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### Population Growth and Regulation

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Today, we will carry forward our discussion on population ecology. We will look at somenumerical examples of different population parameters and then we will move forward tolook at the theories of Population growth and regulation.(Refer Slide Time: 00:31)
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This is the first problem that we look at. A park manager conducts a population estimationexercise within a protected area. He samples 18 quadrates with line transects and obtainsthe following density estimates for sambar. So, here you have 18 different transects 18different areas.
(Refer Slide Time: 00:52)
We will consider that all of these beats have the same area and the sambar density, thenall of these areas is figured out and the number per square kilometer is given here. Nowthe question is what is the average sambar density that is found in the park?(Refer Slide Time: 01:11)
We will make this assumption that these 18 beats are all the beats that we have here andthe area is more or less homogeneous. And this case the average density of sambars willbe given by some of these different densities that we have in the table, we have 8 + 5 + 6+ 5 and so on till the last value which is 5 to till the 18th value which is 5.
We make a sum of all these different densities divide that by 18 and then we get the averagedensity is 101 divided by 18 of 5.61 animals per square kilometer. So, this is a simpleexample of how we use sampling to get one estimate for the whole of the population. So,we took 18 different samples and for all of these samples, we computed the sambar densityis using line transect.(Refer Slide Time: 02:12)
Now line transect is a method in which we move along a straight line. So, this is how weare moving and every time we spot an animal and suppose we are here. When you spotthis animal we find out this distance and we find out this angle. Once that is done we canfind out the perpendicular distance. So, if this is d, this distance will be dsinθ.So, this is the first distance then we saw an animal here and this was our location toprobably this distance, this one is d1 this one is θ1. So, this one becomes d1sinθ1 and soon. And by all of these different perpendicular distances we can compute the area that wehave walked in total; so, with all of these different distances. So, let us call these as D1,D2, D3, D4 and so on. With all of these we will find out a mean distance of the animalsfrom this area.So, suppose this mean distance comes to be say this value of D. So, this distance of D tothe right and this distance of D to the left. And in this case we have observed 4 animalsand with this mean distance we compute the area that has been covered by us. So, this isthe area that has been covered. So, suppose this length is L. So, the area is L x D and from
this we get the density of animals per square kilometer. So, this is what we have done andwe have computed all these different densities and we can take a simple average of all ofthese different densities to find out the average density of sambars in this area.(Refer Slide Time: 04:12)
Now, such computations can then be extended. So, this is the second question. The groupsizes of chital in the core and buffer zones of Corbett Tiger Reserve, Uttarakhand wererecorded during winter of 2009 and the data is given. Estimate the mean group size,standard deviation, standard error, range and coefficient of variation; comment on theresults obtained.
(Refer Slide Time: 04:43)
So, similar to what was done before, here we have group the sizes of different groups. So,earlier we had densities in different areas, here we are looking at different groups and thesizes of all these different groups.So, in the core zone we saw so many groups and these were the number of animals in eachgroup 26, 24, 25, 27; so, these are all close together. Here are the values in the buffer zone.So, this is 26, 11, 7, 3, 15 and so on, so, there is a very large amount of variation. Nowwhat kind of inferences can be make out of such a data? So, we begin by looking at themean group size; now for the mean group size what you do is, you take a total of all ofthese. So, for the core you make a sum of all of these and then the number of groups is 1,2, 3, 4, 5, 6, 7, 8, 9 and 10. So, in these 10 groups this was the total number of animals thatwas seen. So, what is the mean group size?
(Refer Slide Time: 05:44)
So, the sum of all the group sizes and the core divided by total number of groups. So, thatcomes to 252 by 10 which is 25.2 animals per group in the core area.(Refer Slide Time: 05:58)
And similarly you can repeat this process for the buffer area. In the buffer area the numberof animals per group is 20.7. So, one thing that we can see here is that the number ofanimals per group in the buffer area is less than the number of animals per group in thecore area. Now why could we have such a difference; we can then correlate this to theecological parameters that are found in these 2 areas.
