) x (bx)- lambda would be 1.12, we start at 100 and one yr later at 112 survival and fecundity of eachage class

After studying the demography of a large chimpanzee troop in Africa, you construct a static life table depicting the number of individuals that are alive in each of six age classes and the average survival rate of each age class to the next:

Of the individuals that were alive when you collected these data, how many total individuals do you calculate will survive to the next age class? 60*.3(x0)=18 25*.4(x1)=10 24*.5(x2)=12 20*0.2(x3)=4 sum is 44 for these 44 To calculate the number of individuals surviving to the next age class, multiply nx by sx for each age, then calculate the sum to obtain the total individuals that will survive to the next age class

Density-dependent limitations As we move from ? densities to intermediate densities, the effects of positive dependence can play an important role.

Populations are often regulated by both positive and negative density dependence. Increased densities provide more individuals for breeding. Above some density, resources become limiting and negative density dependence begins to play a role. Example: Herring experience low population growth at low population densities, high population growth at intermediate densities, and low population growth at high densities. positive at beginning, too high get crowded out aka pop size/density graph increase w per cap growth rate Although we often think of positive and negative density dependence as isolated phenomena, populations can be regulated by both processes, low to intermde=postive role more, Increased densities provide more individuals for breeding, and the growth rate of the population can improve. Above some intermediate density, resources start to become limiting and negative density dependence begins to play a role. The existence of positive density dependence in the herring population concerns fisheries managers because it indicates that if the herring were driven to low enough densities by fishing, it would be difficult for the population to rebound. In fact, the populations could experience negative growth rates and become extinct. Fortunately, most fish populations do not appear to experience positive density dependence. growth would possibly become negative, since their growth increases with density harder to rebound at lower pops The highest population growth is measured as a RATIO between the number of YOUNG fish and the number of ADULT fish. The highest growth rate of the population occurs at intermediate densities.

Density-dependent limitations: summary of pos and neg density dependences In short, while negative density dependence causes slow population growth due to ?, positive density dependence causes slow population growth due to ?.

Positive density dependence: when the rate of population growth increases as population density increases (also known as inverse density dependence, or Allee effect). -people in N Dakota start moving away Positive density dependence typically occurs when population density is very low, and it can be caused by several different factors. For example, very low densities make it hard for individuals to find mates or, in the case of flowering plants, to obtain pollen. slow initial population growth Very low densities can also lead to the harmful effects of inbreeding, as discussed in Chapter 5. Small population sizes can, by chance, have uneven sex ratios. If a small population has a low proportion of females, it can experience low population growth rates Finally, individuals living in smaller populations can face a higher predation risk than those living in large populations Positive density dependence (also known as inverse density dependence inverse/reverse of what's expected Positive density dependence typically occurs when population densities are low, which may make it hard to find mates, particularly when sex ratios are uneven. Low densities can also lead to harmful effects of inbreeding and a higher predation risk. Example: Populations of cowslip with fewer than 100 individuals produced fewer seeds per plant than larger populations.-->no-one to mate with, get less pollen at first but increase when being established negative growth=overcrowding, positive density dependence causes slow population growth due to undercrowding. positive dep problem for cowslip other spp that prevent self-fertilization bc depend on receiving pollen from other plants, but this can be difficult when individuals live at low densities and are widely spread over an area. In a study of cowslip When they looked at reproduction in populations of different sizes, they found that populations of fewer than 100 individuals produced fewer seeds per plant, as shown in Figure 11.11. This probably occurred because the small population , attracted fewer pollinators. As a result, plants in low-density populations received less pollen At higher densities, a greater number of pollinators were likely to visit, and increased pollination allows each plant to produce many more seeds. positive density dependence also occurs in parasites. In 2012, researchers in British Columbia reported on reproduction in salmon lice (Lepeophtheirus salmonis), which feed on the skin of salmon When breeding, male and female lice form a mating pair. that the probability of an individual forming a mating pair is positively correlated with the number of lice of the opposite sex. low densities have a harder time finding a mate than individuals living at higher densities; therefore, the lice experienced positive density dependence.

Researchers in Georgia collected survivorship data in populations of two plant species, elf orpine (Sedum smallii) and oneflower stitchwort (Minuartia uniflora). If the populations of each species started with 500 individuals, how many individuals would be present in each species after seven months?

