4.9 Population Ecology

population dynamics (def)

changes over time in population size & composition

the slope of an exponential growth curve for any population size is...

dN/dt = rN (r * population size at that point) why get such rapid growth: population size depends on not only rate, but # of individuals currently in population, SO increase at faster rate when population is larger!!

logistic growth (equation + plot/graph)

dN/dt = rN(1 - N/K) K = carrying capacity (max number of individuals that can be supported in a population at that time) at some point, run out of resources (so can't keep growing) GRAPH SHAPE - when N small, trajectory close to that of exponential growth - when N gets large & closer to K, (1 - N/K) gets larger, so multiply rN by smaller fraction, so slows down - at carrying capacity K, rN(1-1) = 0 (growth rate ceases - end up with constant population size - this is more theoretical bc normally don't perfectly stop at K)

ecology (def)

ecology considers the abundance & distribution of species as well as the relationships organisms have with their biotic & abiotic environments

what kind of increase occurs on plot when r is constant?

exponential increase!

carrying capacity (K)

max number of individuals that can be supported in a population at that time

what is r?

measure of the instantaneous rate of change of population size (per individual) (how many offspring an individual has over some unit of time) - expressed in number per unit time per individual - units: 1/time 1/N dN/dt = r - 1/N = per individual - dN/dt = change in # of individuals per change in time the slope of an exponential growth curve for any population size is: dN/dt = rN

overshoot & crash cycles

mentioned that theoretically stop growing once population size reaches K - in actuality, don't stop at K (when reach carrying capacity)!! Tend to see population around K will overshoot (get larger than K), something happens to cause population to crash (resource limiting / disease / etc.), decrease below K, then increase again and >K (so oscillate around K rather than just staying constant at K) (Some populations overshoot carrying capacity, drop below it, and increase and overshoot it again until they settle down close to carrying capacity.)

Reindeer on St. Matthew Island

normally live in tundra type Reindeer able to get to new environment St. Matthew Island 29 reindeer able to get here (1944) Population start small Abundant resources 1944-1957, up to 1350 Mid 60s - 6000 Exponential growth curve! But can't increase forever What happened: huge crash (not enough food) - reindeer starving 1966 - back to 42 from 6000 SO doesn't follow logistic curve where rapid increase & plateau

population density (def)

population size (# individuals) per a given sized area - can be in 2 or 3 dimensions (aquatic environment - volume)

more about r

r is the intrinsic rate of increase per individual when dN/dt (r*N) = 1.0N, means you replace yourself + 1 more = population doubling every generation = increase by 100% every generation when dN/dt (r*N) = 0.5N, means replace yourself + half an individual each generation (grows slower, but can still increase rapidly when hit later generations, and thus have larger population size) rN describes the slope of the line at a particular point. The growth of a population over time is related to both its rate of increase and the number of individuals already in the population. Even with very low positive r, if the population size is very large, population growth every generation can also be very large (as in our own population).

[MCP] r intrinsic rate of increase Can the "replace yourself + 1 more = population doubling every generation" part of r = 1.0 be explained once more? I understand that as N increases by 1, then so should dN/dT, but I don't understand where the "population doubling every generation" is coming from. I was wondering if you could explain again what it means to say that you are "replacing yourself" when talking about the variable r. For example, in the lecture you said "If the r value is zero, that means you are exactly replacing yourself". I am still a bit confused about how this idea of replacement plays into the intrinsic rate of increase.

r measures each individual's contribution to the population from one time point to the next, including themselves - r = additional increase in population over & above yourself (assume your still around next time) So, if the r is 0.3 that means that each individual is contributing (on average) 0.3 individuals to the population in addition to themselves for each time interval (so would multiply population by 1.3) If r is 1 then each individual is contributing 1 more individual to the population at each interval. This is a special case that will result in the population doubling over each time interval. - special case: contribute themselves + 1 additional individual (result in doubling because everyone contributing themselves + 1 more) - would multiply population by 2!

population size + density (details)

recall natural selection- genetic drift balance depends on population size! - genetic drift becomes more important as population size decrease (IMP when population sizes are small!!) density-dependent factors (competition, disease, etc.) depend on population density - at low density factors like competition important, so selection on traits related to competition less strong the distribution of populations is how they are spaced in areas in which they live (density = size in relation to area) (balance between natural selection & drift: relationship depends on population size!)