(Refer Slide Time: 06:26)
So, typically if you consider any tiger reserve. We have this core area, the core area lies inthe centre and in this core area you have less amount of human disturbances and this areais relatively left untouched. Now this area, on the outside goes by the name of the bufferarea. Now why is this area called a buffer area? Because you might have say a village here.Now if you have a village there are situations that people might want to get into a tigerreserve or into a forest and cut some wood for firewood or maybe you have some animalsthat are living in the village and they are getting into the forest areas for grazing or maybeyou have some dogs that are living in the village and these dogs are also getting into theforest areas. So, for all of these different influences whether it is for firewood, whether itis for animals such as cows or for animal such as dogs or for things like pollution or theamount of dust that is being released or the sounds that are released, we can define a zonethat goes by the name of, the zone of influence of this village. Now we want to have thiscore area completely untouched. So, which is by we create a buffer region.In the case of the buffer region, you can have some zones of influence, but then this bufferregion acts as a buffer. So, that the core is completely kept secluded. In the case of thebuffer region you will be having grasses, but then probably the chitals will have to competewith the cows or maybe probably the chitals will have to remain vary of the dogs that arecoming to this area.
So, in that case it is possible that chitals tend to avoid this area which is something that wecan observe by looking at the numbers of chitals that are found in this area and also thegroup size of chitals that are found in this area.(Refer Slide Time: 08:30)
Now, from the group density, we can then move on to the standard deviation. Nowstandard deviation for the population is given by the square root of sum of deviations. So,in this case μ is the average value that we figured out earlier, x is all the different values.So, in the case of core, we saw that the average is 25.2 and the values are 26, 24, 25 andso on. So, when we are computing the standard deviation we will have these values 26, 24and so on minus 25.2 you take a square of all of these, add all of these and divide them bythe total number of observation that you have made. So, here you have 10 number ofobservations, you do this, you get to a standard deviation which is 1.249 animals per group.Now, what does standard deviation tell you? It tells you what is the amount of variationthat we are seen in the group sizes. So, here the variation is 1.249 animals per group.
(Refer Slide Time: 09:36)
Whereas, in the case of buffer area when you repeat the same observation, you can see thatthe standard deviation is much greater 11.385 which gets as an indication that in the caseof the core areas, all these different groups are much more homogeneous.So, if you look at a group here or a group here or a group here all of these groups arehaving the same sizes. But in the case of the buffer region if you are seeing a group hereprobably it has a smaller size, a group here has a larger size, a group here has probably amedium size and so on. So, the amount of variation in the group sizes is less in the coreand its more in the buffer regions in this particular example.
(Refer Slide Time: 10:22)
Now, from the standard deviation we can move on to find out the standard error, which isanother way of expressing the same thing. So, standard error is given by, ( σ / √n ). So, inthis case, for the core zone it comes to 0.395 and in the case of buffer it comes to 3.6.(Refer Slide Time: 10:38)
So, here also we are seeing that in the case of the buffer zone, the standard error is muchgreater than that in the core zone which is another indication that the group size is muchmore heterogeneous in the case of the buffer.
(Refer Slide Time: 10:56)
Then we can compute the range of these values. Now range is given by the highest valueminus the lowest value. Now in the case of the core region, all the group sizes for nearlythe same the largest one was 27, the smallest one was 23, so, the ranges 4 animals pergroup.(Refer Slide Time: 11:17)
Whereas, in the case of the buffer zone groups, the largest size group had 40 animals thelowest size group had 3 animals.