Scientists measure survivorship by counting the number of individuals in a population that are still living at discrete timepoints. In small populations, it may be possible to count all the individuals. In larger populations, scientists need to take a sample of individuals to estimate population survivorship over time. SAMPLE IN POPS FOR survivorship, PERCENTAGE ON LOG SCALE FOR proportion Survivorship is usually expressed as a proportion or a percentage. When plotting a survivorship curve, the proportions are generally transformed to a log‑scale to better represent per capita effects and visualize small proportions that can be obscured on a non-log scale. At the first timepoint, all individuals are assumed to be alive and the proportion surviving equals 1. Over time, the proportion of surviving individuals in each population decreases in a curvilinear fashion until survivorship finally reaches 0. The proportion of surviving individuals decreases more rapidly in oneflower stitchwort than in elf orpine In the incorrect graphs, the 𝑦-axis is not plotted on a log scale. The graph with decreasing numbers on the 𝑦-axis also has the 𝑥-axis plotted incorrectly. The months shown in this graph are row numbers in the data table.

Predicting human growth

The logistic growth model was formulated by Pierre FrançoisVerlhulst to describe human population growth. Verhulst had read Thomas Malthus's 1798 essay about the growth of human populations and sought to formulate a natural law governing the growth of populations Nearly a century later, in 1920, Raymond Pearl and Lowell Reed independently confirmed the logistic growth model as it applies to human population growth. Scientists later confirmed that the U.S. population grew exponentiallyfrom 1790 to 1910-->we only had exponential period .Growth slowed after 1910,suggesting that the populationwas reaching K. that the rate of growth appeared to be declining over time. Pearl and Reed applied their logistic growth equation to the census data and predicted that the population of the United States, which was 91 million in 1910, had a carrying capacity of 197 million, However, they were careful to note that this prediction depended on the population supporting itself using only the land of the United States. Since then, advances intechnology, TECH, SANITAION, MEDICINE sanitation(DISEASE SPREAD, INDOOR PLUMBING), ,medicine, and food production has increased K.-->THESE ALL CAUSED PROJECTED LOG GRWOTH TO NOT BE TRUE FROM VERHULST AND MALTHUS 1910 HUMAN SHOULDVE BEEN LEVELING OFF IN LOG GROWTH MODEL -logistic growth if these advances were limited A census conducted every 10 years from 1790 to 1910 indicated that the U.S. population was continuing to increase. However, the rate of increase started to decline by 1910. Based on these data, Pearl and Reed predicted that the population would reach a maximum of 197 million people. In reality, the U.S. population has continued to grow. logistic prediction correct , but just higher than expected due to TECH, SANITAION, MEDICINE and food

Researchers in Georgia collected survivorship data in populations of two plant species, elf orpine (Sedum smallii) and oneflower stitchwort (Minuartia uniflora). If the populations of each species started with 500 individuals, how many individuals would be present in each species after seven months?

The number of individuals surviving at a given time is a function of the initial number of individuals and the survivorship, 𝑙𝑥, at that specific time. 7 months mean Lx = nx(num indiv any given time)/nnaught at 7 months, Lx = .09=nx/500 so nx=45 for elf orpine Number of oneflower stitchworts individuals at 7 months: .05 *500=25 To calculate the number of individuals alive in each species of plant at a specific time, multiply the starting number of individuals, 𝑁0, by the survivorship, 𝑙𝑥, at that time. For both species, 𝑁0 equals 500. The survivorship for elf orpine at seven months is 0.09. The elf orpine population has 45 individuals remaining at seven months. The survivorship of oneflower stitchwort at seven months is 0.05. The oneflower stitchwort population has 25 individuals remaining at seven months

Identify examples of evidence that a population has a size that is density dependent.

