Do They Stay or Do Do They Stay or Do They Go Now?They Go Now?

Habitat selection of aquatic Habitat selection of aquatic beetles and its impact on spatial beetles and its impact on spatial

distributiondistribution

By Drew Hanson & Justin MarleauBy Drew Hanson & Justin MarleauMay 11May 11thth, 2007, 2007

PIMS Mathematical Biology Summer Workshop

IntroductionIntroduction

The most utilized research programme for the The most utilized research programme for the explanation of species distributions and explanation of species distributions and abundances in community ecology is random abundances in community ecology is random dispersal followed by non-random, site-specific dispersal followed by non-random, site-specific mortality (Binckley & Resetarits 2005). mortality (Binckley & Resetarits 2005).

While other research programmes have been While other research programmes have been developed involving different mechanisms, such developed involving different mechanisms, such as neutral theory (see Hubbell 2001), few have as neutral theory (see Hubbell 2001), few have incorporated important behavioural mechanisms incorporated important behavioural mechanisms which can possibly alter species distributions which can possibly alter species distributions and abundances. and abundances.

IntroductionIntroduction

One such mechanism is habitat selection, which One such mechanism is habitat selection, which involves organisms dispersing and colonizing involves organisms dispersing and colonizing patches with the highest expected fitness.patches with the highest expected fitness.

Our goal is to model this mechanism and Our goal is to model this mechanism and determine if there are significant differences determine if there are significant differences between the emergent distribution and between the emergent distribution and abundance of organisms predicted by random abundance of organisms predicted by random dispersal and non-random site-specific mortality.dispersal and non-random site-specific mortality.

The Organism: BeetleThe Organism: Beetle

Tropisternus lateralisTropisternus lateralis, a , a common predaceous common predaceous diving water beetle.diving water beetle.

Have an initial dispersal Have an initial dispersal flight after hatching that flight after hatching that can be over a half-mile can be over a half-mile (800 metres) in distance (800 metres) in distance (Milliger & Schlicht 1968, (Milliger & Schlicht 1968, Wallace & Anderson Wallace & Anderson 1996).1996).

The Habitat: PondsThe Habitat: Ponds

T. lateralisT. lateralis occurs occurs naturally in small naturally in small ponds (like rice ponds (like rice paddies, temporary paddies, temporary woodland ponds) and woodland ponds) and is considered to be an is considered to be an important species in important species in aquatic systems as a aquatic systems as a predator and a prey predator and a prey (Resetarits 2001).(Resetarits 2001).

Proposed Mechanisms of Habitat Proposed Mechanisms of Habitat SelectionSelection

Pond Size: Beetles are attracted to shiny Pond Size: Beetles are attracted to shiny surfaces, so larger ponds would be more likely surfaces, so larger ponds would be more likely to be seen by beetles flying overhead and to be seen by beetles flying overhead and therefore be colonized by beetles after their therefore be colonized by beetles after their dispersal flight (Wallace & Anderson 1996). dispersal flight (Wallace & Anderson 1996).

Presence of predator: Certain species of beetles Presence of predator: Certain species of beetles are hypothesized to be able to detect chemically are hypothesized to be able to detect chemically the presence of predators once in the pond, the presence of predators once in the pond, making them more likely to leave ponds with making them more likely to leave ponds with predators (Binckley & Resetarits 2005).predators (Binckley & Resetarits 2005).

Other Relevant Biological Other Relevant Biological InformationInformation

Beetles in ponds containing predators are Beetles in ponds containing predators are less active than in ponds containing no less active than in ponds containing no predators (Resetarits 2001).predators (Resetarits 2001).

Ponds can become rapidly saturated with Ponds can become rapidly saturated with beetles as they preferentially stay on the beetles as they preferentially stay on the side of ponds, causing the beetles to leave side of ponds, causing the beetles to leave and colonize other ponds once a threshold and colonize other ponds once a threshold level of abundance is reached (Binckley & level of abundance is reached (Binckley & Resetarits 2005).Resetarits 2005).

How does one model the system?How does one model the system?

As the beetles are undergoing long-distance As the beetles are undergoing long-distance dispersal, we will be using a gravity model dispersal, we will be using a gravity model (Bossenbroek et al. 2001).(Bossenbroek et al. 2001).

A gravity model, which is based on Newton’s law A gravity model, which is based on Newton’s law of gravity, assumes that individuals will be of gravity, assumes that individuals will be attracted to large areas, i.e. large ponds in our attracted to large areas, i.e. large ponds in our model. model.