So, here the range is very large, so, we have 37 animals in the range. So, this is also tellingthis the amount of heterogeneity that is there in the buffer groups.(Refer Slide Time: 11:36)
From here we can move on to find out the coefficient of variation. Now coefficient ofvariation is a term that helps us to look at these differences, these variations very easily.Now in this particular example we had 10 groups in the core and we had 10 groups in thebuffer area. So, that makes comparisons very easily, but suppose in the core we had say25 groups and in the buffer we only had 10 groups.So, in that case when you want to make a comparison between both of these statistic. So,we go for a coefficient of variation. Now coefficient of variation is defined by σ which isthe standard deviation divided by the mean which is given by μ into 100 %, so, it is askingthis question what percentage of the mean value is the standard deviation. So, in the case
of core, it comes to 4.956 %, or close to around 5 %, in the case of buffer it comes to54.998 %, or close to 55 %,.(Refer Slide Time: 12:38)
So, in the case of core we are saying that the standard deviation is just 5%, of the meanvalue. In the case of buffer the standard deviation is as much is 55%, of the mean value.So, in this way we can make comparisons between both of these groups even if they havedifferent sizes.(Refer Slide Time: 13:06)
So, what do we infer out of these values? Now, the inferences that, the group sizes of chitalin the core zone are more or less similar as they shown by this small range value and thesmall coefficient of variation of 5 percent. However, the group sizes of chital in the bufferzone are extremely variable as shown by the larger range value of 37 and coefficient ofvariation of 55 percent. The coefficients of variation also hint that the standard deviationis very far from the mean value in the case of chital groups in the buffer zone, while thestandard deviation is close to the mean in the case of the chital groups in the core zone.(Refer Slide Time: 13:47)
Now these numbers provide an indication of the habitats in the core and the buffer zones.Now the core zones are mostly unfragmented and uniform. So, the group sizes of chitalshow little variations from one group to the next. On the other hand since the buffer zonesare relatively fragmented and non uniform, showing also high anthropogenic influences,each chital group in the buffer zone will show a difference from the other groups,depending on the patch of habitat that was available to it. In this way we may utilizestatistical information to make sense of or even to predict the ecological information.What we are saying here is that, if we considered the chitals in the core zone. So, this zoneand this zone and this area are all the same, there is hardly any difference. But then in thecase of the buffer zone, if there was a chital group that was residing here versus a chitalgroup that was residing here, that would make a very big difference. Because this particularchital group is close to the core zone, it is away from the zone of influence of the villages
and so, it is having a much more protected environment in which to graze and in which toincrease its population. Whereas, in this particular chital group, it is so close to the humaninfluences that, it might be having a very different impact on the group behaviour.In this case because the amount of variation is greater in the buffer area, and the amountof variation is less in the core area so, that is also manifesting itself in the group sizes ofchital in the core area and the buffer area. So, just by looking at group sizes of animals indifferent areas, we can make some inference about what is going on in the ecological terms,which also makes it very pertinent to know different population parameters. In the lastlecture, we looked at different population parameters, in this lecture we are making acorrelation between what the population parameter said and what is the actual ecology ofthat area. If we are seen differences it means that there is some ecological undercurrentthat is flowing there.(Refer Slide Time: 16:05)
Next we look at sampling of rainforest herpetofauna. Now, in the case of larger animals,it is easier to see the animals, to count the animals, to get to a density of animals, whatabout this smaller animals? If you wanted to say know the number of snakes that are thereper unit area in a forest. So, how do you go about and catch a snake? A snake will notmake itself visible to you because you want to count this snakes. This snake wouldprobably lie beneath some rock or maybe it would lie in some tree, or so on.
What about other smaller animals, such as say, frogs. In the case of frogs you want to knowhow many frogs are there per unit area. How do you make an estimate of the number offrogs? You can very easily see the number of tigers that are there in an area, but frogs arevery difficult to see and count.So, what are the methods that we make use of? So, in the case of rainforest herpetofauna;Herpetofauna is basically reptiles and amphibians. These are the methods that areavailable; one is opportunistic encounters. Opportunistic encounters with the species hasgleamed from the researchers encounters or information from locals can be used togenerate a list of species that is found in that area including some cryptic species that maynot be evident in directed service. This is applicable even to sampling in the rainforest.So, there is a rain forest you want to know how many animals are there, what are all speciesof animals are there.(Refer Slide Time: 17:42)
So, we looked at the species discovery curve or the species accumulation curve in whichyou have this time on the x axis and the number of species on the y axis. And we saw thatit increased and then it started breaking to a level of saturation. Now to know more andmore about the species that are found in a rain forest area, you could go for an opportunisticencounter. Opportunistic encounter means that you went into the forest and there was achance encounter of some animal.