The number of progeny per adult decreases as population density increases. A change in a population's size exhibits logistic growth? A population's resources and potential mates are insufficient for all indiviudals. The maximum population limit increases as population density decreases. (no affect on K by logistics models) A dramatic environmental change that causes a change in population size is density independent. Carrying capacity is determined by environmental factors and does not change as population density changes. Population growth can be density dependent and still exhibit exponential or geometric growth. only The number of progeny per adult decreases as population density increases. and A population's resources and potential mates are insufficient for all indiviudals. Population growth is density dependent if the growth rate changes as the number of individuals living within a defined area changes. num indivs correlate to grow rate changes A change in population size exhibits positive density dependence when the rate of population growth increases as population density increases. For example, in a flowering plant population, successful pollination is less likely to occur when population density is low. A change in population size exhibits negative density dependence when the rate of population growth decreases as population density increases. In a population that exhibits negative density‑dependent growth, an increase in the number of individuals decreases the rate of population growth. The decrease in population growth IN NEG DENS DEPENDENCE could be caused by a number of factors, such as increased competition among individuals leading to a decrease in successful reproduction. A change in population size that resulted from deaths due to cold temperatures is an example of density‑independent population growth. The population size changed because of factors not related to how many individuals are present in the population. Carrying capacity is determined by environmental factors and does not change as population density changes. Population growth can be density dependent and still exhibit exponential or geometric growth. ANY GROWTH NO MATER DEPENDENT ON DENSITY, but these growths not just for density dep growth GROWTH CAN BE EITHER WHOLLY DENSITY DEP OR INDEP?

Researchers in Georgia collected survivorship data for populations of two plant species, elf orpine and oneflower stitchwort. What other data would you need to calculate generation time, 𝑇, for each of these plant species?

The rate of survival, 𝑠𝑥, is used to calculate survivorship, 𝑙𝑥. Consider that generation time, 𝑇, is an estimate of how long it takes for an organism to produce its first young. is the age at which an individual first produces young. 𝑇 is calculated using age, 𝑥, survivorship, 𝑙𝑥,and fecundity, 𝑏𝑥. only need the number of individuals in each age class 𝑥, 𝑛𝑥 xlxbx/lxbx The symbol Σ indicates that the products for each age class are summed. For the survivorship of the elf orpine and oneflower stitchwort populations, the age classes are 1, 5, 7, 8, 10, 12, and 13 months. The denominator, Σ(𝑙𝑥⋅𝑏𝑥), is equal to the net reproductive rate, 𝑅0. The table gives 𝑙𝑥 and 𝑥, but lacks 𝑏𝑥 for each age class. The number of individuals in each age class, 𝑛𝑥, the number of individuals that survive to age 𝑥, 𝑠𝑥, and the intrinsic growth rate, 𝜆, are not needed to calculate generation time.

To determine the change in population size (ΔN) between initial population size and t time intervals: pop 100 annual growth rate 1.5, lambda, so 5 yrs from now?

To determine the CHANGE in population size (ΔN) between initial population size and t time intervals: n0(lambda)^t-Nnaught or Nnaught(lambda^t-1) SIZE 100 AND ANNUAL LAMBDA 1.5, 100 yrs from now? laboratories can have very high growth rates, especially for small organisms. Under ideal conditions, the value of λ can be 24 for field voles (Microtus agrestis), 10 billion lab growth modeling (capacity of a population for growth by observing the rapid increase of organisms introduced into a new region with a suitable environment with abundant resources.) maybe invasive

For example, when a species has declined to very low numbers and we wish to improve its numbers, management strategies need to consider how to avoid inbreeding and how to ensure that each female can encounter a sufficient number of mates to fertilize all her eggs

WHICH WOULD INBREED? The concept of positive density dependence also offers an opportunity for ecologists to help control undesirable PESTS FOLLOWING POS DEP species. For example, several pest insect populations have been controlled by releasing sterile males into the population For example, several pest insect populations have been controlled by releasing sterile males into the population. This skews the sex ratio and causes the females to breed with sterile males, leading to a lower growth rate in the pest population. W POS DEPENDENCE CAN JUST researchers simply reduce the size of a pest population to the point that individuals have a hard time finding mates.

To determine the age structure of a population and predict future population growth, we need to collect data on individuals of different ages WITHIN POPULATION

We can do this by constructing either a cohort life table or a static life table. A cohort life table follows a group of individuals born at the same time and then quantifies their survival and fecundity until the death of the last individual. cohort=single group at same time, measure surv and fecund yearly until last death

The ?of ? are also limited at high population densities.