Other components can affect the “attractiveness” Other components can affect the “attractiveness” of lakes, such as the nutrient composition and of lakes, such as the nutrient composition and the presence of predators.the presence of predators.

The Breakdown: Outline of TalkThe Breakdown: Outline of Talk

1. Creating an appropriate gravity model 1. Creating an appropriate gravity model and qualitatively analyse it, without regard and qualitatively analyse it, without regard to presence of predators.to presence of predators.

2. Introducing the predators, but not 2. Introducing the predators, but not introducing predation, in order to compare introducing predation, in order to compare with results of Binckley & Resetarits with results of Binckley & Resetarits (2005).(2005).

3. Introduce predation and multiple 3. Introduce predation and multiple generations for a “realistic” model.generations for a “realistic” model.

Part I: The Set-UpPart I: The Set-Up

Initial Model Assumptions:Initial Model Assumptions: All ponds have same concentrations of All ponds have same concentrations of

nutrients for beetles.nutrients for beetles. There is no mortality of beetles over the There is no mortality of beetles over the

time-frame considered.time-frame considered. Each pond, depending on its size, has a Each pond, depending on its size, has a

carrying capacity of beetles. Beetles will not carrying capacity of beetles. Beetles will not leave a pond if it is under carrying capacity.leave a pond if it is under carrying capacity.

The model is governed by deterministic The model is governed by deterministic equations.equations.

Part I: The Set-upPart I: The Set-up

Hundred randomly distributed ponds of variable size. Hundred randomly distributed ponds of variable size. Original population starts at (0,0) at time 0. Original population starts at (0,0) at time 0.

Part I: Parameters for initial Part I: Parameters for initial deterministic modeldeterministic model

T T = Total number of beetles in the system of ponds= Total number of beetles in the system of ponds TTjj = Total number of beetles in pond = Total number of beetles in pond jj

KKjj = = Carrying capacity of pond Carrying capacity of pond jj

AAii = Balancing coefficient that ensures all beetles leaving pond = Balancing coefficient that ensures all beetles leaving pond ii

arrive to some pond in the systemarrive to some pond in the system ccijij = distance from pond = distance from pond ii to pond to pond jj

NN0j0j = Number of beetles arriving from outside the pond system that = Number of beetles arriving from outside the pond system that

arrive to pond arrive to pond j j during their dispersal flightduring their dispersal flight WWjj = Attractiveness of pond = Attractiveness of pond jj

MMi i = Number of beetles leaving pond = Number of beetles leaving pond ii

= Distance coefficient= Distance coefficient P = P = Total number of ponds in our systemTotal number of ponds in our system

Part I: The deterministic equationsPart I: The deterministic equations

P

jijji

ijjiiij

P

jjj

jjj

cWA

cWANN

cWA

cWANN

1

100

0000

/1

/1

iii

iiiii

KTM

or

KTKTM

,0

,

1

2

Part I: Parameter valuesPart I: Parameter values

WWjj = area of pond = area of pond j j in min m22

KKjj = (1/0.435m= (1/0.435m22)*60*(area of pond )*60*(area of pond jj) (Note: ) (Note:

The (1/0.435mThe (1/0.435m22)*60 term is derived from )*60 term is derived from Binckley & Resetarits (2005))Binckley & Resetarits (2005))

= 1.9= 1.9 TT = 15 000 = 15 000

Part I Results: 15000 at (0,0) at t=0Part I Results: 15000 at (0,0) at t=0

Part I: If we start elsewhere?Part I: If we start elsewhere?

Part I: If we have more beetles?Part I: If we have more beetles?

Part II: Adding greater realismPart II: Adding greater realism

Distance and size of ponds are not the Distance and size of ponds are not the only factors determining the abundance only factors determining the abundance and distribution of beetles, the presence of and distribution of beetles, the presence of fish are also very important.fish are also very important.

Fish act in two ways: they reduce the Fish act in two ways: they reduce the attractiveness of ponds by reducing the attractiveness of ponds by reducing the perceived carrying capacity of ponds and perceived carrying capacity of ponds and they consume beetles.they consume beetles.