So, you went into the rainforest and you saw a frog that was red and yellow in color andprobably you had never seen this frog before. In that case, we will add 1 more species tothe species accumulation curve so, that is an opportunistic encounter. Now opportunisticencounters can also be used to understand the relative population densities of differentanimals in the rainforest. You went into a rainforest in say, January and you saw that therewere say 5 animals that you saw in the whole period of 1 day. You went again, you saw 4animals; you went again you saw 6 animals. So, on an average you are seeing 5 animalsper today. You went to the same rainforest in the January of the next year and probablyyou are seeing only 2 animals per day. So, that would give you an indication that thepopulation size is reducing. So, that is an opportunistic encounter.The second method is complete species inventory; construction of complete speciesinventory by combining data from opportunistic encounters and directed surveys isfeasible in rainforest. So, you are just increasing the amount of effort that you are puttingin to get to a very close approximation of the number of animals and the number of speciesthat are found this area.Next is visual encounter survey. This involves directed surveys for visually seeing speciesin an area, in a procedure that is constrained by time, area or both. Rock flipping or othertechniques may be employed and this is feasible even in rainforest. Now what do you doin the case of a visual encounter survey? We will get into the rainforest and you will saythat you are going to survey this area for the next 1 hour. In this 1 hour you are putting allyour attention all your effort into seeing and counting this species. What you will do is,suppose you are looking for frogs in that area; so, you get into this area.
(Refer Slide Time: 20:11)
So, this is a small area that you are looking and then in this small area you go and there isa rock lying here. So, you lift this rock and suppose you saw 3 frogs there. You catch those3 frog put them into a bag. Then you move to the next rock here also you upturn this rock,probably you saw 1 frog, you take it put it into the bag; you go to another rock. And thenin this area for the next 1 hour you are just going to different rocks, flipping those rocksand taking out all the animals that are there and now you are constraining yourself in termsof area and in terms of time.So, you are saying that this is the area that I am trying to investigate and I am going toinvestigate only for 1 hour. And in that period you suppose collected 300 frogs. So, thenafter 1 hour has elapsed, you will take out all the frogs one by one, you will see whatspecies they are, what is the number of animals that you have. Essentially you will makea table. So, this is species, this is number of animals. Suppose first one is species 1 yousaw an animal, then a species 2 you saw 2 animals, then species 3 you saw an animal, thenspecies 1 use saw another animal then species 4 you saw 3 animals, then again you saw 2animals of species 1, one of species 2, 1 of species 1 and so on.So, for all of these 300 animals you will make this list of what all species are there andhow many animals did you see. At the end of this period you will see that this is 5, this is3, this is 1, this is 3 and so on. And probably you will repeat this measurement at some
other point of time in some other area to make an estimate of the relative density ofdifferent species and different areas.(Refer Slide Time: 22:03)
Next is a quadrat sampling; so, quadrat sampling as we have seen before, fixed areas orsample plots are extensively surveyed for presence of species. Next is distance sampling;distance sampling is what we saw in the case of transact lines a short while back. So, youcan go for transact lines, you can go for point based samplings or you could go for a patchsampling.A patch sampling or an adaptive cluster sampling; in this method sampling begins atrandomly selected points; a patch is selected at that point and particular species of searchedfor in that patch. If that species is found, adjoining patches are searched till a point reacheswhere all the boundary patches are devoid of the particular species. This enablesdiscernment of area of presence of species and is applicable even in the rain forest areas.
(Refer Slide Time: 22:54)
What do you do in the case of a patch sampling is that, you will begin at a random pointand at this point you take this patch. A patch may be say 5 meters by 5 meters patch. Inthis 5 meter by 5 meter patch, you are now looking, you are actively searching for theanimals. Now suppose you found the animals here. You count the number of animals, nextyou go on surveying all the surrounding patches. These are the surrounding patches thatyou have. Suppose you found an animal here, but you did not find animals in other patches.So, then because you found an animal here, now you will go for the patches that aresurrounding this particular patch. Probably you found an animal here, an animal here,nothing here. So, then for this particular patch, now you will look for the surroundingpatches. And you will continue this exercise till a point reaches where you do not find anyanimals in the surrounding patches. So, in this case, we will say that this particular speciesof animal is found in this much of area and in for this area, we can compute the number ofanimals that are found in this area.Now, the size of the patches will depend on which particular species you are interested in.For some species you may go for a larger size patch, for some species you may go for asmaller size patch. So, these are all different methods of estimating populations and theirparameters.