When plants are grown at high densities, each plant has access to fewer resources such as sunlight, water, and soil nutrients.fill in canopy area for light when tree falls The survival, growth, and reproduction of plants are also limited at high population densities., plants limited in survival, growth, and reproduction We can see this outcome in a study of flax plants (Linum usitatissimum) that were grown at a wide range of densities and then dried to determine their mass When seeds were sown at a density of 60 seeds per square meter, the mean dry mass of an individual was approximately 1 g. When seeds were sown at densities of 1,440 and 3,600 per square meter, the mean dry mass of an individual was 0.5 and 0.2, respectively. Given that smaller plants typically experience reduced fecundity, the competition caused by high densities will cause a population of flax plants to grow more slowly. slower Indiv growth, high density When flax seeds are sown at higher densities, the average plant is smaller. Smaller plants are less fecund, so high densities cause plant populations to increase at a slower rate. most in population aggregate around smaller seed mass Under very high densities, competition among conspecifics can cause plants to die. a single extremely high density of 100,000 per square meter. Over time, competition among the tiny seedlings became intense, as you can see in Figure 11.10a. Over an 8-month period, most of them died. The two y axes in the figure, which are on log scales, reveal that while there was a hundredfold decrease in population density over time, there was a thousandfold increase in the average mass of the surviving individuals density-dependent competition caused high mortality of the horseweed seedlings flax and horseweed=density dependent limiters of seedling size and thus survival or just grow slow at high density but now with the changing density of surviving plants, not all plants in general higher surv=lower dry mass later in yr from N to J average howseweed mass increased, density went down , when startingform , were sown at a density of 100,000 per square meter, 100 by summer, number of survivors declined by 100 (10 log 2), while the average mass of the surviving plants increased by 1,000. self-thinning curve, which is a graphical relationship that shows how decreases in population density over time lead to increases in the mass of each individual in the population. . The self-thinning phenomenon has been observed across a wide variety of species. The insights that emerge from the self-thinning curve have a number of practical uses. For example, the curve can be used to predict survival and growth of crop plants that might be sown at different densities in agricultural fields growth and survival of tree seedlings that might be planted at different densities in forest plantations. ag, forestapplications all data = number plants Example: Horseweed plants were sown at a density of 100,000 per m2. Over time, many individuals died, leading to a hundredfold decrease in density. As density decreased, there was a thousandfold increase in the weight of surviving individuals. Self-thinning curve: a graphical relationship that shows how decreases in population density over time lead to increases in the size of each individual in the population; often has a slope of -3/2 outcompete if whole bunch in one pot

Homework

When the intrinsic growth rate (r) of a population equals zero, the population size after one year (N1) is EQUAL TO the initial population size (N0). Therefore, the annual growth rate (λ) of the population equals ONE, BC RATIO OF N1/NNAUGHT The intrinsic growth rate (r) describes the highest per capita growth rate that a population can experience. An intrinsic growth rate equal to one indicates that the population grows by ONE for every INDIVIDUAL in the population PERFECT REPLACEMENT PER INDIV. An intrinsic growth rate equal to zero means that the population does not grow at all. The annual growth rate (λ) describes the ratio of the population size after one year (N1) relative to the initial population size (N0). LAMBDA=ANNUAL, R = INTRINSIC λ=𝑁1𝑁0 In a population with an intrinsic growth rate equal to zero, N1 is equal to N0. Thus, the annual growth rate equals 1.

Which factor is MOST likely to cause positive density dependence?

a low proportion of females, more fem as pop grows

It is determined by the number of prey consumed by the predator population (cNP), which we saw in the prey equation above, multiplied by the efficiency of converting consumed prey into predator offspring (a).

acnp-

By considering the survival and fecundity of individuals of all ages during a single time interval, differences among the age classes are quantified under the same environmental conditions, so age is not ? with extreme environmental events.

age not wonky/confounded with these events In addition, static life tables allow us to look at the survival and fecundity of all individuals during a snapshot in time, which means we can examine species that are highly mobile as well as species that have long life spans. MOBILE AND LIVE LONG W STATIC We can also quantify survival and fecundity at more than one snapshot in time. think tree growth rings, looking at dif in age groups w static table you must be able to assign ages to all individuals, for static

we need a way to incorporate this information into our estimates of population growth rates. I

birth and death rates among age, size, and life history classes, To determine how age, size, or life history classes affect the growth of a population, we use life tables, which compile class-specific survival and fecundity data. Life tables are typically based on female (class-specific survival and fecundity data.(, and fecundity is defined as the number of female offspring per reproductive female However, we have to remember that the actual population size, which is comprised of both males and females, is twice as large as that estimated by a life table. number of individuals in each age class is denoted by n x . The value of n x represents the number of individuals present immediately after the population has produced offspring The fecundity of each age class is denoted by b x . (You can think of "b" for birth.) new offspring cannot reproduce, but 1-year-olds can each produce one offspring, 2-year-olds can each produce three offspring,

r sel species

breed, lots offspring low investment (high birth and pop growth rate/POTENTIAL k selected p:bison and pandas, low birth rate, most offspring to adult, low pop growth rate POTENTIAL to survive some spp specialize to do well thrive in specific conditions specialized spp good competitors for resources they've specialized in generalist spp thrive in wide range conditions(humans)