Part II: Beetle Eating MachinePart II: Beetle Eating Machine

Enneacanthus obesusEnneacanthus obesus: blue-stripped sunfish: blue-stripped sunfish

Part II: The Effects of the Blue-Part II: The Effects of the Blue-Stripped SunfishStripped Sunfish

Can reduce its prey population by 70% in Can reduce its prey population by 70% in a single day at an intermediate size a single day at an intermediate size (3.75g) (Chalcraft & Resetarits 2004).(3.75g) (Chalcraft & Resetarits 2004).

Mere presence reduces the attractiveness Mere presence reduces the attractiveness of ponds (carrying capacity) by 80% to of ponds (carrying capacity) by 80% to beetles and greatly decreases the activity beetles and greatly decreases the activity of beetles remaining in the ponds of beetles remaining in the ponds (Resetarits 2001, Binckley & Resetarits (Resetarits 2001, Binckley & Resetarits 2005).2005).

Part II: Investigating non-lethal Part II: Investigating non-lethal impact of predatorsimpact of predators

In order to see if our model could properly In order to see if our model could properly model the non-lethal effects observed by model the non-lethal effects observed by Resetarits and associates, we re-created Resetarits and associates, we re-created one of their experimental set-ups within one of their experimental set-ups within our model framework and we assumed our model framework and we assumed that the carrying capacity of ponds was the that the carrying capacity of ponds was the substantial difference between ponds (as substantial difference between ponds (as was the case with Binckley & Resetarits was the case with Binckley & Resetarits 2005).2005).

Part II: Visual Representation of Part II: Visual Representation of Binckley & Resetarits (2005)Binckley & Resetarits (2005)

Part II : ResultsPart II : Results

Part III: The “generalized” modelPart III: The “generalized” model

In this section, we allow for predation, multiple In this section, we allow for predation, multiple generations of beetles and the carrying capacity generations of beetles and the carrying capacity is lowered by the presence of fish. is lowered by the presence of fish.

As beetles are univoltine (one generation alive at As beetles are univoltine (one generation alive at a time), we assume that beetles lay eggs (10 a time), we assume that beetles lay eggs (10 eggs per adult) near the end of the year, and eggs per adult) near the end of the year, and expire before the next generation is hatched. expire before the next generation is hatched. (Zola et al. 1980).(Zola et al. 1980).

We also assume that newly-hatched beetles all We also assume that newly-hatched beetles all leave their original pond to colonize new ponds, leave their original pond to colonize new ponds, but do not leave the pond system.but do not leave the pond system.

Part III: Changes to EquationsPart III: Changes to Equations

TTjj = = TTjj – min(0.7*T – min(0.7*Tjj *number of fish in pond *number of fish in pond

j, 70*number of fish in pond j)j, 70*number of fish in pond j) The above equation takes into account the The above equation takes into account the

voracious appetite of the predators in voracious appetite of the predators in modifying the beetle populations. modifying the beetle populations.

Part III: ResultPart III: Result

Part III: Differences between detecting Part III: Differences between detecting and non-detecting beetlesand non-detecting beetles

Part III: Differences between detecting Part III: Differences between detecting and non-detecting beetlesand non-detecting beetles

Part III: Differences between detecting Part III: Differences between detecting and non-detecting beetlesand non-detecting beetles

After one hundred random samplings After one hundred random samplings (from different starting points), we (from different starting points), we discovered:discovered:

Mean of detecting beetles: 5345Mean of detecting beetles: 5345 Standard Deviation: 707Standard Deviation: 707 Mean of non-detecting beetles: 4979Mean of non-detecting beetles: 4979 Standard Deviation: 759Standard Deviation: 759

Part III: Differences between detecting Part III: Differences between detecting and non-detecting beetlesand non-detecting beetles

These differences are highly dependent on These differences are highly dependent on when the predation, the number of when the predation, the number of predators present, the location of the predators present, the location of the predators and the birth rates of the predators and the birth rates of the beetles. Greater analysis is needed before beetles. Greater analysis is needed before any firm conclusions can be drawn.any firm conclusions can be drawn.

Part III: Pros and ConsPart III: Pros and ConsPROSPROS The beetle population, regardless of initial conditions, The beetle population, regardless of initial conditions,

goes to a global steady state over some number of goes to a global steady state over some number of years.years.

The model is straightforward, and seems to accurately fit The model is straightforward, and seems to accurately fit limited experimental data that exists.limited experimental data that exists.

CONSCONS The assumption of habitat selection reduces the overall The assumption of habitat selection reduces the overall

capacity of the pond system. This leads to a increased capacity of the pond system. This leads to a increased population density of selective beetles rather than an population density of selective beetles rather than an increased overall population.increased overall population.

