61BL3313 Population and Community Ecology Lecture 01 Simple density independent growth Spring 2013 Dr Ed Harris

2 Today -lecture + lab -handbook and schedule -Moodle + unit website -issues, comments?

3 What is population ecology?

4 -study of a group of organisms taxonomically or functionally related to one another -emphasis on fundamental properties of these populations such as prowth in number, survivorship and reproduction -the tradition is based on the interplay of theory, lab work and field work -an organized way of communicating our ideas about nature with others

5 Fundamental principles and population data -the basic goal of ecology is to describe properties of populations explicitly (e.g., mathematically ) -population biology is the search for basic principles that are common to all populations -What factor is the most important? -E.g., the biomass of a bacterium is several orders of magnitude smaller than that of an elephant. The generation time is several orders of magnitude faster!

6 fundamental "laws" of populations -movement in the past few decades to "re-invent" population biology (and evolution and ecology in general), as a vigorous, predictive science with principle truths like the laws of Newton i. populations tend to grow exponentially ii. populations show self-limitation iii. consumer-resource interactions tend to oscillate -Sutherland (1996), Turchin (2003)

7 How do we begin to study pop. growth? -what if we wanted to study the size of a population through time, for example the critically endangered Florida panther... -What information do we need to know? How do we gather it? What do we do with it?

8 How do we begin to study pop. growth? population growth is basically a combination of factors: 1. reproduction 2. mortality 3. immigration 4. emigration

9 How do we begin to study pop. growth? A way to think of this mathematically popN (t+1) = popN (t) + (births – deaths) + (immigration - emigration)

10 How do we begin to study pop. growth? Let's look at each of these factors 1. reproduction 2. mortality 3. immigration 4. emigration

11 How do we begin to study pop. growth? 1. reproduction The addition of new individuals to the population Can be measured by: A. Fecundity – potential reproductive output under ideal circumstances B. Fertility – actual reproductive output under prevailing environmental conditions

12 How do we begin to study pop. growth? 1. reproduction In practice, fecundity or fertility is usually expressed as a rate For example, the number of offspring per individual in the population (i.e., the rate per individual per some unit of time) *For humans, the rate is often expressed in # offspring per 1,000 people per year 1981->28/ >22/1000 * for continuously breeding species like humans, we need to know the fertility rate for each age class!

13 How do we begin to study pop. growth? 2. Mortality -also usually expressed as a rate -e.g., the average number of deaths per individual (or per 1,000) per time unit -as with fertility, useful to know the rate for each age category Mortality rate in humans: 1981 = 11/ = 9/1000

14 How do we begin to study pop. growth? Important here to begin to think about how many individuals are in each age class in a population. -This might change over time -The shape (of the distibution) matters!

15 How do we begin to study pop. growth? -can we interpret these data? -which population is growting faster and why? -Speaking of (r)...

16 How do we begin to study pop. growth? Population measure: The intrinsic rate of increase, otherwise known simply as "little r" -r is the population growth rate per individual per time unit (e.g. a year) -you can estimate this from birth and death rate data r = b – d (per individual per unit time)

17 How do we begin to study pop. growth? -for human rates expressed in 1k units: r = (b – d) / 1000 individuals (per unit time)

18 How do we begin to study pop. growth? You can see: Asia has a +r: the population is predicted to grow Europe has a -r: the population is predicted to shrink (slowly)

19 How do we begin to study pop. growth? A few finer points: -if r for these 2 regions were the same (and positive), the population in Asia would still grow faster than Europe for some years because of having > reproductive age individuals -estimation of r assumes a "stable age distribution" (proportion of individuals in each age class is the same through time)

20 How do we begin to study pop. growth? 3. immigration (rate) -the number of individuals that join a population per time unit due to immigration -ideally, we would like to know the ages of these individuals (why?)

21 How do we begin to study pop. growth? 4. emigration (rate) -the number of individuals that leave a population per time unit -again, we would like to know the ages of these individuals

22 How do we begin to study pop. growth? immigration and emigration -hard to measure accurately -often ignored as a consequence -common assumption is that of a "closed population" where immigration and emigration is negligible

23 How do we begin to study pop. growth? immigration and emigration -> metapopulations Metapopulation: a "population of populations", where local populations exists in a mosaic of suitable and non-suitable habitat -Recent shift in scientific practice from single populations to metapopulation ecology -Advances in theory and field studies have solidified this approach

24 How do we begin to study pop. growth? immigration and emigration -> metapopulations

25 How do we begin to study pop. growth? immigration and emigration -> metapopulations -This approach is particularly useful in the context of conservation problems The bottom line: We'll begin this unit by focussing on single populations to get the basics, keep in mind though that metapopulations and communities are the modern focus

26 How do we begin to study pop. growth? How to describe population size with numbers? Let's rewrite the equation from above:

27 How do we begin to study pop. growth? How to describe population size with numbers? We can rearrange the equation a little -for now, we'll also assume I and E are negligible, thus we are left with B and D - B and D are generally expressed as rates -the notation for rate values is to use lowercase b and d

28 How do we begin to study pop. growth? How to describe population size with numbers? -the difference between b and d was described above as "little" r, which is a per individual in the population rate -if the unit of time we calculate b – d is a generation, we refer to the value as "big" R which we call the net reproductive rate (i.e. the net growth rate per generation), which is a per generation rate

29 How do we begin to study pop. growth? How to describe population size with numbers? Now we can write the equation as -this equation can be used to predict the change in population size each generation -this is called discrete growth

30 How do we begin to study pop. growth? discrete growth

31 How do we begin to study pop. growth? A lot of spescies, like humans and many animals most familiar to us, reproduce irrespective of season and therefore the population grows continuously To estimate this, we use the instantaneous growth rate which is the change in population N over a very small time period -in a sense here, r measure the probability of a birth or death occurring per tiny time interval

32 How do we begin to study pop. growth? continuous growth

33 How do we begin to study pop. growth? We've been talking about population growth in a very simple way, ignoring several factors that can affect population growth. Primary amongst them is how population density might influence population growth Hence, we've been talking about density independent population growth (as opposed to density dependent growth, which we'll consider later on) The important thing to keep in mind is that we are ignoring limiting resources like water, food, nest sites, space, etc.

34 How do we begin to study pop. growth? Discrete growth in populations -non-overlapping generations -no adult survivors that can reporduce from generation to generation -annual plants and insects and some other special species...

35 How do we begin to study pop. growth? Discrete growth in populations... like salmon, century plants, periodical cicadas, etc.

36 How do we begin to study pop. growth? Discrete growth in populations Some important variables before we go on r = intrinsic rate of increase (per individual per unit time) R = net reproductive rate (for the population per generation) There is one more we will encounter soon: λ λ = finite rate of increase (per specific time unit*, usually per year) *note that λ = R when generation time == the time unit in question e.g. in annual plants, insects

37 How do we begin to study pop. growth? R = net reproductive rate (per generation) λ = finite rate of increase (per specific time unit)? Periodic cicadas -emerge for a generation every 10, 13 or 17 years -hard to directly estimate R!

38 How do we begin to study pop. growth? Need to estimate successive population growth rates Let's break it down:

39 How do we begin to study pop. growth? If R stays the same through time which leads to

40 How do we begin to study pop. growth? To reiterate is the same as when λ = R when generation time == the time unit in question

41 How do we begin to study pop. growth?

42 Next time Exponential growth in populations with overlapping generations aka continuous population growth