The Lotka‒Volterra model incorporates oscillations in the abundances of predator and prey populations and shows predator numbers lagging behind those of their prey. It does this by ? the increase or decrease of the prey and predator populations at any point in time depends on the current number of prey and predators that are present

calculating the rate of change in both the prey population and the predator population. growth in prey-pop not acting for time delay

Calculating the Intrinsic Rate of Increase When an intrinsic rate of increase is estimated from a life table, we assume that the life table has a ? age distribution.

connections between life tables and our earlier population growth models by using life table data to estimate the population's intrinsic rate of increase stable distribution However, stable age distributions rarely occur in nature because the environment varies from year to year in ways that can affect survival and fecundity. There are complicated equations to estimate λ and r. However, we can provide close approximations, denoted as λ a and, (where the letter a indicates an approximation) lambda(a)=Ro(NRR)^1/T Note that this value of 1.46 is close to our observed λ of about 1.49 after the population achieved a stable age distributio close to annual growth w stable distribution calculating. ra using logeRo/T A population grows when R 0 exceeds 1, which is the replacement level of reproduction for a population In contrast, a population declines when R 0 < 1 .

Polar bears are considered vulnerable to extinction because of habitat loss caused by melting sea ice. Which technique for predicting how polar bear populations will change in abundance over time is MOST useful for scientists wishing to conserve polar bears?

constructing an age structure pyramid by determining the number of individuals in different age classes Age structure pyramids indicate whether a population is generally increasing, decreasing, or remaining stable and do NOT predict precise NUMERIC changes in ABUNDANCES creating a survivorship curve by graphing survival among different age classes The survivorship curve for polar bear individuals will likely remain the same even if the population size decreases. just how many survive to any age class producing a cohort life table by continually tracking marked individuals over the course of their entire lives Polar bears are relatively long-lived, so constructing a cohort life table would take a long time, and scientists need information quickly if they want to prevent an imminent extinction. cohort hard for long-lived generating a static life table by compiling survival and fecundity data of individuals of all ages during a single time interval-need information quickly if they want to prevent an imminent extinction.

Two time delays caused the populations to cycle in Huffaker expt : The predators?than did their prey, and the predators needed time to increase their population size through ?

dispersed more slowly between food patches , esp when impeded by pegs and vaseline, and increased thru reproduction

eco footprints of some NATIONS exceed ?, for certain people (LOOK AT ONLINE RECORDING)

ecological capacity MEASURED IN HECTARES, ECO FOOTPRINT ABOVE CURVE? look at this part can see avail capacity in ha per person vs eco footprint American lifestyle above 8 hectares footprint, while capacity around 6 hectares, import materials from those below line (footprint below capacity means they may be able to give certain resources? at 49:30 -city less carbon emissions, standalone unit heating and need cars -heat contained in apartment

Tech increases K for human

food prod increased at faster rate than population enough for 3,130 cal.day and 2,730 cal/day in un(developed) countries w tech, support 1000 x times as many more ppl than 10k years ago

humans are ?, in wide ? of conditiond

generalists, survive in many enviro conditions and use dif resources ticks are generalists, all 50 states, wide range -death rates=function of age in organism-->type 1 higher old age , type 2 instant death rate like birds, type 3, high death young age becomes lower at older age (fish spp)

Select the population growth model for a small group of white‑tailed deer, which give birth each spring.