Birth rates are constant among all beetles, while Birth rates are constant among all beetles, while realistically, beetles who are living in a pond with realistically, beetles who are living in a pond with predators have much lower fitness.predators have much lower fitness.

SummarySummary

It is possible and useful to model dispersal flights of It is possible and useful to model dispersal flights of beetles as a simple gravity model.beetles as a simple gravity model.

The gravity model with changes in carrying capacity due The gravity model with changes in carrying capacity due to the presence of predators is capable of generating to the presence of predators is capable of generating results that are similar to those of experimental studies.results that are similar to those of experimental studies.

There can be global steady-states independent of initial There can be global steady-states independent of initial conditions and beetle detection strategy if multiple conditions and beetle detection strategy if multiple generations are considered and the birth rates are large generations are considered and the birth rates are large enough. enough.

The actual dynamics of multiple generations is highly The actual dynamics of multiple generations is highly dependent on parameter values and require greater dependent on parameter values and require greater study.study.

AcknowledgementsAcknowledgements

We would like to thank Mark and Caroline We would like to thank Mark and Caroline for their insightful advice in the formulation for their insightful advice in the formulation of our project as well as everyone of our project as well as everyone participating and organizing this workshop participating and organizing this workshop for creating such a great atmosphere.for creating such a great atmosphere.

ReferencesReferences

Binckley, C.A. & Resetarits, W. 2005 Habitat selection Binckley, C.A. & Resetarits, W. 2005 Habitat selection determines abundance, richness and species determines abundance, richness and species composition of beetles in aquatic communities. composition of beetles in aquatic communities. Biol. Lett. Biol. Lett. 11, 370-374., 370-374.

Resetarits, W. 2001 Colonization under threat of Resetarits, W. 2001 Colonization under threat of predation: avoidance of fish by an aquatic beetle, predation: avoidance of fish by an aquatic beetle, Tropisternus lateralisTropisternus lateralis (Coleoptera: Hydorphilidae). (Coleoptera: Hydorphilidae). OecologiaOecologia 129129, 155-160., 155-160.

Wallace, J.B. & Anderson, N.H. 1996 Habitat, life history Wallace, J.B. & Anderson, N.H. 1996 Habitat, life history and behavioral adaptations of aquatic insects. In and behavioral adaptations of aquatic insects. In An An introduction to the aquatic insects of North America introduction to the aquatic insects of North America (ed. (ed. R.W. Merritt & K.W. Cummins), pp. 41-73. Dubuque, R.W. Merritt & K.W. Cummins), pp. 41-73. Dubuque, Kendall/Hunt.Kendall/Hunt.

ReferencesReferences

Milliger, L.E. & Schlicht, H.E. 1968 Passive Milliger, L.E. & Schlicht, H.E. 1968 Passive dispersal of viable algae and protozoa by an dispersal of viable algae and protozoa by an aquatic beetle. aquatic beetle. Trans. Amer. Microsc. Soc.Trans. Amer. Microsc. Soc. 8787, , 443-448.443-448.

Hubbell, S.P. 2001 Hubbell, S.P. 2001 Unified Theory of Biodiversity Unified Theory of Biodiversity and Biogeographyand Biogeography. Princeton.. Princeton.

Bossenbroek, J.M., Clifford, E.K. & Nekola, J.C. Bossenbroek, J.M., Clifford, E.K. & Nekola, J.C. 2001 Prediction of long-distance dispersal using 2001 Prediction of long-distance dispersal using gravity models: zebra mussel invasion of inland gravity models: zebra mussel invasion of inland lakes. lakes. Ecological ApplicationsEcological Applications, , 1111, 1778-1788., 1778-1788.

ReferencesReferences

Zalom, F.G., Grigarick, A.A. & Way, M.O. Zalom, F.G., Grigarick, A.A. & Way, M.O. 1980 Habits and relative population 1980 Habits and relative population densities of some hydrophilids in California densities of some hydrophilids in California rice fields. rice fields. HydrobiologiaHydrobiologia, , 7575, 195-200., 195-200.

Chalcraft, D.R. & Resetarits, W.J. 2004 Chalcraft, D.R. & Resetarits, W.J. 2004 Metabolic rate models and the Metabolic rate models and the substitutability of predator populations. substitutability of predator populations. Journal of Animal BiologyJournal of Animal Biology, , 7373, 323-332., 323-332.