(Refer Slide Time: 24:19)
You would go for an audio strip transect. Now in audio strip transects, the sounds or callsof various species such as male frogs are utilized to discern the relative abundance of alladults of the species, the species composition of the area, the breeding habitat ormicrohabitat use and the time of breeding for different species. This is even useful in rainforest areas where some species can hide in the leaf litter may be identified through theircalls.(Refer Slide Time: 24:51)
So, what we are saying here is that, you have some frog species; you have this big area ofthe rainforest and then say there are some trees here, there is a small water body heremaybe the other areas have some grasses or maybe you have some shrubs somewhere.Now you cannot go and search inside a shrub or you cannot go and dive into this waterbody to search all the frog samples. You go to this area in the breeding season and in thebreeding season the male frogs will give out calls.So, now what you can do is, you can put a tape recorder at this area. You can say, float 1tape recorder here, put a tape recorder here, put one in the trees, put one in the shrubs andso on and then you can record the voices of these male frogs. Now different species givea different kinds of calls. We can even identify different species even though we are notable to see them, but we can identify them through their vocalizations. We can identify thespecies and the number of calls that are made give you an estimate of the number ofanimals that are there in this area. So, this is another way in which we can locate thepopulation of different animals in an area.Next is mark recapture method. So, what we saw a short while back. Mark recapture or acapture recapture method works by capturing the species, marking them using dyes or pittags. So, pit tags are a small or are small are transponder tags that you can put beneath thisskin of an animal. So, that remains with a animal and you can use it you can scan thosetags later on to understand whether this animal is marked or not and what was the numberof this animal. Or by capturing natural body marks photographically, releasing the animals,capturing them again and utilizing the data of the number of marked and unmarkedindividuals to estimate the population size of this species.So, in this case what we are doing is, suppose we get to know from our experiment thatthe frogs are only found in this particular lake. So, in this case we will capture some frogsfrom this area, we will mark them by say a dye or using a pit tag, we will release themagain, we will allow them to mix randomly with all the population of frogs that are therein this pond and we will take out another sample and look at the number of markedindividuals that are there in the second sample. And use that data to make an estimate ofthe total number of animals that are there in this particular pond.
(Refer Slide Time: 27:26)
Next you could go for pitfall trapping or funnel trapping. Now this method traps theherpetofaunal species and this may be used in combination with mark release recapturemethods for estimating the population sizes. So, in this case what you are doing is, youknow that these frogs are there in this water body and probably they will come out aftersometime and probably they will go into the grasses. If this is the behaviour of such ananimal so, in that case you will set up a pitfall trap. So, in this case you set up 2 plasticcurtains and at this point you set up a bucket.Now, when this frog comes to this area. You have this frog here, once it gets to a wall ittries to move along the wall. So, that his behaviour of the animal. It becomes from here tohere, then it jumps from here to here and then in the next jump it falls into the trap. Nowin this case, you can capture your angles and then this pitfall trap is a method that can beused to estimate the relative density of animals. Because you can set up a pitfall trap hereand you can say set up a pitfall trap at this location. Now in this bucket, you probably saw,you probably were able to capture 100 frogs, in this trap you were able to capture only 2frogs. Then you can say that this area that was being covered by this trap is having lessdensity of animals, than this area that is being covered by the first track. And then you canuse it in combination with the mark recapture technique because here you are able tocapture the animals in a live state. So, you can mark them and then you can release themagain for the mark recapture method.
Next you could go for a covered board survey. In this method cover boards are randomlythrown in survey areas and the regions below the cover boards are then extensivelysurveyed to look for species.So, in this case what you are doing is, you are taking some cardboard boards. They arearound say this much in size and once you have those boards you just flip them over intothe forest area wherever the land you just go and you can look for the species below them.This is one way of doing a random sampling in your particular area. Another one is surveyof the breeding sites, ponds and stream habitats that are breeding sites for severalamphibian and reptilian species can be surveyed in detail to estimate the presence relativeabundance and size of the species. So, this is also another thing that you can do.(Refer Slide Time: 30:11)
Population estimation is such an important requirement for management of populations ormanagement of habitats, that we have figured out so many different techniques to measurethese population parameters. You could even go for a quantitative sampling of amphibianlarvae. For instance you are not able to capture the frogs, but when you go to the ponds,so, you are able to capture the larvae. In that case you can do a quantitative sampling ofthe larvae as well; or you can go for instrumentation. In the case of instrumentation, youcan put a camera traps. A camera trap is a device that has a sensor so that if an animalcomes near to it; it takes a photograph.
(Refer Slide Time: 30:55)
So, then camera trap is also way another way of getting data about these animals.