population dynamics (details)

studies the size & age compositions of populations & the environmental processes affecting them - collect + analyze descriptive data: density, size, birth + death rates - generate + evaluate mathematical models to estimate things like: growth rates, carrying capacity, density dependence + independence

population ecology (def)

study of the processes that control single populations or species

density-independent factors

tend to be ABIOTIC affect a population, regardless of its size, but can serve to decrease the population - storm - fire / flood - avalanche (so tend to be natural disasters)

density-dependent factors

tend to be BIOTIC effects of them increase as population grow & cause growth to slow until 0 when the population reaches the carrying capacity, K (so populations grow until hit some density-dependent factor) - competition (for resources, mates, etc.) - disease - predation the effect on the population changes depending on the density of the population!

biotic & abiotic factors in population regulation

there could be many different abiotic / biotic factors organisms need, but only some of them will be limiting factors ex: need water to live, but it's not a limiting factor, but availability of food for fish = limiting factor

exponential population growth

x-axis: breeding cycle (some time unit, like generations) y-axis: population size (# of individuals) SHAPE - at first, growth is slow (not many mice to have babies) - as each produces 10 offspring, population rapidly increases - reproductive rate hasn't changed, but constant rate of reproduction gives huge # of offspring

human population growth through history - where are we on the curve?

x-axis: years y-axis: population green arrows show stages of human development up until after industrial revolution, population < 1 bil after, rapid increase where we are on the curve: how much room before reach our carrying capacity? - depends on how much (energy? / resources?) people use, if we're able to be more efficient, etc. (see slide 8 of 4.9 population ecology 2 pt 2 ppt for actual curve)

[MCP] r versus K: do r strategists or K strategists have a greater number of reproductive events in their lifetime? Also, I know that r strategists produce more offspring, but how do the ultimate population sizes of r strategists vs K strategists compare?

•I'm not sure which ones have a greater number of reproductive events. It would depend on the generation time and survival for each species. Population size of r strategists may vary from small to large, but they generally are below the carrying capacity. K strategists, due to their high survival have populations closer to their carrying capacities. - r strategists have shorter lifespan (most have fewer reproductive events) - K strategists may have higher # reproductive events bc of life (but will have fewer # offspring per event) - But this all just varies (could depend) POPULATION SISZE - Varies over time - r: tend to be large (to keep reproducing rapidly, have to be below their carrying capacity) - K: bc of high survival, tend to be close to carrying capacity + close to using up all available resources (fewer population, but each individual will use more resources)

rate of population change (def)

(brith rate + immigration rate) - (death rate + emigration rate) look at this especially in relation to population size!

[MCP] Altruism or kin selection example

- Datana ministra caterpillars have bright red and yellow coloration indicating their toxicity and when threatened adopt a posture with head and tail turned up - A predator must kill one of these creatures to learn to avoid similar animals in the future (if bird eats 1 of caterpillars, unlikely to go back to eat them) - These caterpillars aggregate in kin groups since they come from the same egg mass - The death of one individual is likely to benefit its siblings - The altruistic act of posturing is likely to be favored by kin selection (posturing so bird will just eat 1 caterpillar rather than >1) SO altruistic act results in kin selection - Loss of 1 caterpillar saves its siblings - Shows how altruism related to kin selection!!

[MCP] Inclusive fitness: Are kin selection and inclusive fitness completely unrelated? Are they subcategories of altruistic acts or how exactly does inclusive fitness relate to altruistic behavior?

- they are related concepts: inclusive fitness is the passing on of your genes through relatives as well as through your own reproductive output - selection for behavior that lowers you're your own fitness but enhances the reproductive success of a relative is kin selection. - We would expect altruism - Altruistic behaviors lower your own fitness but enable other individuals to save themselves (increase others' fitness) (e.g. warning calls) - Can select for behaviors to increase inclusive fitness (not just your own fitness)

[MCP] Exponential growth: since populations cannot sustain exponential growth forever, does that mean that all exponential growth curves eventually turn into logistic growth curves?