geometric growth It models species that reproduce at discrete intervals. The intrinsic growth rate, r, describes the change in a population size that accounts for the number of individuals born and the number of individuals who died. Using the intrinsic growth rate, an ecologist can quantify how a population changes over time using a population growth model. For species that reproduce at discrete intervals, such as white‑tailed deer, the geometric growth model describes population changes. The formula for calculating geometric growth includes the term lambda (λ) , which is the ratio of current population size to the population size in the preceding year. For organisms that reproduce throughout the year, such as humans, the exponential growth model calculates the population size at a given time (𝑁𝑡) depending on the starting population size (𝑁0) , the growth rate (𝑟) , and the interval of time (𝑡) . The constant 𝑒 is the base of the natural log. A linear growth curve depicts a population that grows by the same amount in each time period. The white‑tailed deer population does not exhibit linear growth because it expands according to the population in the previous time period., LINEAR NOT EXPAND BY PREVIOUS. POPS A logistic growth curve models slowing expansion of a population at high density. Because the population of white‑tailed deer is small, the logistic growth curve would not accurately model its expansion., NOT HIGH ENOIGH DENSITY YET

life expectancy is rising worldwide

growing but at slower rate, avg age newborn can expect to attain is life expectancy in 100 years , went 40 to 67.2 yrs ,improvements in food, wealth, medicine CDR=number deaths per 1000 developing countries=more youth and fewer elderly than in a slower, developed country (bout 6 in Brazil, 10 in western, 20 in Africa)

human pop growth differs over time

historically very slow human pop growth -pre-ag: few hundred thousand/yr -5000 BC pop was 50 million -old Stone Age-handheld tools, better ways to live, plague=decline in pop New Stone Age saw ag rev , then Bronze Age, Iron Age , middle ages BIM after Stone Age , modern saw Indust rev -1800 B.C.: 1 billion current growth=1.13 percent which is 79 mil new ppl/yr currently

sep exponential human graph

human population has been growing exponentially during the past 300 years. ideal conditions can experience a rapid increase in population size. This produces a J-shaped curve. (b) Human population growth is an excellent example of a J-shaped curve.

no population can sustain exponential growth ?. As populations become more abundant, they are limited by factors such as competition, predation, and pathogen

indefinitely, limited by comp, pred, and pathogens

The age structure of a population is the proportion of individuals that occurs in different age classes. A population's age structure can tell us a great deal about?

its past growth and its potential for future growth. . In these figures, known as age structure pyramids, we see that the nations of India, the United States, and Germany all have declining numbers of people after 50 years of age, due to senescence. But each has a very different pyramid shape below 50 years of age. Age structure pyramids with broad bases reflect growing populations, pyramids with straight sides reflect stable populations, and pyramids with narrow bases reflect declining populations. If the young age classes experience good nutrition and health care, they will survive well and the number of reproductive individuals 2 decades from now will be much greater than it is today, young in India will become larger repro group , will cause the population to grow. The number of people in the younger age classes is very similar to those in the middle age classes. In this case, we would predict that 2 decades from now, we would have a similar number of reproductive individuals, so the population should remain relatively stable. the number of people in the younger age classes is less than the number in the middle age classes. If we project ahead 2 decades, we would predict that there will be fewer reproductive individuals in the future and, as a result, the population in Germany should decline.

After constructing a life table for a red fox population, you determine the population's net reproductive rate (R0) is 3.2 and the generation time (T) is 1.3 years. Therefore, you approximate the intrinsic rate of increase as: λa= _____ and rα = _____.

lamba=Ro(3.2)^1/1.3=2.45 and ra 2.45; 0.39 This λa is correct, but to find ra, divide the natural log of R0 by T. 2.45; 0.89 I did base 10 log

You are hired by a farmer to solve her problem with groundhogs eating her crops. You look up groundhog life history and find that these animals mate and produce young only in the spring. You know that to address the farmer's problem with the groundhogs you must first understand how large the population is and how fast it is growing. You estimate that the current size of the groundhog population is 32 individuals and that the annual rate of growth is 1.73. What do you estimate the change in population size will be after 2 more years?

lammbad=1.73*Nnaught=new pop , A λ value greater than 1 means the population size has increased from 1 year to the next because there have been more births than deaths Nt = (32)(1.73**2)=99ish-32, this gets CHANGE or like net total after 2 years To find the change in groundhog population size, use the geometric growth model with a λ of 1.73 to calculate the population size after 2 years, then subtract the starting population size from the year 2 population size. 63 individuals

In a life table, survivorship for any age class is calculated by _____ the prior year's _____ by the prior year's _____.

multiplying prior year survivorship by survival rate

The net reproductive rate (R0) is calculated by _____ the _____ by the _____ and summing the results.

multiplying; probability of living to each age class (lx); fecundity of that age class (bx)

In life tables, R0 represents the _____ of a population.

net reproductive rate

d. With global warming, there is more food in the streams and the young salmon can grow much faster. As a result, they migrate to the oceans as 1-year-olds.

normally spend 2 years living in freshwater streams and lakes and then migrate to the oceans where they become reproductively mature at 4-5 However, when they arrive in the ocean, they face intense competition from other salmon, which has the potential to be a strong density-dependent force on their population growth. remember comp and pred and disease as ensity-dependent forces on population growth.