Basically, yes. Exponential growth occurs only when no resources are limiting. When resources are become limiting the population will slow it's rate of growth (logistic growth) or collapse (population crash). (no limited resource doesn't exist!)

current world population + population ecology

Climate change reducing resources Less availability of water, reducing availability of land as sea rise As get more developed, use more resources Don't know where we are on the curve We need to learn how to use less!

abundance vs distribution

abundance = how many individuals present distribution = how arranged

exponential growth- what should wildlife managers do? (about reindeer on st matthew island)

add predators? cull the herd (hunt)? move them? (could move them to place with available resources) do nothing (let them starve)? have to do with cost, what's best for deer, society, etc. (continuation of reindeer on st matthew island)

population (def)

all the individuals of a species living together in the same area

limiting factor

an environmental factor that (potentially) restricts the growth of populations

abiotic factor

any nonliving thing that affects an ecosystem: water, sunlight, oxygen, soil, and climate (availability of these things)

4 processes that control popualtions

1. births 2. deaths 3. immigration (migration in) 4. emigration (migration out) how do immigration / emigration relate to gene flow? for simplicity, will look at closed population (no immigration / emigration)

patterns for population growth (3)

1. exponential growth: population grows by a constant factor each generation ("J curve") 2. logistic growth: population size increases rapidly at first, but then slows down as population grows large ("S curve") 3. carrying capacity: the maximum number of individuals an area can support - many different factors can contribute to this (e.g. limited amount of resources available)

what the different values of r mean

1. r < 0 - replacing less than yourself each time - exponential decay - population size declining over time 2. r = 0 - replacing just yourself - population remains constant over time 3. r > 0 - replacing more than yourself each time - exponential growth - population size increasing over time

population characteristics (2)

1. size (abundance): the number of organisms in a population 2. population density: the number of organisms per unit area of volume

modeling population growth

N = population size rate of change = change in N per unit of time ∆N/∆t: rate of change of population for discrete time units / steps dN/dt = rate of change of population for continuous time units / steps simplest model: - assume no migration (closed population) - assume per capita (per individual) rates of birth and death are constant: b = per capita birth rate, d = per capita death rate (1/N)(∆N/∆t) = b-d r = b-d (1/N means per individual 1/N * change in whole population over time per individual = births - deaths r = births - deaths)

[MCP] Strong Selective Pressure to decrease length of each stage On the slide "Survivorship of Swallowtail Butterflies" (Survivorship Lecture in Intro to Ecology), is the "strong selective pressure" decreasing the life stage in response to vulnerability (i.e. decrease life stage of pupae so less pupae have the time to die) OR is it decreasing the life stage in order to make it more vulnerable? I was confused by this because in the next slide on Type I curves, it was said that the sharp decline at old age is a result of selective pressure, which suggests the selective pressure itself causes vulnerability rather than responding to vulnerability.

Survivorship of Swallowtail Butterflies - There is therefore strong selective pressure to decrease the length of each stage, especially those stages most vulnerable to mortality. - This figure indicates that, for some reason, there is high mortality at the egg and pupal stages. It would be to the animal's selective advantage to shorten these stages, to lessen the time spent in vulnerable stages. - Graph of survivorship at different stages for group of eggs that started at same time - Slopes different during each stage - For some reason, eggs & pupa vulnerable to mortality events - From natural selection perspective, if could shorten those vulnerable stages, expect to overall increase survivorship for those animals Type 1 survivorship: - High survivorship early in life - Steep decline after avg age - Why see this: natural selection - Humans have long lifespan where alive but post reproductive - Natural selection really only affect reproductive traits - After old, lack of selection bc already reproduced - RESULT: organisms can accumulate genes / genetic traits that are negative at older ages - just won't be selected against bc no reproductive benefit (The sharp decline seen late in life in type 1 curves is actually due to a lack of selection at later ages. Selection occurs for traits that affect reproductive success. Negative traits that act after the age of reproduction will not be selected against. (Remember, this is the reason skin cancer couldn't explain the evolution of skin color).)

populations display various patterns of growth!

When resources are unlimited there will be exponential growth. When Resources become scarce • Individuals starve or are unable to find habitat for reproduction. •Aggression and competition increase. •There is pressure from predation. Population size increasing while the growth rate decreases is logistic growth—the S-shaped curve. PICTURE: 1: both growing 2: approach K - resistance factors start to slow population growth rate (changes from J to S curve shape) 3: carrying capacity: population growth stops at K

biotic factor

a living thing that influences an ecosystem, such as prey, predators, pathogens and competition for resources (availability of these things)