The data in this life table allow us to calculate the expected size of the population after ?

one year

Cohort life tables are readily applied to populations of ? in which marked individuals can be ? over the course of their entire life.

plants and sessile animals, indivs continually tracked over life The cohort life table does not work well for species that are highly mobile or for species with very long life spans, such as trees. BUT trees not used bc life span, think either life span or mobile One of the problems in using a cohort life table is that a substantial change in the environment during 1 year can affect survival and fecundity of the cohort that year. This makes it difficult to disentangle the effects of age from the effects of changing environmental conditions.

Population growth that increases as population density increases is called _____density dependence, and _____ density dependence tends to maintain population abundance at a level close to the maximum number that can be supported by the environment.

positive; negative density dep like neg feedback, tends to maintain population abundance at a level close to the maximum number that can be supported by the environment.

The second term (cNP) represents the loss of prey due to predation. The model assumes that the predation rate is determined by the?)

probability of a random encounter between predators and prey (NP) from random predation encounters (NP) times capture rate c

The difference between survival rate and survivorship (sx) is that the survival rate is the _____, whereas survivorship (lx) is the _____

proportion of individuals that survive from one age class to the next; probability of surviving from birth to age class x survivorship to any age class x

continually exceed K>

public US grazing lands, track if they can feed on land, overusing land resources w increasing cattle eating vegetation, above.K consuming too much will slowly start to decrease carrying capacity, until state change where biome becomes desert and cannot support ANY cattle state change from sparse veg letting soil be los tthru wind-blown erosion deer depleting seedlings in westchester forest, nothing in canopy to replace them , big dif in vegetation within areas where deer area, need longer deer season bc over K , elim deer's apex preds

R vs k selected k selected low ? growth ? potential

r selected-breed offspring many, high birth and population growth but low parental investment, few survive to adulthood, termite, rabbit k-selected bison , giant panda, most offspring from Low birth rate survive to adult , low population growth RATE potential many species do need to specialize in certain conditions, specialize in resource in environment

For the geometric model, the equation is nearly the same. Recall that r = loge λ, so we can replace r with logeλ:

rearranging the exponential growth model:(shown below) *GO BACK

climate change can have large impacts on the survival and fecundity of different life stages. For example, researchers in 2019 reported that sockeye salmon normally spend 2 years living in freshwater streams and lakes and then ? where they become reproductively ? when they are?

salmon migrate to the oceans, become mature when 4 or 5 years old. migrate earlier when more stream food As a result, they migrate to the oceans as 1-year-olds. However, when they arrive in the ocean, they face intense competition from other salmon, which has the potential to be a strong density-dependent force on their population growth. Thus, life tables for many species may have to be modified as global climate change increasingly alters life histories. For example, for decades, paleontologists have been excavating fossil bones of dinosaurs in Montana, including the tibiae, or shin bones, of a single species known as the "good mother lizard tibia lizard . Finding the fossilized bones of a single individual of any dinosaur species is an unusual event, but these researchers found an amazing 50 fossils of a single species They also recognized that they could age the fossil bones—based on the size and structures found in the tibiae—and this would provide data for a static life table. many fossils for STATIC table In 2015, they published their data as a survival curve, which is shown in Figure 11.22. Resembling a type I survivorship curve, the youngest age class individuals had high death rates, the middle-aged individuals had high survival rates, and the oldest age classes had high death rates. The simplest population models are helpful starting points, but they are not sufficient for most species that have survival and fecundity rates that vary with age, size, or life history stage. Although populations commonly grow rapidly when at low densities, they become limited as the populations grow larger

In contrast, a ? life table quantifies the survival and fecundity of all individuals in a population—spanning ? ages—during a single time interval.

static = all ages during a time during a single time interval. (for us or people not moving easily) when maybe cannot track over lifetime

When a population has a stable age distribution, the _____ and _____ of each age class remains constant over time.

survival; fecundity

Geometric growth model exponential=repro throughout year (humans), geometric whereas the second model applies to species that reproduce only during ? times of the year.

tech increase carrying capacity bc food production increase faster than population growth (over 3,000 cal per day in developed) -distribution problem with food, but tech helps give hypothetical food availability -most birds and mammals reproduce in the spring and summer when there are abundant resources available for their offspring -no birth during harshest season particular yr time to rreproduce -In both models, we assume that a population is not changing in size due to immigration or emigration of individuals. Populations initially grow slowly because there is a small number of reproductive individuals; growth rate increases with the number of reproductive individuals. Most species have discrete breeding seasons (e.g., the California quail breeds only during the spring). spring busy mating so give birth in summer quail spring eggs Geometric growth model: a model of population growth that compares population sizes at regular time intervals. due to discrete breeding The geometric growth model is expressed as a ratio of a population's size in one year to its size in the preceding year (λ). When λ > 1, population size has increased (more births than deaths between years with greater than 1 lambda); when λ < 1, population size has decreased; λ cannot be negative. -no neg because predicting population SIZES, neg indivs not seen 100 chipmunks and we have an annual growth rate of λ = 1.5 .only need No (100) orig pop and growth rate 1.5, then raise 1.5^5 for years and new pop is 759 You can see the changes in population sizes in Figure 11.2, where each color in the graph represents the new generation of young quail that are produced each sprin human replacement = 2

In life tables, x represents the

the age class

We can also use life tables to calculate the generation time (T) of a population, which is the average time between ?

the birth of an individual and the birth of its offsprin First, within each age class, we multiply the age (x), survivorship ( l x ) , and fecundity ( b x ) . Second, we take the sum of these products. This provides us with the expected number of births for a female, weighted by the ages at which she produced the offspring. SUM x (the age) times lx bx / lxbx This tells us that in our hypothetical population, the average time between the birth of an individual and the birth of its offspring is about 2 years. We can make connections between life tables and our earlier population growth models by using life table data to estimate the population's intrinsic rate of increase ( λ or r). When an intrinsic rate of increase is estimated from a life table, we assume that the life table has a stable age distribution. As a result, any approximation of λ or r is necessarily restricted to the set of environmental conditions that the population experiences. There are complicated equations to estimate λ and r. However, we can provide close approximations, denoted as λ a and r a (where the letter a indicates an approximation), based on our estimates of net reproductive rate ( R 0 ) and generation time (T): approximate growth = NRR (Rnaught)^1/T Note that this value of 1.46 is close to our observed λ of about 1.49 after the population achieved a stable age distribution this is estimate not describing a stable age distribution, giving approx ra You can see that a population's intrinsic rate of increase depends on both the net reproductive rate ( R 0 ) and the generation time (T). The greater the net reproductive rate and the shorter the generation time, the higher will be the intrinsic rate of population increase. A population grows when R 0 exceeds 1, which is the replacement level of reproduction for a population. In contrast, a population declines when R 0 < 1 . The rate at which a population can change increases with shorter generation times.

In our discussion of population models so far, we have assumed that all individuals in the population have an identical intrinsic growth rate—that is, ?

they have the same birth rates and death rates. individuals cannot reproduce until they have achieved reproductive maturity. In terms of individual size, individuals with greater mass typically have higher fecundity In terms of life history stages, we know that different organisms experience different fecundity rates during each life stage. For example, tadpoles experience low survival and no fecundity, whereas later in life, as frogs, they experience high survival and high fecundity. . In this section, we will examine how changes in survival and fecundity among different age classes in a population—such as kangaroos that are 0, 1, 2, or 3 years old—affect population growth grows-survival and fecund each age class the same calculations apply to individuals in different size classes or life history classes. US ABOUT 0.8 , POP INCREASE ACUTALLY DECREASE WORLDWIDE

continually exceeding carrying capacity density for deer hunting

tragedy of commons, increase resources , western US public grazing land for cattle, mark and let them feed on land, overuse resources and increase cattle that eat constantly and reach carrying capacity, then carrying capacity will decrease of enviro w more cattle, bc changing ecosystem by degrading it density for deer hunting, forest ecosystems shifting bc deer have populations have reached/gone above carrying capacity, deer depleted seedlings -nothing to replace resources in certain vegetation zones, elim apex predators needing to keep deer in check